(INIT-LIB (QUOTE (LOCAL-UNDO-TUPLES EVENT IMMEDIATE-DEPENDENTS0 MAIN-EVENT SATELLITES CONTROLLER-POCKETS ELIMINATE-DESTRUCTORS-DESTS ELIMINATE-DESTRUCTORS-SEQ IDATE JUSTIFICATIONS LEVEL-NO INDUCTION-MACHINE TYPE-RESTRICTIONS LISP-CODE SDEFN QUICK-BLOCK-INFO LINEAR-LEMMAS LEMMAS TYPE-PRESCRIPTION-LST)) (QUOTE (NONCONSTRUCTIVE-AXIOM-NAMES 1BTM-OBJECTS RECOGNIZER-ALIST SHELL-ALIST SINGLETON-TYPE-SETS GENERALIZE-LEMMAS SHELL-POCKETS DISABLED-LEMMAS CHRONOLOGY))) 
(SETQ NONCONSTRUCTIVE-AXIOM-NAMES (QUOTE (H-COMMUTIVITY2 NUMBERP-CALL))) 
(SETQ 1BTM-OBJECTS (QUOTE (ZERO))) 
(SETQ RECOGNIZER-ALIST (QUOTE ((IF-EXPRP . 128.) (STACKP . 64.) (NEGATIVEP . 32.) (LISTP . 16.) (LITATOM . 8.) (NUMBERP . 4.) (TRUEP . 2.) (FALSEP . 1.)))) 
(SETQ SHELL-ALIST (QUOTE ((CONS-IF . 7.) (PUSH . 6.) (MINUS . 5.) (CONS . 4.) (PACK . 3.) (ADD1 . 2.) (TRUE . 1.) (FALSE . 0.)))) 
(SETQ SINGLETON-TYPE-SETS (QUOTE (2. 1.))) 
(SETQ GENERALIZE-LEMMAS (QUOTE ((GENERALIZE-LEMMA SORT2-GEN (AND (PLISTP (SORT2 X)) (ORDERED2 (SORT2 X)))) (GENERALIZE-LEMMA LESSP-REMAINDER2 (EQUAL (LESSP (REMAINDER X Y) Y) (NOT (ZEROP Y)))) (GENERALIZE-LEMMA PLISTP-REVERSE (PLISTP (REVERSE X)))))) 
(SETQ SHELL-POCKETS (QUOTE ((CONS-IF TEST LEFT-BRANCH RIGHT-BRANCH) (PUSH TOP POP) (MINUS NEGATIVE-GUTS) (CONS CAR CDR) (PACK UNPACK) (ADD1 SUB1) (TRUE) (FALSE)))) 
(SETQ DISABLED-LEMMAS (QUOTE ((SQUARES SQUARES-OFF . T) (COMPLEMENT COMPLEMENT-OFF . T) (INVERSE G0219 . T) (PDIFFERENCE G0006 . T) (TIMES G0005 . T) (IF-TIMES-THEN-DIVIDES G0004 . T) (QUOTIENT-DIVIDES G0003 . T) (EUCLID G0002 . T)))) 
(SETQ CHRONOLOGY (QUOTE (LAW-OF-QUADRATIC-RECIPROCITY EQUAL-PLUS-QUOT-LIST-WINS EMPTY-INTERSECT-MULTS EMPTY-INTERSECT-MULTS-1 ALL-NON-ZEROP-MULTS RESIDUE-QUOT-LIST GAUSS-COROLLARY EQUAL-WINS-PLUS-QUOT-LIST EQUAL-QUOT-WINS1 LEQ-WINS1-QUOT LEQ-WINS1 LEQ-WINS1-WINS2 LEQ-WINS1-N LEQ-WINS2 WINS2 LEQ-QUOT-WINS1 LEQ-QUOT-WINS1-2 LEQ-QUOT-WINS1-1 LEQ-QUOT-TIMES-2 MONOTONE-QUOT MONOTONE-QUOT-INDUCTION LEQ-QUOT-TIMES LEQ-TIMES-QUOT QUOT-QUOT-INDUCTION MONOTONE-WINS1 LEQ-N-WINS1 LENGTH-MULTS MULTS A-WINNER-EVERY-TIME EQUAL-LOSSES-WINS WIN-SOME-LOSE-SOME-2 WIN-SOME-LOSE-SOME-1 LOSSES LOSSES1 WINS WINS1 RES1-QUOT-LIST EQUALS-HAVE-SAME-PARITY PLUS-REFLECT-LIST EVEN3-EVEN PERM-PLUS-LIST PERM-PLUS-LIST-1 EVEN3-REM-REFLECT EVEN3-REM EVEN3-TIMES EVEN3-DIFF EVEN3-PLUS EVEN3 REM-QUOT-LIST REM-LIST QUOT-LIST PLUS-LIST GAUSS-LEMMA TWO-EVEN RES1-REM-2 REMAINDER-LESSP RES1-REM-1 RES1-REM-1-1 PLUS-X-X-EVEN TIMES-REFLECT-LIST ALL-DISTINCT-REFLECT-LIST ALL-DISTINCT-REFLECT-LIST-10 ALL-DISTINCT-REFLECT-LIST-9 ALL-DISTINCT-REFLECT-LIST-8 ALL-DISTINCT-REFLECT-LIST-7 ALL-DISTINCT-REFLECT-LIST-6 ALL-DISTINCT-REFLECT-LIST-5 ALL-DISTINCT-REFLECT-LIST-4 PLUS-MOD-2 PLUS-MOD-1 ALL-DISTINCT-REFLECT-LIST-3 NUMBERP-REMAINDER ALL-DISTINCT-REFLECT-LIST-2 ALL-DISTINCT-REFLECT-LIST-1 ALL-NON-ZEROP-REFLECT-LIST ALL-LESSEQP-REFLECT-LIST ALL-LESSEQP-REFLECT-LIST-1 LENGTH-REFLECT-LIST REM-REFLECT-LIST REM-REFLECT-LIST-BASE-CASE REM-REFLECT-LIST-4 DOUBLE-REFLECT REM-REFLECT-LIST-3 REM-REFLECT-LIST-2 REM-REFLECT-LIST-1 TIMES-EXP-FACT REFLECT-COMMUTES-WITH-TIMES-2 REFLECT-COMMUTES-WITH-TIMES-1 REM-DIFF-TIMES DIFF-MOD-1 REFLECT-LIST REFLECT RES1 EULER-2 EULER-2-4 EULER-2-3 EULER-2-2 EULER-2-1 LENGTH-POSITIVES EQUAL-LENGTH-PERM SUB1-LENGTH-DELETE TIMES-COMP-LIST TIMES-COMP-LIST-5 TIMES-COMP-LIST-4 TIMES-COMP-LIST-3 QUOTIENT-PLUS-1 TIMES-COMP-LIST-2 TIMES-COMP-LIST-1 TIMES-MOD-4 COMP-LIST-FACT PERM-POSITIVES-COMP-LIST ALL-DISTINCT-COMP-LIST ALL-DISTINCT-COMP-LIST-1 COMP-LIST-CLOSED-2 COMP-LIST-CLOSED-1 SUBSETP-POSITIVES-COMP-LIST BOUNDED-COMP-LIST ALL-NON-ZEROP-COMP-LIST COMP-LIST COMPLEMENT-OF-COMPLEMENT NO-SELF-COMPLEMENT SQUARES-OFF COMPLEMENT-IS-UNIQUE NON-ZEROP-COMPLEMENT COMPLEMENT-OFF BOUNDED-COMPLEMENT COMPLEMENT-WORKS G0219 COMPLEMENT EULER-1 EULER-1-7 EULER-1-6 EULER-1-5 EULER-1-4 EULER-1-3 EULER-1-2 EULER-1-1 ALL-SQUARES ALL-SQUARES-2 ALL-SQUARES-1 RESIDUE SQUARES WILSON-THM W-T-LEMMA INVERSE-LIST-FACT PERM-POSITIVES-INVERSE-LIST PIGEONHOLE2 PIGEONHOLE2-INDUCTION NONZEROP-LESSEQP-ZERO SUBSETP-POSITIVES-DELETE POSITIVES-BOUNDED ALL-LESSEQP-DELETE DELETE-MEMBER-LEAVE-SUBSET DELETE-X-LEAVE-A TIMES-INVERSE-LIST T-I-L-LEMMA4 T-I-L-LEMMA3 T-I-L-LEMMA T-I-L-LEMMA1 ALL-DISTINCT-INVERSE-LIST A-D-I-L-LEMMA3 A-D-I-L-LEMMA2 A-D-I-L-LEMMA1 INVERSE-1 SUBSETP-POSITIVES BOUNDED-INVERSE-LIST ALL-NON-ZEROP-INVERSE-LIST INVERSE-LIST BOUNDED-INVERSE B-I-LEMMA1 B-I-LEMMA2 NON-ZEROP-INVERSE N-Z-I-LEMMA INVERSE-OF-INVERSE I-O-I-LEMMA NO-OTHER-INVOLUTIONS N-O-I-LEMMA4 N-O-I-LEMMA3 N-O-I-LEMMA2 N-O-I-LEMMA1 SUB1-P-IS-INVOLUTION S-P-I-I-LEMMA2 S-P-I-I-LEMMA1 INVERSE-IS-UNIQUE INVERSE-INVERTS INVERSE-INVERTS-LEMMA INVERSE CRYPT-INVERTS CRYPT-INVERTS-STEP-2 CRYPT-INVERTS-STEP-1B CRYPT-INVERTS-STEP-1A CRYPT-INVERTS-STEP-1 FERMAT-THM LENGTH-S ALL-LESSEQP-S ALL-NON-ZEROP-S ALL-DISTINCT-S ALL-DISTINCT-S-LEMMA REMAINDER-TIMES-LIST-S S PRIME-FACT TIMES-LIST-EQUAL-FACT TIMES-LIST-POSITIVES PERM-TIMES-LIST PIGEON-HOLE-PRINCIPLE PIGEON-HOLE-INDUCTION PERM-MEMBER PIGEON-HOLE-PRINCIPLE-LEMMA-2 PIGEON-HOLE-PRINCIPLE-LEMMA-1 ALL-DISTINCT-DELETE ALL-NON-ZEROP-DELETE MEMBER-POSITIVES CAR-POSITIVES LISTP-POSITIVES POSITIVES ALL-NON-ZEROP ALL-LESSEQP ALL-DISTINCT COROLLARY-55 THM-55-SPECIALIZED-TO-PRIMES COROLLARY-53 THM-53-SPECIALIZED-TO-PRIMES PRODUCT-DIVIDES PRODUCT-DIVIDES-LEMMA PRIME-KEY-TRICK G0006 EQUAL-MODS-TRICK-2 EQUAL-MODS-TRICK-1 TIMES-DISTRIBUTES-OVER-PDIFFERENCE PDIFFERENCE EXP-MOD-IS-1 REMAINDER-EXP REMAINDER-EXP-LEMMA TIMES-MOD-3 CRYPT-CORRECT TIMES-MOD-2 TIMES-MOD-1 CRYPT G0005 G0004 G0003 G0002 SUBST2-OK SUBST2 EVAL2 APPLY2 LESSP-REMAINDER-DIVISOR TIMES-TIMES-LIST-DELETE PRIME-KEY-REWRITE REMAINDER-DIFFERENCE-TIMES LENGTH-DELETE EQUAL-LENGTH-0 REMAINDER-OF-1 REMAINDER-TIMES-1 REMAINDER-PLUS-TIMES-2 REMAINDER-PLUS-TIMES-1 EXP-EXP EXP-TIMES EXP-BY-0 EXP-OF-1 EXP-OF-0 TIMES-2 TIMES-1 SQUARE EVEN F91-IS-F0 F91 F0-SATISFIES-F91-EQUATION F0 H-EQ H-LEMMA H-AC H-PR H-COMMUTIVITY2 H SIGMA-IS-HALF-PRODUCT HALF-PLUS DIFFERENCE-2 CORRECTNESS-OF-INTERPRETED-SIGMA INTERPRETER-INPUT-PATH INTERPRETER-LOOP-INVRT EXECUTE-OPENED-UP EXECUTE1-OPENED-UP EXECUTE1-4 EXECUTE1-3 EXECUTE1-1 LENGTH-CONS6 LENGTH-5 CORRECTNESS-OF-SET-SIMPLIFIER SET-SIMPLIFIER CORRECTNESS-OF-GET-SIMPLIFIER GET-SIMPLIFIER EXECUTE EXECUTE1 GET-SET GET SET SIGMA-OUTPUT-PATH SIGMA-LOOP-INVRT SIGMA-INPUT-PATH CORRECTNESS-OF-FUNCTIONAL-SIGMA FUNCTIONAL-LOOP-INVRT PROG-TRANS-OF-SIGMA DIFFERENCE-1 SIGMA COUNT-LIST-SORT2 DSORT-SORT2 SORT2-DELETE SORT2-DELETE-CONS LESSP-MAXIMUM-ADDTOLIST2 ADDTOLIST2-KLUDGE DELETE-ADDTOLIST2 ADDTOLIST2-DELETE SORT2-GEN SORT2-GEN-2 SORT2-GEN-1 SORT2 ADDTOLIST2 DSORT ORDERED2 LESSP-DELETE-REWRITE MEMBER-MAXIMUM MAXIMUM PRIME-FACTORIZATION-UNIQUENESS DIVIDES-IMPLIES-TIMES PRIME-MEMBER TIMES-EQUAL-1 IF-TIMES-THEN-DIVIDES PRIME-LIST-TIMES-LIST TIMES-LIST-DELETE DISTRIBUTIVITY-OF-DIVIDES QUOTIENT-TIMES DIVIDES-TIMES-LIST PRIME-LIST-DELETE REMAINDER-TIMES PERM LESSP-COUNT-DELETE LITTLE-STEP QUOTIENT-DIVIDES PRIME-KEY GCD-DISTRIBUTES-OVER-AN-OPENED-UP-TIMES PRIME-GCD HACK1 KLUDGE-BRIDGE TIMES-IDENTITY TIMES-IDENTITY1 DIVIDES-TIMES1 REMAINDER-GCD-1 REMAINDER-GCD PRIME-BASIC GREATEREQPR-REMAINDER GREATEREQPR-LESSP PRIME1-BASIC TIMES-ID-IFF-1 GREATEREQPR PRIME-FACTORIZATION-EXISTENCE ENOUGH-FACTORS QUOTIENT-LESSP QUOTIENT-TIMES1 PRIME-LIST-PRIME-FACTORS PRIME-LIST-APPEND TIMES-LIST-APPEND TIMES-LIST PRIME-LIST PRIME-FACTORS NUMBERP-GREATEST-FACTOR GREATEST-FACTOR-1 REMAINDER-0-CROCK GREATEST-FACTOR-0 GREATEST-FACTOR-DIVIDES GREATEST-FACTOR-LESSP GREATEST-FACTOR PRIME PRIME1 CORRECTNESS-OF-SAMEFRINGE GOPHER-RETURNS-CORRECT-STATE GOPHER-RETURNS-LEFTMOST-ATOM SAMEFRINGE LISTP-GOPHER GOPHER-PRESERVES-COUNT GOPHER LEFTCOUNT FLATTEN-SINGLETON TAUTOLOGY-CHECKER-IS-SOUND TAUTOLOGY-CHECKER-SOUNDNESS-BRIDGE TAUTOLOGY-CHECKER-IS-COMPLETE TAUTOLOGY-CHECKER-COMPLETENESS-BRIDGE NORMALIZE-NORMALIZES NORMALIZE-IS-SOUND TAUTOLOGYP-FAILS-MEANS-FALSIFY1-WINS FALSIFY1-FALSIFIES FALSIFY1-EXTENDS-MODELS FALSIFY FALSIFY1 TAUTOLOGY-CHECKER TAUTOLOGYP-IS-SOUND ASSIGNMENT-IMPLIES-ASSIGNED VALUE-SHORT-CUT VALUE-CAN-IGNORE-REDUNDANT-ASSIGNMENTS ASSIGNMENT-APPEND TAUTOLOGYP ASSUME-FALSE ASSUME-TRUE ASSIGNEDP NORMALIZED-IF-EXPRP NORMALIZE IF-COMPLEXITY-GOES-DOWN2 IF-COMPLEXITY-GOES-DOWN1 IF-COMPLEXITY-NOT-0 IF-COMPLEXITY IF-DEPTH VALUE ASSIGNMENT CONS-IF GCD-IS-THE-GREATEST GCD-DIVIDES-BOTH DISTRIBUTIVITY-OF-TIMES-OVER-GCD LESSP-PLUS-CANCELLATION3 LESSP-TIMES-CANCELLATION EUCLID DIVIDES-PLUS-REWRITE-COMMUTED LESSP-PLUS-CANCELATION DIVIDES-PLUS-REWRITE DIVIDES-PLUS-REWRITE2 DIVIDES-PLUS-REWRITE1 REMAINDER-ADD1 DIFFERENCE-ADD1-CANCELLATION DIFFERENCE-PLUS3 DIVIDES-TIMES DIVIDES TIMES-DIFFERENCE DIFFERENCE-PLUS-CANCELATION DIFFERENCE-PLUS2 DIFFERENCE-PLUS1 NTH-APPEND COMMUTATIVITY-OF-GCD GCD-0 GCD-EQUAL-0 NUMBERP-GCD GCD CORRECTNESS-OF-BIG-PLUS POWER-EVAL-POWER-REP POWER-REP LESSP-REMAINDER1 LESSP-QUOTIENT1 LESSP-TIMES-2 LESSP-TIMES-1 REMAINDER-QUOTIENT-ELIM REMAINDER-X-X LESSP-REMAINDER2 REMAINDER-WRT-12 REMAINDER-WRT-1 POWER-EVAL-BIG-PLUS BIG-PLUS POWER-EVAL-BIG-PLUS1 REMAINDER-QUOTIENT BIG-PLUS1 POWER-EVAL DIFFERENCE-ELIM EQUAL-LESSP APPEND-CANCELLATION COUNT-SORT-LP ORDERED-SORT-LP ORDERED-ADDTOLIST SORT-LP REVERSE-REVERSE- REVERSE-APPEND REVERSE-LOOP-REVERSE REVERSE-LOOP-APPEND-REVERSE REVERSE- REVERSE-LOOP FACT-FACT FACT-LOOP-FACT FACT- FACT-LOOP FACT COUNTPS-COUNTPS COUNTPS COUNTPS- COUNTPS-LOOP OCCUR-SUBST OCCUR SUBST-A-A SUBST SORT-ORDERED CROCK-DUE-TO-LACK-OF-BOUNCE XOR SORT-OF-ORDERED-NUMBER-LIST ADDTOLIST-OF-ORDERED-NUMBER-LIST ORDERED-SORT NUMBER-LISTP LEQ-HALF ORDERED-APPEND COUNT-LIST-SORT COUNT-LIST LENGTH-SORT MEMBER-SORT LEQ-NTH EVEN1-EVEN2 EXP-PLUS EXP LAST-REVERSE LAST-APPEND SUBSETP-CONS DOUBLE-TIMES-2 DOUBLE-HALF HALF-DOUBLE HALF EVEN1-DOUBLE DOUBLE EVEN2 EVEN1 ODD ASSOCIATIVITY-OF-EQUAL NTH-APPEND1 NTH-NIL NTH-0 IFF-EQUAL-EQUAL IFF BOOLEAN ASSOC SORT ADDTOLIST ORDERED TRANSITIVITY-OF-LEQ GREATEREQP NTH SUBSETP-INTERSECT SUBSETP-UNION MEMBER-UNION UNION MEMBER-INTERSECT INTERSECT LENGTH-REVERSE MEMBER-REVERSE MEMBER-APPEND FLATTEN-MC-FLATTEN MC-FLATTEN FLATTEN REVERSE-REVERSE TRICHOTOMY-OF-LESSP EQP LESSP-NOT-REFLEXIVE TRANSITIVITY-OF-LESSP CORRECTNESS-OF-OPTIMIZING-COMPILER CORRECTNESS-OF-CODEGEN SEQUENTIAL-EXECUTION EXEC CORRECTNESS-OF-OPTIMIZE FORMP-OPTIMIZE COMPILE CODEGEN OPTIMIZE EVAL CADR-CROCK EXPRESSIONP NUMBERP-CALL GETVALUE CALL PUSH EQUAL-TIMES-0 ASSOCIATIVITY-OF-TIMES COMMUTATIVITY2-OF-TIMES COMMUTATIVITY-OF-TIMES TIMES-ADD1 DISTRIBUTIVITY-OF-TIMES-OVER-PLUS TIMES-ZERO2 APPEND-REVERSE PLISTP-REVERSE APPEND-RIGHT-ID PLISTP ASSOCIATIVITY-OF-APPEND REVERSE CORRECTNESS-OF-CANCEL MEMBER-IMPLIES-NUMBERP PLUS-TREE-PLUS-FRINGE MEANING-PLUS-TREE-APPEND BRIDGE-TO-SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP NUMBERP-MEANING-BRIDGE PLUS-TREE-BAGDIFF SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP PLUS-TREE-DELETE MEMBER-IMPLIES-PLUS-TREE-GREATEREQP NUMBERP-MEANING-PLUS-TREE NUMBERP-MEANING-PLUS FORMP-PLUS-TREE FORM-LSTP-BAGDIFF FORM-LSTP-DELETE FORM-LSTP-PLUS-FRINGE FORM-LSTP-APPEND CANCEL PLUS-TREE PLUS-FRINGE SUBBAGP-BAGINT2 SUBBAGP-BAGINT1 SUBBAGP-CDR2 SUBBAGP-CDR1 SUBBAGP-DELETE COMMUTATIVITY-OF-DELETE MEMBER-DELETE DELETE-NON-MEMBER BAGINT BAGDIFF SUBBAGP DELETE APPEND DIFFERENCE-CANCELLATION-1 DIFFERENCE-CANCELLATION-0 EQUAL-DIFFERENCE-0 DIFFERENCE-0 PLUS-CANCELLATION DIFFERENCE-PLUS DIFFERENCE-X-X PLUS-EQUAL-0 ASSOCIATIVITY-OF-PLUS COMMUTATIVITY-OF-PLUS COMMUTATIVITY2-OF-PLUS PLUS-ADD1 PLUS-RIGHT-ID2 GROUND-ZERO))) 
(SETQ LIB-ATOMS-WITH-PROPS (QUOTE (LAW-OF-QUADRATIC-RECIPROCITY EQUAL-PLUS-QUOT-LIST-WINS EMPTY-INTERSECT-MULTS EMPTY-INTERSECT-MULTS-1 ALL-NON-ZEROP-MULTS RESIDUE-QUOT-LIST GAUSS-COROLLARY EQUAL-WINS-PLUS-QUOT-LIST EQUAL-QUOT-WINS1 LEQ-WINS1-QUOT LEQ-WINS1 LEQ-WINS1-WINS2 LEQ-WINS1-N LEQ-WINS2 1WINS2 WINS2 LEQ-QUOT-WINS1 LEQ-QUOT-WINS1-2 LEQ-QUOT-WINS1-1 LEQ-QUOT-TIMES-2 MONOTONE-QUOT 1MONOTONE-QUOT-INDUCTION MONOTONE-QUOT-INDUCTION LEQ-QUOT-TIMES LEQ-TIMES-QUOT 1QUOT-QUOT-INDUCTION QUOT-QUOT-INDUCTION MONOTONE-WINS1 LEQ-N-WINS1 LENGTH-MULTS 1MULTS MULTS A-WINNER-EVERY-TIME EQUAL-LOSSES-WINS WIN-SOME-LOSE-SOME-2 WIN-SOME-LOSE-SOME-1 1LOSSES LOSSES 1LOSSES1 LOSSES1 1WINS WINS 1WINS1 WINS1 RES1-QUOT-LIST EQUALS-HAVE-SAME-PARITY PLUS-REFLECT-LIST EVEN3-EVEN PERM-PLUS-LIST PERM-PLUS-LIST-1 EVEN3-REM-REFLECT EVEN3-REM EVEN3-TIMES EVEN3-DIFF EVEN3-PLUS 1EVEN3 EVEN3 REM-QUOT-LIST 1REM-LIST REM-LIST 1QUOT-LIST QUOT-LIST 1PLUS-LIST PLUS-LIST GAUSS-LEMMA TWO-EVEN RES1-REM-2 QUOTE REMAINDER-LESSP RES1-REM-1 RES1-REM-1-1 PLUS-X-X-EVEN TIMES-REFLECT-LIST ALL-DISTINCT-REFLECT-LIST ALL-DISTINCT-REFLECT-LIST-10 ALL-DISTINCT-REFLECT-LIST-9 ALL-DISTINCT-REFLECT-LIST-8 ALL-DISTINCT-REFLECT-LIST-7 ALL-DISTINCT-REFLECT-LIST-6 ALL-DISTINCT-REFLECT-LIST-5 ALL-DISTINCT-REFLECT-LIST-4 PLUS-MOD-2 PLUS-MOD-1 ALL-DISTINCT-REFLECT-LIST-3 NUMBERP-REMAINDER ALL-DISTINCT-REFLECT-LIST-2 ALL-DISTINCT-REFLECT-LIST-1 ALL-NON-ZEROP-REFLECT-LIST ALL-LESSEQP-REFLECT-LIST ALL-LESSEQP-REFLECT-LIST-1 LENGTH-REFLECT-LIST REM-REFLECT-LIST REM-REFLECT-LIST-BASE-CASE REM-REFLECT-LIST-4 DOUBLE-REFLECT REM-REFLECT-LIST-3 REM-REFLECT-LIST-2 REM-REFLECT-LIST-1 TIMES-EXP-FACT REFLECT-COMMUTES-WITH-TIMES-2 REFLECT-COMMUTES-WITH-TIMES-1 REM-DIFF-TIMES DIFF-MOD-1 1REFLECT-LIST REFLECT-LIST 1REFLECT REFLECT 1RES1 RES1 EULER-2 EULER-2-4 EULER-2-3 EULER-2-2 EULER-2-1 LENGTH-POSITIVES EQUAL-LENGTH-PERM SUB1-LENGTH-DELETE TIMES-COMP-LIST TIMES-COMP-LIST-5 TIMES-COMP-LIST-4 TIMES-COMP-LIST-3 QUOTIENT-PLUS-1 TIMES-COMP-LIST-2 TIMES-COMP-LIST-1 TIMES-MOD-4 COMP-LIST-FACT PERM-POSITIVES-COMP-LIST ALL-DISTINCT-COMP-LIST ALL-DISTINCT-COMP-LIST-1 COMP-LIST-CLOSED-2 COMP-LIST-CLOSED-1 SUBSETP-POSITIVES-COMP-LIST BOUNDED-COMP-LIST ALL-NON-ZEROP-COMP-LIST 1COMP-LIST COMP-LIST COMPLEMENT-OF-COMPLEMENT NO-SELF-COMPLEMENT SQUARES-OFF COMPLEMENT-IS-UNIQUE NON-ZEROP-COMPLEMENT COMPLEMENT-OFF BOUNDED-COMPLEMENT COMPLEMENT-WORKS G0219 1COMPLEMENT COMPLEMENT EULER-1 EULER-1-7 EULER-1-6 EULER-1-5 EULER-1-4 EULER-1-3 EULER-1-2 EULER-1-1 ALL-SQUARES ALL-SQUARES-2 ALL-SQUARES-1 1RESIDUE RESIDUE 1SQUARES SQUARES WILSON-THM W-T-LEMMA INVERSE-LIST-FACT PERM-POSITIVES-INVERSE-LIST PIGEONHOLE2 1PIGEONHOLE2-INDUCTION PIGEONHOLE2-INDUCTION NONZEROP-LESSEQP-ZERO SUBSETP-POSITIVES-DELETE POSITIVES-BOUNDED ALL-LESSEQP-DELETE DELETE-MEMBER-LEAVE-SUBSET DELETE-X-LEAVE-A TIMES-INVERSE-LIST T-I-L-LEMMA4 T-I-L-LEMMA3 T-I-L-LEMMA T-I-L-LEMMA1 ALL-DISTINCT-INVERSE-LIST A-D-I-L-LEMMA3 A-D-I-L-LEMMA2 A-D-I-L-LEMMA1 INVERSE-1 SUBSETP-POSITIVES BOUNDED-INVERSE-LIST ALL-NON-ZEROP-INVERSE-LIST 1INVERSE-LIST INVERSE-LIST BOUNDED-INVERSE B-I-LEMMA1 B-I-LEMMA2 NON-ZEROP-INVERSE N-Z-I-LEMMA INVERSE-OF-INVERSE I-O-I-LEMMA NO-OTHER-INVOLUTIONS N-O-I-LEMMA4 N-O-I-LEMMA3 N-O-I-LEMMA2 N-O-I-LEMMA1 SUB1-P-IS-INVOLUTION S-P-I-I-LEMMA2 S-P-I-I-LEMMA1 INVERSE-IS-UNIQUE INVERSE-INVERTS INVERSE-INVERTS-LEMMA 1INVERSE INVERSE CRYPT-INVERTS CRYPT-INVERTS-STEP-2 CRYPT-INVERTS-STEP-1B CRYPT-INVERTS-STEP-1A CRYPT-INVERTS-STEP-1 FERMAT-THM LENGTH-S ALL-LESSEQP-S ALL-NON-ZEROP-S ALL-DISTINCT-S ALL-DISTINCT-S-LEMMA REMAINDER-TIMES-LIST-S 1S S PRIME-FACT TIMES-LIST-EQUAL-FACT TIMES-LIST-POSITIVES PERM-TIMES-LIST PIGEON-HOLE-PRINCIPLE 1PIGEON-HOLE-INDUCTION PIGEON-HOLE-INDUCTION PERM-MEMBER PIGEON-HOLE-PRINCIPLE-LEMMA-2 PIGEON-HOLE-PRINCIPLE-LEMMA-1 ALL-DISTINCT-DELETE ALL-NON-ZEROP-DELETE MEMBER-POSITIVES CAR-POSITIVES LISTP-POSITIVES 1POSITIVES POSITIVES 1ALL-NON-ZEROP ALL-NON-ZEROP 1ALL-LESSEQP ALL-LESSEQP 1ALL-DISTINCT ALL-DISTINCT COROLLARY-55 THM-55-SPECIALIZED-TO-PRIMES COROLLARY-53 THM-53-SPECIALIZED-TO-PRIMES PRODUCT-DIVIDES PRODUCT-DIVIDES-LEMMA PRIME-KEY-TRICK G0006 EQUAL-MODS-TRICK-2 EQUAL-MODS-TRICK-1 TIMES-DISTRIBUTES-OVER-PDIFFERENCE 1PDIFFERENCE PDIFFERENCE EXP-MOD-IS-1 REMAINDER-EXP REMAINDER-EXP-LEMMA TIMES-MOD-3 CRYPT-CORRECT TIMES-MOD-2 TIMES-MOD-1 1CRYPT CRYPT G0005 G0004 G0003 G0002 SUBST2-OK 1SUBST2 SUBST2 EVAL2 APPLY2 LESSP-REMAINDER-DIVISOR TIMES-TIMES-LIST-DELETE PRIME-KEY-REWRITE REMAINDER-DIFFERENCE-TIMES LENGTH-DELETE EQUAL-LENGTH-0 REMAINDER-OF-1 REMAINDER-TIMES-1 REMAINDER-PLUS-TIMES-2 REMAINDER-PLUS-TIMES-1 EXP-EXP EXP-TIMES EXP-BY-0 EXP-OF-1 EXP-OF-0 TIMES-2 TIMES-1 1SQUARE SQUARE 1EVEN EVEN F91-IS-F0 1F91 F91 F0-SATISFIES-F91-EQUATION 1F0 F0 H-EQ H-LEMMA H-AC H-PR H-COMMUTIVITY2 H SIGMA-IS-HALF-PRODUCT HALF-PLUS DIFFERENCE-2 CORRECTNESS-OF-INTERPRETED-SIGMA INTERPRETER-INPUT-PATH INTERPRETER-LOOP-INVRT EXECUTE-OPENED-UP EXECUTE1-OPENED-UP EXECUTE1-4 EXECUTE1-3 EXECUTE1-1 LENGTH-CONS6 LENGTH-5 CORRECTNESS-OF-SET-SIMPLIFIER 1SET-SIMPLIFIER SET-SIMPLIFIER CORRECTNESS-OF-GET-SIMPLIFIER 1GET-SIMPLIFIER GET-SIMPLIFIER 1EXECUTE EXECUTE 1EXECUTE1 EXECUTE1 GET-SET 1GET GET 1SET SET SIGMA-OUTPUT-PATH SIGMA-LOOP-INVRT SIGMA-INPUT-PATH CORRECTNESS-OF-FUNCTIONAL-SIGMA FUNCTIONAL-LOOP-INVRT 1PROG-TRANS-OF-SIGMA PROG-TRANS-OF-SIGMA DIFFERENCE-1 1SIGMA SIGMA COUNT-LIST-SORT2 DSORT-SORT2 SORT2-DELETE SORT2-DELETE-CONS LESSP-MAXIMUM-ADDTOLIST2 ADDTOLIST2-KLUDGE DELETE-ADDTOLIST2 ADDTOLIST2-DELETE SORT2-GEN SORT2-GEN-2 SORT2-GEN-1 1SORT2 SORT2 1ADDTOLIST2 ADDTOLIST2 1DSORT DSORT 1ORDERED2 ORDERED2 LESSP-DELETE-REWRITE MEMBER-MAXIMUM 1MAXIMUM MAXIMUM PRIME-FACTORIZATION-UNIQUENESS DIVIDES-IMPLIES-TIMES PRIME-MEMBER TIMES-EQUAL-1 IF-TIMES-THEN-DIVIDES PRIME-LIST-TIMES-LIST TIMES-LIST-DELETE DISTRIBUTIVITY-OF-DIVIDES QUOTIENT-TIMES DIVIDES-TIMES-LIST PRIME-LIST-DELETE REMAINDER-TIMES 1PERM PERM LESSP-COUNT-DELETE LITTLE-STEP QUOTIENT-DIVIDES PRIME-KEY GCD-DISTRIBUTES-OVER-AN-OPENED-UP-TIMES PRIME-GCD HACK1 KLUDGE-BRIDGE TIMES-IDENTITY TIMES-IDENTITY1 DIVIDES-TIMES1 REMAINDER-GCD-1 REMAINDER-GCD PRIME-BASIC GREATEREQPR-REMAINDER GREATEREQPR-LESSP PRIME1-BASIC TIMES-ID-IFF-1 1GREATEREQPR GREATEREQPR PRIME-FACTORIZATION-EXISTENCE ENOUGH-FACTORS QUOTIENT-LESSP QUOTIENT-TIMES1 PRIME-LIST-PRIME-FACTORS PRIME-LIST-APPEND TIMES-LIST-APPEND 1TIMES-LIST TIMES-LIST 1PRIME-LIST PRIME-LIST 1PRIME-FACTORS PRIME-FACTORS NUMBERP-GREATEST-FACTOR GREATEST-FACTOR-1 REMAINDER-0-CROCK GREATEST-FACTOR-0 GREATEST-FACTOR-DIVIDES GREATEST-FACTOR-LESSP 1GREATEST-FACTOR GREATEST-FACTOR 1PRIME PRIME 1PRIME1 PRIME1 CORRECTNESS-OF-SAMEFRINGE GOPHER-RETURNS-CORRECT-STATE GOPHER-RETURNS-LEFTMOST-ATOM 1SAMEFRINGE SAMEFRINGE LISTP-GOPHER GOPHER-PRESERVES-COUNT 1GOPHER GOPHER 1LEFTCOUNT LEFTCOUNT FLATTEN-SINGLETON TAUTOLOGY-CHECKER-IS-SOUND TAUTOLOGY-CHECKER-SOUNDNESS-BRIDGE TAUTOLOGY-CHECKER-IS-COMPLETE TAUTOLOGY-CHECKER-COMPLETENESS-BRIDGE NORMALIZE-NORMALIZES NORMALIZE-IS-SOUND TAUTOLOGYP-FAILS-MEANS-FALSIFY1-WINS FALSIFY1-FALSIFIES FALSIFY1-EXTENDS-MODELS 1FALSIFY FALSIFY 1FALSIFY1 FALSIFY1 1TAUTOLOGY-CHECKER TAUTOLOGY-CHECKER TAUTOLOGYP-IS-SOUND ASSIGNMENT-IMPLIES-ASSIGNED VALUE-SHORT-CUT VALUE-CAN-IGNORE-REDUNDANT-ASSIGNMENTS ASSIGNMENT-APPEND 1TAUTOLOGYP TAUTOLOGYP 1ASSUME-FALSE ASSUME-FALSE 1ASSUME-TRUE ASSUME-TRUE 1ASSIGNEDP ASSIGNEDP 1NORMALIZED-IF-EXPRP NORMALIZED-IF-EXPRP 1NORMALIZE NORMALIZE IF-COMPLEXITY-GOES-DOWN2 IF-COMPLEXITY-GOES-DOWN1 IF-COMPLEXITY-NOT-0 1IF-COMPLEXITY IF-COMPLEXITY 1IF-DEPTH IF-DEPTH 1VALUE VALUE 1ASSIGNMENT ASSIGNMENT COUNT-CONS-IF TEST-LEFT-BRANCH-RIGHT-BRANCH-ELIM CONS-IF-TEST-LEFT-BRANCH-RIGHT-BRANCH CONS-IF-EQUAL RIGHT-BRANCH-LESSEQP RIGHT-BRANCH-LESSP RIGHT-BRANCH-NIF-EXPRP RIGHT-BRANCH-CONS-IF LEFT-BRANCH-LESSEQP LEFT-BRANCH-LESSP LEFT-BRANCH-NIF-EXPRP LEFT-BRANCH-CONS-IF TEST-LESSEQP TEST-LESSP TEST-NIF-EXPRP TEST-CONS-IF 1RIGHT-BRANCH RIGHT-BRANCH 1LEFT-BRANCH LEFT-BRANCH 1TEST TEST 1IF-EXPRP IF-EXPRP 1CONS-IF CONS-IF GCD-IS-THE-GREATEST GCD-DIVIDES-BOTH DISTRIBUTIVITY-OF-TIMES-OVER-GCD LESSP-PLUS-CANCELLATION3 LESSP-TIMES-CANCELLATION EUCLID DIVIDES-PLUS-REWRITE-COMMUTED LESSP-PLUS-CANCELATION DIVIDES-PLUS-REWRITE DIVIDES-PLUS-REWRITE2 DIVIDES-PLUS-REWRITE1 REMAINDER-ADD1 DIFFERENCE-ADD1-CANCELLATION DIFFERENCE-PLUS3 DIVIDES-TIMES 1DIVIDES DIVIDES TIMES-DIFFERENCE DIFFERENCE-PLUS-CANCELATION DIFFERENCE-PLUS2 DIFFERENCE-PLUS1 NTH-APPEND COMMUTATIVITY-OF-GCD GCD-0 GCD-EQUAL-0 NUMBERP-GCD 1GCD GCD CORRECTNESS-OF-BIG-PLUS POWER-EVAL-POWER-REP 1POWER-REP POWER-REP LESSP-REMAINDER1 LESSP-QUOTIENT1 LESSP-TIMES-2 LESSP-TIMES-1 REMAINDER-QUOTIENT-ELIM REMAINDER-X-X LESSP-REMAINDER2 REMAINDER-WRT-12 REMAINDER-WRT-1 POWER-EVAL-BIG-PLUS 1BIG-PLUS BIG-PLUS POWER-EVAL-BIG-PLUS1 REMAINDER-QUOTIENT 1BIG-PLUS1 BIG-PLUS1 1POWER-EVAL POWER-EVAL DIFFERENCE-ELIM EQUAL-LESSP APPEND-CANCELLATION COUNT-SORT-LP ORDERED-SORT-LP ORDERED-ADDTOLIST 1SORT-LP SORT-LP REVERSE-REVERSE- REVERSE-APPEND REVERSE-LOOP-REVERSE REVERSE-LOOP-APPEND-REVERSE 1REVERSE- REVERSE- 1REVERSE-LOOP REVERSE-LOOP FACT-FACT FACT-LOOP-FACT 1FACT- FACT- 1FACT-LOOP FACT-LOOP 1FACT FACT COUNTPS-COUNTPS COUNTPS COUNTPS- COUNTPS-LOOP OCCUR-SUBST 1OCCUR OCCUR SUBST-A-A 1SUBST SUBST SORT-ORDERED CROCK-DUE-TO-LACK-OF-BOUNCE 1XOR XOR SORT-OF-ORDERED-NUMBER-LIST ADDTOLIST-OF-ORDERED-NUMBER-LIST ORDERED-SORT 1NUMBER-LISTP NUMBER-LISTP LEQ-HALF ORDERED-APPEND COUNT-LIST-SORT 1COUNT-LIST COUNT-LIST LENGTH-SORT MEMBER-SORT LEQ-NTH EVEN1-EVEN2 EXP-PLUS 1EXP EXP LAST-REVERSE LAST-APPEND SUBSETP-CONS DOUBLE-TIMES-2 DOUBLE-HALF HALF-DOUBLE 1HALF HALF EVEN1-DOUBLE 1DOUBLE DOUBLE 1EVEN2 EVEN2 1EVEN1 EVEN1 1ODD ODD ASSOCIATIVITY-OF-EQUAL NTH-APPEND1 NTH-NIL NTH-0 IFF-EQUAL-EQUAL 1IFF IFF 1BOOLEAN BOOLEAN 1ASSOC ASSOC 1SORT SORT 1ADDTOLIST ADDTOLIST 1ORDERED ORDERED TRANSITIVITY-OF-LEQ 1GREATEREQP GREATEREQP 1NTH NTH SUBSETP-INTERSECT SUBSETP-UNION MEMBER-UNION 1UNION UNION MEMBER-INTERSECT 1INTERSECT INTERSECT LENGTH-REVERSE MEMBER-REVERSE MEMBER-APPEND FLATTEN-MC-FLATTEN 1MC-FLATTEN MC-FLATTEN 1FLATTEN FLATTEN REVERSE-REVERSE TRICHOTOMY-OF-LESSP 1EQP EQP LESSP-NOT-REFLEXIVE TRANSITIVITY-OF-LESSP CORRECTNESS-OF-OPTIMIZING-COMPILER CORRECTNESS-OF-CODEGEN SEQUENTIAL-EXECUTION EXEC CORRECTNESS-OF-OPTIMIZE FORMP-OPTIMIZE COMPILE 1CODEGEN CODEGEN OPTIMIZE EVAL CADR-CROCK 1EXPRESSIONP EXPRESSIONP NUMBERP-CALL GETVALUE CALL COUNT-PUSH TOP-POP-ELIM PUSH-TOP-POP PUSH-EQUAL POP-LESSEQP POP-LESSP POP-NSTACKP POP-PUSH TOP-LESSEQP TOP-LESSP TOP-NSTACKP TOP-PUSH 1POP POP 1TOP TOP 1STACKP STACKP 1PUSH PUSH EQUAL-TIMES-0 ASSOCIATIVITY-OF-TIMES COMMUTATIVITY2-OF-TIMES COMMUTATIVITY-OF-TIMES TIMES-ADD1 DISTRIBUTIVITY-OF-TIMES-OVER-PLUS TIMES-ZERO2 APPEND-REVERSE PLISTP-REVERSE APPEND-RIGHT-ID 1PLISTP PLISTP ASSOCIATIVITY-OF-APPEND 1REVERSE REVERSE CORRECTNESS-OF-CANCEL MEMBER-IMPLIES-NUMBERP PLUS-TREE-PLUS-FRINGE MEANING-PLUS-TREE-APPEND BRIDGE-TO-SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP NUMBERP-MEANING-BRIDGE PLUS-TREE-BAGDIFF SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP PLUS-TREE-DELETE MEMBER-IMPLIES-PLUS-TREE-GREATEREQP NUMBERP-MEANING-PLUS-TREE NUMBERP-MEANING-PLUS FORMP-PLUS-TREE FORM-LSTP-BAGDIFF FORM-LSTP-DELETE FORM-LSTP-PLUS-FRINGE FORM-LSTP-APPEND 1CANCEL CANCEL 1PLUS-TREE PLUS-TREE 1PLUS-FRINGE PLUS-FRINGE SUBBAGP-BAGINT2 SUBBAGP-BAGINT1 SUBBAGP-CDR2 SUBBAGP-CDR1 SUBBAGP-DELETE COMMUTATIVITY-OF-DELETE MEMBER-DELETE DELETE-NON-MEMBER 1BAGINT BAGINT 1BAGDIFF BAGDIFF 1SUBBAGP SUBBAGP 1DELETE DELETE 1APPEND APPEND DIFFERENCE-CANCELLATION-1 DIFFERENCE-CANCELLATION-0 EQUAL-DIFFERENCE-0 DIFFERENCE-0 PLUS-CANCELLATION DIFFERENCE-PLUS DIFFERENCE-X-X PLUS-EQUAL-0 ASSOCIATIVITY-OF-PLUS COMMUTATIVITY-OF-PLUS COMMUTATIVITY2-OF-PLUS PLUS-ADD1 PLUS-RIGHT-ID2 P 1CHECK CHECK 1SPLIT SPLIT MEANING-LST MEANING APPLY FORM-LSTP FORMP ARITY 1LOOKUP LOOKUP 1SYMBOLP SYMBOLP 1LEGAL-CHAR-CODE-SEQ LEGAL-CHAR-CODE-SEQ 1LAST LAST 1SUBSETP SUBSETP 1MEMBER MEMBER 1LENGTH LENGTH 1ILLEGAL-FIRST-CHAR-CODES ILLEGAL-FIRST-CHAR-CODES 1LEGAL-CHAR-CODES LEGAL-CHAR-CODES REMAINDER QUOTIENT TIMES DIFFERENCE COUNT-MINUS NEGATIVE-GUTS-ELIM MINUS-NEGATIVE-GUTS MINUS-EQUAL NEGATIVE-GUTS-LESSEQP NEGATIVE-GUTS-LESSP NEGATIVE-GUTS-TYPE-RESTRICTION NEGATIVE-GUTS-NNEGATIVEP NEGATIVE-GUTS-MINUS NEGATIVE-GUTS NEGATIVEP MINUS NLISTP COUNT-CONS CAR-CDR-ELIM CONS-CAR-CDR CONS-EQUAL CDR-LESSEQP CDR-LESSP CDR-NLISTP CDR-CONS CAR-LESSEQP CAR-LESSP CAR-NLISTP CAR-CONS LISTP CONS COUNT-PACK UNPACK-ELIM PACK-UNPACK PACK-EQUAL UNPACK-LESSEQP UNPACK-LESSP UNPACK-NLITATOM UNPACK-PACK UNPACK LITATOM PACK COUNT-NOT-LESSP COUNT-NUMBERP PLUS FIX ZEROP LEX3 CDR LEX2 CAR 1GEQ GEQ 1LEQ LEQ 1GREATERP GREATERP COUNT-ADD1 SUB1-ELIM ADD1-SUB1 ADD1-EQUAL SUB1-LESSEQP SUB1-LESSP LESSP SUB1-TYPE-RESTRICTION SUB1-NNUMBERP SUB1-ADD1 ZERO SUB1 NUMBERP ADD1 IMPLIES OR AND NOT TRUEP TRUE FALSEP FALSE COUNT EQUAL IF GROUND-ZERO))) 
(SETQ LIB-ATOMS-WITH-DEFS (QUOTE (1WINS2 1MONOTONE-QUOT-INDUCTION 1QUOT-QUOT-INDUCTION 1MULTS 1LOSSES 1LOSSES1 1WINS 1WINS1 1EVEN3 1REM-LIST 1QUOT-LIST 1PLUS-LIST 1REFLECT-LIST 1REFLECT 1RES1 1COMP-LIST 1COMPLEMENT 1RESIDUE 1SQUARES 1PIGEONHOLE2-INDUCTION 1INVERSE-LIST 1INVERSE 1S 1PIGEON-HOLE-INDUCTION 1POSITIVES 1ALL-NON-ZEROP 1ALL-LESSEQP 1ALL-DISTINCT 1PDIFFERENCE 1CRYPT 1SUBST2 1SQUARE 1EVEN 1F91 1F0 1SET-SIMPLIFIER 1GET-SIMPLIFIER 1EXECUTE 1EXECUTE1 1GET 1SET 1PROG-TRANS-OF-SIGMA 1SIGMA 1SORT2 1ADDTOLIST2 1DSORT 1ORDERED2 1MAXIMUM 1PERM 1GREATEREQPR 1TIMES-LIST 1PRIME-LIST 1PRIME-FACTORS 1GREATEST-FACTOR 1PRIME 1PRIME1 1SAMEFRINGE 1GOPHER 1LEFTCOUNT 1FALSIFY 1FALSIFY1 1TAUTOLOGY-CHECKER 1TAUTOLOGYP 1ASSUME-FALSE 1ASSUME-TRUE 1ASSIGNEDP 1NORMALIZED-IF-EXPRP 1NORMALIZE 1IF-COMPLEXITY 1IF-DEPTH 1VALUE 1ASSIGNMENT 1RIGHT-BRANCH 1LEFT-BRANCH 1TEST 1IF-EXPRP 1CONS-IF 1DIVIDES 1GCD 1POWER-REP 1BIG-PLUS 1BIG-PLUS1 1POWER-EVAL 1SORT-LP 1REVERSE- 1REVERSE-LOOP 1FACT- 1FACT-LOOP 1FACT 1OCCUR 1SUBST 1XOR 1NUMBER-LISTP 1COUNT-LIST 1EXP 1HALF 1DOUBLE 1EVEN2 1EVEN1 1ODD 1IFF 1BOOLEAN 1ASSOC 1SORT 1ADDTOLIST 1ORDERED 1GREATEREQP 1NTH 1UNION 1INTERSECT 1MC-FLATTEN 1FLATTEN 1EQP 1CODEGEN 1EXPRESSIONP 1POP 1TOP 1STACKP 1PUSH 1PLISTP 1REVERSE 1CANCEL 1PLUS-TREE 1PLUS-FRINGE 1BAGINT 1BAGDIFF 1SUBBAGP 1DELETE 1APPEND 1CHECK 1SPLIT 1LOOKUP 1SYMBOLP 1LEGAL-CHAR-CODE-SEQ 1LAST 1SUBSETP 1MEMBER 1LENGTH 1ILLEGAL-FIRST-CHAR-CODES 1LEGAL-CHAR-CODES 1GEQ 1LEQ 1GREATERP))) 
(PUT1-LST (QUOTE LAW-OF-QUADRATIC-RECIPROCITY) (QUOTE (IDATE 840118055840. EVENT (PROVE-LEMMA LAW-OF-QUADRATIC-RECIPROCITY NIL (IMPLIES (AND (PRIME P) (PRIME Q) (NOT (EQUAL P Q)) (NOT (EQUAL P 2.)) (NOT (EQUAL Q 2.))) (EQUAL (EQUAL (RESIDUE Q P) (RESIDUE P Q)) (EVEN (TIMES (QUOTIENT P 2.) (QUOTIENT Q 2.))))) ((USE (RESIDUE-QUOT-LIST) (EVEN3-EVEN (P (TIMES (QUOTIENT P 2.) (QUOTIENT Q 2.))))) (HANDS-OFF QUOTIENT QUOT-LIST EVEN3 RESIDUE TIMES) (DISABLE RESIDUE PRIME1 QUOT-LIST PLUS-LIST EVEN3-PLUS LESSP-REMAINDER-DIVISOR))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQUAL-PLUS-QUOT-LIST-WINS . LAW-OF-QUADRATIC-RECIPROCITY) (IMMEDIATE-DEPENDENTS0 ALL-NON-ZEROP-MULTS . LAW-OF-QUADRATIC-RECIPROCITY) (IMMEDIATE-DEPENDENTS0 EMPTY-INTERSECT-MULTS . LAW-OF-QUADRATIC-RECIPROCITY) (IMMEDIATE-DEPENDENTS0 LESSP-QUOTIENT1 . LAW-OF-QUADRATIC-RECIPROCITY) (IMMEDIATE-DEPENDENTS0 LENGTH-MULTS . LAW-OF-QUADRATIC-RECIPROCITY) (IMMEDIATE-DEPENDENTS0 A-WINNER-EVERY-TIME . LAW-OF-QUADRATIC-RECIPROCITY) (IMMEDIATE-DEPENDENTS0 PRIME-KEY-REWRITE . LAW-OF-QUADRATIC-RECIPROCITY) (IMMEDIATE-DEPENDENTS0 DIVIDES . LAW-OF-QUADRATIC-RECIPROCITY) (IMMEDIATE-DEPENDENTS0 RESIDUE-QUOT-LIST . LAW-OF-QUADRATIC-RECIPROCITY) (IMMEDIATE-DEPENDENTS0 EVEN3-EVEN . LAW-OF-QUADRATIC-RECIPROCITY) (IMMEDIATE-DEPENDENTS0 EVEN . LAW-OF-QUADRATIC-RECIPROCITY) (IMMEDIATE-DEPENDENTS0 RESIDUE . LAW-OF-QUADRATIC-RECIPROCITY) (IMMEDIATE-DEPENDENTS0 PRIME . LAW-OF-QUADRATIC-RECIPROCITY))))) 
(PUT1-LST (QUOTE EQUAL-PLUS-QUOT-LIST-WINS) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118055618. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LAW-OF-QUADRATIC-RECIPROCITY) EVENT (PROVE-LEMMA EQUAL-PLUS-QUOT-LIST-WINS (REWRITE) (IMPLIES (AND (PRIME P) (PRIME Q) (NOT (EQUAL P Q))) (EQUAL (PLUS-LIST (QUOT-LIST (QUOTIENT P 2.) Q P)) (WINS (MULTS (QUOTIENT P 2.) Q) (MULTS (QUOTIENT Q 2.) P)))) ((USE (EQUAL-WINS-PLUS-QUOT-LIST (J (QUOTIENT P 2.)))) (DISABLE EQUAL-WINS-PLUS-QUOT-LIST MULTS QUOT-LIST WINS PLUS-LIST PRIME1))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . EQUAL-PLUS-QUOT-LIST-WINS) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . EQUAL-PLUS-QUOT-LIST-WINS) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . EQUAL-PLUS-QUOT-LIST-WINS) (IMMEDIATE-DEPENDENTS0 LITTLE-STEP . EQUAL-PLUS-QUOT-LIST-WINS) (IMMEDIATE-DEPENDENTS0 DIVIDES . EQUAL-PLUS-QUOT-LIST-WINS) (IMMEDIATE-DEPENDENTS0 EQUAL-WINS-PLUS-QUOT-LIST . EQUAL-PLUS-QUOT-LIST-WINS) (IMMEDIATE-DEPENDENTS0 MULTS . EQUAL-PLUS-QUOT-LIST-WINS) (IMMEDIATE-DEPENDENTS0 WINS . EQUAL-PLUS-QUOT-LIST-WINS) (IMMEDIATE-DEPENDENTS0 QUOT-LIST . EQUAL-PLUS-QUOT-LIST-WINS) (IMMEDIATE-DEPENDENTS0 PLUS-LIST . EQUAL-PLUS-QUOT-LIST-WINS) (IMMEDIATE-DEPENDENTS0 PRIME . EQUAL-PLUS-QUOT-LIST-WINS) (LEMMAS PLUS-LIST . EQUAL-PLUS-QUOT-LIST-WINS))))) 
(PUT1-LST (QUOTE EMPTY-INTERSECT-MULTS) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118055513. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LAW-OF-QUADRATIC-RECIPROCITY) EVENT (PROVE-LEMMA EMPTY-INTERSECT-MULTS (REWRITE) (IMPLIES (AND (PRIME P) (PRIME Q) (NOT (EQUAL P Q)) (LESSP I Q)) (NOT (LISTP (INTERSECT (MULTS I P) (MULTS (QUOTIENT P 2.) Q))))) ((USE (EMPTY-INTERSECT-MULTS-1 (J (QUOTIENT P 2.)))) (INDUCT (MULTS I P)) (DISABLE PRIME1 QUOTIENT EMPTY-INTERSECT-MULTS-1 LESSP-REMAINDER-DIVISOR))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LESSP-QUOTIENT1 . EMPTY-INTERSECT-MULTS) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO2 . EMPTY-INTERSECT-MULTS) (IMMEDIATE-DEPENDENTS0 EMPTY-INTERSECT-MULTS-1 . EMPTY-INTERSECT-MULTS) (IMMEDIATE-DEPENDENTS0 MULTS . EMPTY-INTERSECT-MULTS) (IMMEDIATE-DEPENDENTS0 INTERSECT . EMPTY-INTERSECT-MULTS) (IMMEDIATE-DEPENDENTS0 PRIME . EMPTY-INTERSECT-MULTS) (LEMMAS LISTP . EMPTY-INTERSECT-MULTS))))) 
(PUT1-LST (QUOTE EMPTY-INTERSECT-MULTS-1) (QUOTE (IDATE 840118055306. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EMPTY-INTERSECT-MULTS) EVENT (PROVE-LEMMA EMPTY-INTERSECT-MULTS-1 (REWRITE) (IMPLIES (AND (PRIME P) (PRIME Q) (NOT (EQUAL P Q)) (LESSP I Q) (LESSP J P)) (NOT (MEMBER (TIMES I P) (MULTS J Q)))) ((INDUCT (MULTS J Q)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 HACK1 . EMPTY-INTERSECT-MULTS-1) (IMMEDIATE-DEPENDENTS0 LITTLE-STEP . EMPTY-INTERSECT-MULTS-1) (IMMEDIATE-DEPENDENTS0 DIVIDES . EMPTY-INTERSECT-MULTS-1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-GCD . EMPTY-INTERSECT-MULTS-1) (IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-TIMES-OVER-GCD . EMPTY-INTERSECT-MULTS-1) (IMMEDIATE-DEPENDENTS0 PRIME-GCD . EMPTY-INTERSECT-MULTS-1) (IMMEDIATE-DEPENDENTS0 TIMES-IDENTITY . EMPTY-INTERSECT-MULTS-1) (IMMEDIATE-DEPENDENTS0 MULTS . EMPTY-INTERSECT-MULTS-1) (IMMEDIATE-DEPENDENTS0 PRIME . EMPTY-INTERSECT-MULTS-1) (LEMMAS MEMBER . EMPTY-INTERSECT-MULTS-1))))) 
(PUT1-LST (QUOTE ALL-NON-ZEROP-MULTS) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118054716. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LAW-OF-QUADRATIC-RECIPROCITY) EVENT (PROVE-LEMMA ALL-NON-ZEROP-MULTS (REWRITE) (IMPLIES (NOT (ZEROP P)) (ALL-NON-ZEROP (MULTS N P)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . ALL-NON-ZEROP-MULTS) (IMMEDIATE-DEPENDENTS0 MULTS . ALL-NON-ZEROP-MULTS) (IMMEDIATE-DEPENDENTS0 ALL-NON-ZEROP . ALL-NON-ZEROP-MULTS) (LEMMAS ALL-NON-ZEROP . ALL-NON-ZEROP-MULTS))))) 
(PUT1-LST (QUOTE RESIDUE-QUOT-LIST) (QUOTE (IDATE 840118054715. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LAW-OF-QUADRATIC-RECIPROCITY) EVENT (PROVE-LEMMA RESIDUE-QUOT-LIST NIL (IMPLIES (AND (PRIME P) (PRIME Q) (NOT (EQUAL P Q)) (NOT (EQUAL P 2.)) (NOT (EQUAL Q 2.))) (EQUAL (EQUAL (RESIDUE Q P) (RESIDUE P Q)) (EVEN3 (PLUS (PLUS-LIST (QUOT-LIST (QUOTIENT P 2.) Q P)) (PLUS-LIST (QUOT-LIST (QUOTIENT Q 2.) P Q)))))) ((USE (RES1-QUOT-LIST (A Q)) (RES1-QUOT-LIST (A P) (P Q)) (EVEN3-EVEN) (EVEN3-EVEN (P Q))) (DISABLE RESIDUE RES1 QUOTIENT QUOT-LIST PLUS-LIST LESSP-REMAINDER-DIVISOR DIFFERENCE LESSP))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LITTLE-STEP . RESIDUE-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 GAUSS-COROLLARY . RESIDUE-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 EVEN3-PLUS . RESIDUE-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 DIVIDES . RESIDUE-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 RES1-QUOT-LIST . RESIDUE-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 EVEN3-EVEN . RESIDUE-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 QUOT-LIST . RESIDUE-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 PLUS-LIST . RESIDUE-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 EVEN3 . RESIDUE-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 RESIDUE . RESIDUE-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 PRIME . RESIDUE-QUOT-LIST))))) 
(PUT1-LST (QUOTE GAUSS-COROLLARY) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118054609. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (RESIDUE-QUOT-LIST) EVENT (PROVE-LEMMA GAUSS-COROLLARY (REWRITE) (IMPLIES (AND (PRIME P) (PRIME Q) (NOT (EQUAL P 2.)) (NOT (EQUAL Q 2.)) (NOT (EQUAL P Q))) (EQUAL (RES1 (QUOTIENT P 2.) Q P) (RESIDUE Q P))) ((USE (GAUSS-LEMMA (A Q))) (DISABLE RES1 RESIDUE QUOTIENT PRIME1 REMAINDER))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LITTLE-STEP . GAUSS-COROLLARY) (IMMEDIATE-DEPENDENTS0 DIVIDES . GAUSS-COROLLARY) (IMMEDIATE-DEPENDENTS0 GAUSS-LEMMA . GAUSS-COROLLARY) (IMMEDIATE-DEPENDENTS0 RESIDUE . GAUSS-COROLLARY) (IMMEDIATE-DEPENDENTS0 RES1 . GAUSS-COROLLARY) (IMMEDIATE-DEPENDENTS0 PRIME . GAUSS-COROLLARY) (LEMMAS RES1 . GAUSS-COROLLARY))))) 
(PUT1-LST (QUOTE EQUAL-WINS-PLUS-QUOT-LIST) (QUOTE (IDATE 840118054606. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EQUAL-PLUS-QUOT-LIST-WINS) EVENT (PROVE-LEMMA EQUAL-WINS-PLUS-QUOT-LIST (REWRITE) (IMPLIES (AND (PRIME P) (NOT (DIVIDES P Q)) (NOT (ZEROP Q)) (NOT (ZEROP J)) (LEQ J (QUOTIENT P 2.))) (EQUAL (WINS (MULTS J Q) (MULTS (QUOTIENT Q 2.) P)) (PLUS-LIST (QUOT-LIST J Q P)))) ((INDUCT (MULTS J Q)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . EQUAL-WINS-PLUS-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 EQUAL-QUOT-WINS1 . EQUAL-WINS-PLUS-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . EQUAL-WINS-PLUS-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL . EQUAL-WINS-PLUS-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 QUOT-LIST . EQUAL-WINS-PLUS-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 PLUS-LIST . EQUAL-WINS-PLUS-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 MULTS . EQUAL-WINS-PLUS-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 WINS . EQUAL-WINS-PLUS-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 DIVIDES . EQUAL-WINS-PLUS-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 PRIME . EQUAL-WINS-PLUS-QUOT-LIST) (LEMMAS WINS . EQUAL-WINS-PLUS-QUOT-LIST))))) 
(PUT1-LST (QUOTE EQUAL-QUOT-WINS1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118054327. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EQUAL-WINS-PLUS-QUOT-LIST) EVENT (PROVE-LEMMA EQUAL-QUOT-WINS1 (REWRITE) (IMPLIES (AND (PRIME P) (NOT (DIVIDES P Q)) (LEQ J (QUOTIENT P 2.)) (NOT (ZEROP J)) (NOT (ZEROP Q))) (EQUAL (WINS1 (TIMES J Q) (MULTS (QUOTIENT Q 2.) P)) (QUOTIENT (TIMES J Q) P))) ((USE (LEQ-QUOT-WINS1) (LEQ-WINS1-QUOT (A (TIMES J Q)) (N (QUOTIENT Q 2.)))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LEQ-QUOT-WINS1 . EQUAL-QUOT-WINS1) (IMMEDIATE-DEPENDENTS0 LEQ-WINS1-QUOT . EQUAL-QUOT-WINS1) (IMMEDIATE-DEPENDENTS0 MULTS . EQUAL-QUOT-WINS1) (IMMEDIATE-DEPENDENTS0 WINS1 . EQUAL-QUOT-WINS1) (IMMEDIATE-DEPENDENTS0 DIVIDES . EQUAL-QUOT-WINS1) (IMMEDIATE-DEPENDENTS0 PRIME . EQUAL-QUOT-WINS1) (LEMMAS WINS1 . EQUAL-QUOT-WINS1))))) 
(PUT1-LST (QUOTE LEQ-WINS1-QUOT) (QUOTE (IDATE 840118054218. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EQUAL-QUOT-WINS1) EVENT (PROVE-LEMMA LEQ-WINS1-QUOT NIL (IMPLIES (NOT (ZEROP P)) (LEQ (WINS1 A (MULTS N P)) (QUOTIENT A P))) ((USE (MONOTONE-QUOT (I A) (J (TIMES (WINS1 A (MULTS N P)) P))) (LEQ-WINS1)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . LEQ-WINS1-QUOT) (IMMEDIATE-DEPENDENTS0 QUOTIENT-TIMES . LEQ-WINS1-QUOT) (IMMEDIATE-DEPENDENTS0 MONOTONE-QUOT . LEQ-WINS1-QUOT) (IMMEDIATE-DEPENDENTS0 LEQ-WINS1 . LEQ-WINS1-QUOT) (IMMEDIATE-DEPENDENTS0 MULTS . LEQ-WINS1-QUOT) (IMMEDIATE-DEPENDENTS0 WINS1 . LEQ-WINS1-QUOT))))) 
(PUT1-LST (QUOTE LEQ-WINS1) (QUOTE (IDATE 840118054215. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LEQ-WINS1-QUOT) EVENT (PROVE-LEMMA LEQ-WINS1 NIL (LEQ (TIMES (WINS1 A (MULTS N P)) P) A) ((USE (LEQ-WINS2) (LEQ-WINS1-WINS2) (LESSP-TIMES-CANCELLATION (X (WINS1 A (MULTS N P))) (Y (WINS2 A N P)) (Z P))) (DISABLE LESSP-TIMES-CANCELLATION))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . LEQ-WINS1) (IMMEDIATE-DEPENDENTS0 EQUAL-LESSP . LEQ-WINS1) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . LEQ-WINS1) (IMMEDIATE-DEPENDENTS0 TIMES-IDENTITY . LEQ-WINS1) (IMMEDIATE-DEPENDENTS0 LEQ-WINS2 . LEQ-WINS1) (IMMEDIATE-DEPENDENTS0 LEQ-WINS1-WINS2 . LEQ-WINS1) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES-CANCELLATION . LEQ-WINS1) (IMMEDIATE-DEPENDENTS0 MULTS . LEQ-WINS1) (IMMEDIATE-DEPENDENTS0 WINS1 . LEQ-WINS1))))) 
(PUT1-LST (QUOTE LEQ-WINS1-WINS2) (QUOTE (IDATE 840118054209. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LEQ-WINS1) EVENT (PROVE-LEMMA LEQ-WINS1-WINS2 NIL (LEQ (WINS1 A (MULTS N P)) (WINS2 A N P)) ((USE (LEQ-WINS1-N)) (INDUCT (WINS2 A N P)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-IDENTITY . LEQ-WINS1-WINS2) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . LEQ-WINS1-WINS2) (IMMEDIATE-DEPENDENTS0 LEQ-WINS1-N . LEQ-WINS1-WINS2) (IMMEDIATE-DEPENDENTS0 MULTS . LEQ-WINS1-WINS2) (IMMEDIATE-DEPENDENTS0 WINS1 . LEQ-WINS1-WINS2) (IMMEDIATE-DEPENDENTS0 WINS2 . LEQ-WINS1-WINS2))))) 
(PUT1-LST (QUOTE LEQ-WINS1-N) (QUOTE (IDATE 840118054157. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LEQ-WINS1-WINS2) EVENT (PROVE-LEMMA LEQ-WINS1-N NIL (LEQ (WINS1 A (MULTS N P)) N)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 MULTS . LEQ-WINS1-N) (IMMEDIATE-DEPENDENTS0 WINS1 . LEQ-WINS1-N))))) 
(PUT1-LST (QUOTE LEQ-WINS2) (QUOTE (IDATE 840118054147. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LEQ-WINS1) EVENT (PROVE-LEMMA LEQ-WINS2 NIL (LEQ (TIMES (WINS2 A N P) P) A)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-IDENTITY . LEQ-WINS2) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . LEQ-WINS2) (IMMEDIATE-DEPENDENTS0 WINS2 . LEQ-WINS2))))) 
(PUT1-LST (QUOTE 1WINS2) (QUOTE NIL)) 
(PUT1-LST (QUOTE WINS2) (QUOTE (TYPE-PRESCRIPTION-LST ((WINS2 4. NIL NIL NIL)) LEMMAS NIL LINEAR-LEMMAS NIL QUICK-BLOCK-INFO (UNCHANGING SELF-REFLEXIVE UNCHANGING) SDEFN (LAMBDA (A N P) (IF (EQUAL N (QUOTE 0.)) (QUOTE 0.) (IF (NUMBERP N) (IF (LESSP (TIMES N P) A) N (WINS2 A (SUB1 N) P)) (QUOTE 0.)))) LISP-CODE 1WINS2 INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP N)) NIL) (TESTS-AND-CASES ((NOT (ZEROP N)) (LESSP (TIMES N P) A)) NIL) (TESTS-AND-CASES ((NOT (ZEROP N)) (NOT (LESSP (TIMES N P) A))) ((A (SUB1 N) P)))) LEVEL-NO 3. JUSTIFICATIONS ((JUSTIFICATION (N) (COUNT N) LESSP (ZERO ZEROP COUNT-NUMBERP))) IDATE 840118054142. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (2.) SATELLITES (1WINS2) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LEQ-WINS1-WINS2 LEQ-WINS2) EVENT (DEFN WINS2 (A N P) (IF (ZEROP N) 0. (IF (LESSP (TIMES N P) A) N (WINS2 A (SUB1 N) P)))) LOCAL-UNDO-TUPLES ((DCELL . 1WINS2))))) 
(PUT1-LST (QUOTE LEQ-QUOT-WINS1) (QUOTE (IDATE 840118054142. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EQUAL-QUOT-WINS1) EVENT (PROVE-LEMMA LEQ-QUOT-WINS1 NIL (IMPLIES (AND (PRIME P) (NOT (DIVIDES P Q)) (LEQ J (QUOTIENT P 2.)) (NOT (ZEROP J)) (NOT (ZEROP Q))) (LEQ (QUOTIENT (TIMES J Q) P) (WINS1 (TIMES J Q) (MULTS (QUOTIENT Q 2.) P)))) ((USE (LEQ-QUOT-TIMES-2) (MONOTONE-WINS1 (A (TIMES J Q)) (N (QUOTIENT (TIMES J Q) P)) (M (QUOTIENT Q 2.))) (LEQ-N-WINS1 (A (TIMES J Q)) (N (QUOTIENT (TIMES J Q) P))) (LEQ-QUOT-WINS1-2)) (DISABLE PRIME))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-1 . LEQ-QUOT-WINS1) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO2 . LEQ-QUOT-WINS1) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . LEQ-QUOT-WINS1) (IMMEDIATE-DEPENDENTS0 TIMES-2 . LEQ-QUOT-WINS1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . LEQ-QUOT-WINS1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-PLUS . LEQ-QUOT-WINS1) (IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-TIMES-OVER-PLUS . LEQ-QUOT-WINS1) (IMMEDIATE-DEPENDENTS0 PLUS-EQUAL-0 . LEQ-QUOT-WINS1) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . LEQ-QUOT-WINS1) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . LEQ-QUOT-WINS1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . LEQ-QUOT-WINS1) (IMMEDIATE-DEPENDENTS0 LEQ-QUOT-TIMES-2 . LEQ-QUOT-WINS1) (IMMEDIATE-DEPENDENTS0 MONOTONE-WINS1 . LEQ-QUOT-WINS1) (IMMEDIATE-DEPENDENTS0 LEQ-N-WINS1 . LEQ-QUOT-WINS1) (IMMEDIATE-DEPENDENTS0 LEQ-QUOT-WINS1-2 . LEQ-QUOT-WINS1) (IMMEDIATE-DEPENDENTS0 MULTS . LEQ-QUOT-WINS1) (IMMEDIATE-DEPENDENTS0 WINS1 . LEQ-QUOT-WINS1) (IMMEDIATE-DEPENDENTS0 DIVIDES . LEQ-QUOT-WINS1) (IMMEDIATE-DEPENDENTS0 PRIME . LEQ-QUOT-WINS1))))) 
(PUT1-LST (QUOTE LEQ-QUOT-WINS1-2) (QUOTE (IDATE 840118053820. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LEQ-QUOT-WINS1) EVENT (PROVE-LEMMA LEQ-QUOT-WINS1-2 NIL (IMPLIES (AND (PRIME P) (NOT (DIVIDES P Q)) (NOT (ZEROP Q)) (NOT (ZEROP J)) (LESSP J P)) (LESSP (TIMES (QUOTIENT (TIMES J Q) P) P) (TIMES J Q))) ((USE (LEQ-QUOT-WINS1-1 (X (TIMES J Q)))) (DISABLE PRIME QUOTIENT TIMES))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PRIME-KEY-REWRITE . LEQ-QUOT-WINS1-2) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . LEQ-QUOT-WINS1-2) (IMMEDIATE-DEPENDENTS0 LEQ-QUOT-WINS1-1 . LEQ-QUOT-WINS1-2) (IMMEDIATE-DEPENDENTS0 DIVIDES . LEQ-QUOT-WINS1-2) (IMMEDIATE-DEPENDENTS0 PRIME . LEQ-QUOT-WINS1-2))))) 
(PUT1-LST (QUOTE LEQ-QUOT-WINS1-1) (QUOTE (IDATE 840118053805. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LEQ-QUOT-WINS1-2) EVENT (PROVE-LEMMA LEQ-QUOT-WINS1-1 NIL (IMPLIES (NOT (DIVIDES P X)) (LESSP (TIMES (QUOTIENT X P) P) X))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REMAINDER-WRT-12 . LEQ-QUOT-WINS1-1) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO2 . LEQ-QUOT-WINS1-1) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . LEQ-QUOT-WINS1-1) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . LEQ-QUOT-WINS1-1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . LEQ-QUOT-WINS1-1) (IMMEDIATE-DEPENDENTS0 DIVIDES . LEQ-QUOT-WINS1-1))))) 
(PUT1-LST (QUOTE LEQ-QUOT-TIMES-2) (QUOTE (IDATE 840118053753. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LEQ-QUOT-WINS1) EVENT (PROVE-LEMMA LEQ-QUOT-TIMES-2 NIL (IMPLIES (LEQ J (QUOTIENT P 2.)) (LEQ (QUOTIENT (TIMES J Q) P) (QUOTIENT Q 2.))) ((USE (LEQ-QUOT-TIMES) (MONOTONE-QUOT (J (TIMES J Q)) (I (TIMES (QUOTIENT P 2.) Q))) (LESSP-TIMES-CANCELLATION (X J) (Y (QUOTIENT P 2.)) (Z Q))) (DISABLE LESSP-TIMES-CANCELLATION))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . LEQ-QUOT-TIMES-2) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . LEQ-QUOT-TIMES-2) (IMMEDIATE-DEPENDENTS0 EQUAL-LESSP . LEQ-QUOT-TIMES-2) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO2 . LEQ-QUOT-TIMES-2) (IMMEDIATE-DEPENDENTS0 TIMES-IDENTITY . LEQ-QUOT-TIMES-2) (IMMEDIATE-DEPENDENTS0 LEQ-QUOT-TIMES . LEQ-QUOT-TIMES-2) (IMMEDIATE-DEPENDENTS0 MONOTONE-QUOT . LEQ-QUOT-TIMES-2) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES-CANCELLATION . LEQ-QUOT-TIMES-2))))) 
(PUT1-LST (QUOTE MONOTONE-QUOT) (QUOTE (IDATE 840118053636. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LEQ-WINS1-QUOT LEQ-QUOT-TIMES-2) EVENT (PROVE-LEMMA MONOTONE-QUOT NIL (IMPLIES (LEQ J I) (LEQ (QUOTIENT J P) (QUOTIENT I P))) ((INDUCT (MONOTONE-QUOT-INDUCTION I J P)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . MONOTONE-QUOT) (IMMEDIATE-DEPENDENTS0 MONOTONE-QUOT-INDUCTION . MONOTONE-QUOT))))) 
(PUT1-LST (QUOTE 1MONOTONE-QUOT-INDUCTION) (QUOTE NIL)) 
(PUT1-LST (QUOTE MONOTONE-QUOT-INDUCTION) (QUOTE (TYPE-PRESCRIPTION-LST ((MONOTONE-QUOT-INDUCTION 2. NIL NIL NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE SELF-REFLEXIVE UNCHANGING) SDEFN (LAMBDA (I J P) (IF (EQUAL P (QUOTE 0.)) (QUOTE 1TRUE) (IF (NUMBERP P) (IF (LESSP I P) (QUOTE 1TRUE) (IF (LESSP J P) (QUOTE 1TRUE) (MONOTONE-QUOT-INDUCTION (DIFFERENCE I P) (DIFFERENCE J P) P))) (QUOTE 1TRUE)))) LISP-CODE 1MONOTONE-QUOT-INDUCTION INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP P)) NIL) (TESTS-AND-CASES ((NOT (ZEROP P)) (LESSP I P)) NIL) (TESTS-AND-CASES ((NOT (ZEROP P)) (NOT (LESSP I P)) (LESSP J P)) NIL) (TESTS-AND-CASES ((NOT (ZEROP P)) (NOT (LESSP I P)) (NOT (LESSP J P))) (((DIFFERENCE I P) (DIFFERENCE J P) P)))) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (I) (COUNT I) LESSP (ZERO COUNT-NOT-LESSP ZEROP COUNT-NUMBERP)) (JUSTIFICATION (J) (COUNT J) LESSP (ZERO COUNT-NOT-LESSP ZEROP COUNT-NUMBERP))) IDATE 840118053615. CONTROLLER-POCKETS (1. 2.) SATELLITES (1MONOTONE-QUOT-INDUCTION) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (MONOTONE-QUOT) EVENT (DEFN MONOTONE-QUOT-INDUCTION (I J P) (IF (ZEROP P) T (IF (LESSP I P) T (IF (LESSP J P) T (MONOTONE-QUOT-INDUCTION (DIFFERENCE I P) (DIFFERENCE J P) P))))) LOCAL-UNDO-TUPLES ((DCELL . 1MONOTONE-QUOT-INDUCTION))))) 
(PUT1-LST (QUOTE LEQ-QUOT-TIMES) (QUOTE (IDATE 840118053614. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LEQ-QUOT-TIMES-2) EVENT (PROVE-LEMMA LEQ-QUOT-TIMES NIL (LEQ (QUOTIENT (TIMES (QUOTIENT P 2.) Q) P) (QUOTIENT Q 2.)) ((USE (LEQ-TIMES-QUOT (A (TIMES (QUOTIENT P 2.) Q)) (D P) (C Q) (B 2.))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . LEQ-QUOT-TIMES) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-PLUS . LEQ-QUOT-TIMES) (IMMEDIATE-DEPENDENTS0 LESSP-PLUS-CANCELATION . LEQ-QUOT-TIMES) (IMMEDIATE-DEPENDENTS0 TIMES-IDENTITY . LEQ-QUOT-TIMES) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES-CANCELLATION . LEQ-QUOT-TIMES) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . LEQ-QUOT-TIMES) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . LEQ-QUOT-TIMES) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . LEQ-QUOT-TIMES) (IMMEDIATE-DEPENDENTS0 TIMES-2 . LEQ-QUOT-TIMES) (IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-TIMES-OVER-PLUS . LEQ-QUOT-TIMES) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-TIMES . LEQ-QUOT-TIMES) (IMMEDIATE-DEPENDENTS0 LEQ-TIMES-QUOT . LEQ-QUOT-TIMES))))) 
(PUT1-LST (QUOTE LEQ-TIMES-QUOT) (QUOTE (IDATE 840118053518. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LEQ-QUOT-TIMES) EVENT (PROVE-LEMMA LEQ-TIMES-QUOT NIL (IMPLIES (AND (NOT (ZEROP B)) (LEQ (TIMES A B) (TIMES C D))) (LEQ (QUOTIENT A D) (QUOTIENT C B))) ((INDUCT (QUOT-QUOT-INDUCTION A B C D)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LESSP-TIMES-2 . LEQ-TIMES-QUOT) (IMMEDIATE-DEPENDENTS0 TIMES-1 . LEQ-TIMES-QUOT) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-PLUS . LEQ-TIMES-QUOT) (IMMEDIATE-DEPENDENTS0 TIMES-ADD1 . LEQ-TIMES-QUOT) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-PLUS . LEQ-TIMES-QUOT) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES-1 . LEQ-TIMES-QUOT) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . LEQ-TIMES-QUOT) (IMMEDIATE-DEPENDENTS0 TIMES-DIFFERENCE . LEQ-TIMES-QUOT) (IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-TIMES-OVER-PLUS . LEQ-TIMES-QUOT) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . LEQ-TIMES-QUOT) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . LEQ-TIMES-QUOT) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . LEQ-TIMES-QUOT) (IMMEDIATE-DEPENDENTS0 TIMES-IDENTITY . LEQ-TIMES-QUOT) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . LEQ-TIMES-QUOT) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO2 . LEQ-TIMES-QUOT) (IMMEDIATE-DEPENDENTS0 QUOT-QUOT-INDUCTION . LEQ-TIMES-QUOT))))) 
(PUT1-LST (QUOTE 1QUOT-QUOT-INDUCTION) (QUOTE NIL)) 
(PUT1-LST (QUOTE QUOT-QUOT-INDUCTION) (QUOTE (TYPE-PRESCRIPTION-LST ((QUOT-QUOT-INDUCTION 2. NIL NIL NIL NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE UNCHANGING SELF-REFLEXIVE UNCHANGING) SDEFN (LAMBDA (A B C D) (IF (EQUAL B (QUOTE 0.)) (QUOTE 1TRUE) (IF (NUMBERP B) (IF (EQUAL D (QUOTE 0.)) (QUOTE 1TRUE) (IF (NUMBERP D) (IF (LESSP A D) (QUOTE 1TRUE) (IF (LESSP C B) (QUOTE 1TRUE) (QUOT-QUOT-INDUCTION (DIFFERENCE A D) B (DIFFERENCE C B) D))) (QUOTE 1TRUE))) (QUOTE 1TRUE)))) LISP-CODE 1QUOT-QUOT-INDUCTION INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP B)) NIL) (TESTS-AND-CASES ((NOT (ZEROP B)) (ZEROP D)) NIL) (TESTS-AND-CASES ((NOT (ZEROP B)) (NOT (ZEROP D)) (LESSP A D)) NIL) (TESTS-AND-CASES ((NOT (ZEROP B)) (NOT (ZEROP D)) (NOT (LESSP A D)) (LESSP C B)) NIL) (TESTS-AND-CASES ((NOT (ZEROP B)) (NOT (ZEROP D)) (NOT (LESSP A D)) (NOT (LESSP C B))) (((DIFFERENCE A D) B (DIFFERENCE C B) D)))) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (A) (COUNT A) LESSP (ZERO COUNT-NOT-LESSP ZEROP COUNT-NUMBERP)) (JUSTIFICATION (C) (COUNT C) LESSP (ZERO COUNT-NOT-LESSP ZEROP COUNT-NUMBERP))) IDATE 840118053333. CONTROLLER-POCKETS (1. 4.) SATELLITES (1QUOT-QUOT-INDUCTION) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LEQ-TIMES-QUOT) EVENT (DEFN QUOT-QUOT-INDUCTION (A B C D) (IF (ZEROP B) T (IF (ZEROP D) T (IF (LESSP A D) T (IF (LESSP C B) T (QUOT-QUOT-INDUCTION (DIFFERENCE A D) B (DIFFERENCE C B) D)))))) LOCAL-UNDO-TUPLES ((DCELL . 1QUOT-QUOT-INDUCTION))))) 
(PUT1-LST (QUOTE MONOTONE-WINS1) (QUOTE (IDATE 840118053333. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LEQ-QUOT-WINS1) EVENT (PROVE-LEMMA MONOTONE-WINS1 NIL (IMPLIES (LEQ N M) (LEQ (WINS1 A (MULTS N P)) (WINS1 A (MULTS M P)))) ((INDUCT (MULTS M P)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 MULTS . MONOTONE-WINS1) (IMMEDIATE-DEPENDENTS0 WINS1 . MONOTONE-WINS1))))) 
(PUT1-LST (QUOTE LEQ-N-WINS1) (QUOTE (IDATE 840118053321. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LEQ-QUOT-WINS1) EVENT (PROVE-LEMMA LEQ-N-WINS1 NIL (IMPLIES (LESSP (TIMES N P) A) (LEQ N (WINS1 A (MULTS N P)))) ((INDUCT (MULTS N P)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-ADD1 . LEQ-N-WINS1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . LEQ-N-WINS1) (IMMEDIATE-DEPENDENTS0 TIMES-IDENTITY . LEQ-N-WINS1) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . LEQ-N-WINS1) (IMMEDIATE-DEPENDENTS0 MULTS . LEQ-N-WINS1) (IMMEDIATE-DEPENDENTS0 WINS1 . LEQ-N-WINS1))))) 
(PUT1-LST (QUOTE LENGTH-MULTS) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118053315. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LAW-OF-QUADRATIC-RECIPROCITY) EVENT (PROVE-LEMMA LENGTH-MULTS (REWRITE) (EQUAL (LENGTH (MULTS N P)) (FIX N))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 MULTS . LENGTH-MULTS) (LEMMAS LENGTH . LENGTH-MULTS))))) 
(PUT1-LST (QUOTE 1MULTS) (QUOTE NIL)) 
(PUT1-LST (QUOTE MULTS) (QUOTE (TYPE-PRESCRIPTION-LST ((MULTS 24. NIL NIL)) LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE UNCHANGING) SDEFN (LAMBDA (N P) (IF (EQUAL N (QUOTE 0.)) (QUOTE NIL) (IF (NUMBERP N) (CONS (TIMES N P) (MULTS (SUB1 N) P)) (QUOTE NIL)))) LISP-CODE 1MULTS INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP N)) NIL) (TESTS-AND-CASES ((NOT (ZEROP N))) (((SUB1 N) P)))) LEVEL-NO 3. JUSTIFICATIONS ((JUSTIFICATION (N) (COUNT N) LESSP (ZERO ZEROP COUNT-NUMBERP))) IDATE 840118053311. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1MULTS) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EQUAL-PLUS-QUOT-LIST-WINS EMPTY-INTERSECT-MULTS EMPTY-INTERSECT-MULTS-1 ALL-NON-ZEROP-MULTS EQUAL-WINS-PLUS-QUOT-LIST EQUAL-QUOT-WINS1 LEQ-WINS1-QUOT LEQ-WINS1 LEQ-WINS1-WINS2 LEQ-WINS1-N LEQ-QUOT-WINS1 MONOTONE-WINS1 LEQ-N-WINS1 LENGTH-MULTS) EVENT (DEFN MULTS (N P) (IF (ZEROP N) NIL (CONS (TIMES N P) (MULTS (SUB1 N) P)))) LOCAL-UNDO-TUPLES ((DCELL . 1MULTS))))) 
(PUT1-LST (QUOTE A-WINNER-EVERY-TIME) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118053311. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LAW-OF-QUADRATIC-RECIPROCITY) EVENT (PROVE-LEMMA A-WINNER-EVERY-TIME (REWRITE) (IMPLIES (AND (NLISTP (INTERSECT L M)) (ALL-NON-ZEROP L) (ALL-NON-ZEROP M)) (EQUAL (PLUS (WINS L M) (WINS M L)) (TIMES (LENGTH L) (LENGTH M)))) ((USE (WIN-SOME-LOSE-SOME-2)) (DISABLE WIN-SOME-LOSE-SOME-2))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQUAL-LOSSES-WINS . A-WINNER-EVERY-TIME) (IMMEDIATE-DEPENDENTS0 WIN-SOME-LOSE-SOME-2 . A-WINNER-EVERY-TIME) (IMMEDIATE-DEPENDENTS0 WINS . A-WINNER-EVERY-TIME) (IMMEDIATE-DEPENDENTS0 ALL-NON-ZEROP . A-WINNER-EVERY-TIME) (IMMEDIATE-DEPENDENTS0 INTERSECT . A-WINNER-EVERY-TIME) (LEMMAS PLUS . A-WINNER-EVERY-TIME))))) 
(PUT1-LST (QUOTE EQUAL-LOSSES-WINS) (QUOTE (IDATE 840118053309. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (A-WINNER-EVERY-TIME) EVENT (PROVE-LEMMA EQUAL-LOSSES-WINS (REWRITE) (EQUAL (LOSSES L M) (WINS M L))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PLUS-ADD1 . EQUAL-LOSSES-WINS) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-PLUS . EQUAL-LOSSES-WINS) (IMMEDIATE-DEPENDENTS0 WINS1 . EQUAL-LOSSES-WINS) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL . EQUAL-LOSSES-WINS) (IMMEDIATE-DEPENDENTS0 LOSSES1 . EQUAL-LOSSES-WINS) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . EQUAL-LOSSES-WINS) (IMMEDIATE-DEPENDENTS0 WINS . EQUAL-LOSSES-WINS) (IMMEDIATE-DEPENDENTS0 LOSSES . EQUAL-LOSSES-WINS) (LEMMAS LOSSES . EQUAL-LOSSES-WINS))))) 
(PUT1-LST (QUOTE WIN-SOME-LOSE-SOME-2) (QUOTE (IDATE 840118053253. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (A-WINNER-EVERY-TIME) EVENT (PROVE-LEMMA WIN-SOME-LOSE-SOME-2 (REWRITE) (IMPLIES (AND (NLISTP (INTERSECT L M)) (ALL-NON-ZEROP L) (ALL-NON-ZEROP M)) (EQUAL (PLUS (WINS L M) (LOSSES L M)) (TIMES (LENGTH L) (LENGTH M))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-IDENTITY . WIN-SOME-LOSE-SOME-2) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL . WIN-SOME-LOSE-SOME-2) (IMMEDIATE-DEPENDENTS0 WIN-SOME-LOSE-SOME-1 . WIN-SOME-LOSE-SOME-2) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-PLUS . WIN-SOME-LOSE-SOME-2) (IMMEDIATE-DEPENDENTS0 TIMES-ADD1 . WIN-SOME-LOSE-SOME-2) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . WIN-SOME-LOSE-SOME-2) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . WIN-SOME-LOSE-SOME-2) (IMMEDIATE-DEPENDENTS0 LOSSES . WIN-SOME-LOSE-SOME-2) (IMMEDIATE-DEPENDENTS0 WINS . WIN-SOME-LOSE-SOME-2) (IMMEDIATE-DEPENDENTS0 ALL-NON-ZEROP . WIN-SOME-LOSE-SOME-2) (IMMEDIATE-DEPENDENTS0 INTERSECT . WIN-SOME-LOSE-SOME-2) (LEMMAS PLUS . WIN-SOME-LOSE-SOME-2))))) 
(PUT1-LST (QUOTE WIN-SOME-LOSE-SOME-1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118053225. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (WIN-SOME-LOSE-SOME-2) EVENT (PROVE-LEMMA WIN-SOME-LOSE-SOME-1 (REWRITE) (IMPLIES (AND (NOT (MEMBER X L)) (ALL-NON-ZEROP L)) (EQUAL (PLUS (LOSSES1 X L) (WINS1 X L)) (LENGTH L)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 WINS1 . WIN-SOME-LOSE-SOME-1) (IMMEDIATE-DEPENDENTS0 LOSSES1 . WIN-SOME-LOSE-SOME-1) (IMMEDIATE-DEPENDENTS0 ALL-NON-ZEROP . WIN-SOME-LOSE-SOME-1) (LEMMAS PLUS . WIN-SOME-LOSE-SOME-1))))) 
(PUT1-LST (QUOTE 1LOSSES) (QUOTE NIL)) 
(PUT1-LST (QUOTE LOSSES) (QUOTE (TYPE-PRESCRIPTION-LST ((LOSSES 4. NIL NIL)) LEMMAS ((REWRITE-RULE EQUAL-LOSSES-WINS NIL (EQUAL (LOSSES L M) (WINS M L)) NIL)) LINEAR-LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE UNCHANGING) SDEFN (LAMBDA (K L) (IF (LISTP K) (PLUS (LOSSES1 (CAR K) L) (LOSSES (CDR K) L)) (QUOTE 0.))) LISP-CODE 1LOSSES INDUCTION-MACHINE ((TESTS-AND-CASES ((NLISTP K)) NIL) (TESTS-AND-CASES ((NOT (NLISTP K))) (((CDR K) L)))) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (K) (COUNT K) LESSP (CDR-LESSP NLISTP ZERO CDR-LESSEQP))) IDATE 840118053217. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1LOSSES) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EQUAL-LOSSES-WINS WIN-SOME-LOSE-SOME-2) EVENT (DEFN LOSSES (K L) (IF (NLISTP K) 0. (PLUS (LOSSES1 (CAR K) L) (LOSSES (CDR K) L)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LOSSES1 . LOSSES) (DCELL . 1LOSSES))))) 
(PUT1-LST (QUOTE 1LOSSES1) (QUOTE NIL)) 
(PUT1-LST (QUOTE LOSSES1) (QUOTE (TYPE-PRESCRIPTION-LST ((LOSSES1 4. NIL NIL)) LEMMAS NIL LINEAR-LEMMAS NIL QUICK-BLOCK-INFO (UNCHANGING SELF-REFLEXIVE) SDEFN (LAMBDA (X L) (IF (LISTP L) (IF (LESSP X (CAR L)) (ADD1 (LOSSES1 X (CDR L))) (LOSSES1 X (CDR L))) (QUOTE 0.))) LISP-CODE 1LOSSES1 INDUCTION-MACHINE ((TESTS-AND-CASES ((NLISTP L)) NIL) (TESTS-AND-CASES ((NOT (NLISTP L)) (LESSP X (CAR L))) ((X (CDR L)))) (TESTS-AND-CASES ((NOT (NLISTP L)) (NOT (LESSP X (CAR L)))) ((X (CDR L))))) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (L) (COUNT L) LESSP (CDR-LESSP NLISTP ZERO CDR-LESSEQP))) IDATE 840118053215. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (2.) SATELLITES (1LOSSES1) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EQUAL-LOSSES-WINS WIN-SOME-LOSE-SOME-1 LOSSES) EVENT (DEFN LOSSES1 (X L) (IF (NLISTP L) 0. (IF (LESSP X (CAR L)) (ADD1 (LOSSES1 X (CDR L))) (LOSSES1 X (CDR L))))) LOCAL-UNDO-TUPLES ((DCELL . 1LOSSES1))))) 
(PUT1-LST (QUOTE 1WINS) (QUOTE NIL)) 
(PUT1-LST (QUOTE WINS) (QUOTE (TYPE-PRESCRIPTION-LST ((WINS 4. NIL NIL)) LEMMAS ((REWRITE-RULE EQUAL-WINS-PLUS-QUOT-LIST ((PRIME P) (NOT (DIVIDES P Q)) (NUMBERP Q) (NOT (EQUAL Q (QUOTE 0.))) (NUMBERP J) (NOT (EQUAL J (QUOTE 0.))) (NOT (LESSP (QUOTIENT P (QUOTE 2.)) J))) (EQUAL (WINS (MULTS J Q) (MULTS (QUOTIENT Q (QUOTE 2.)) P)) (PLUS-LIST (QUOT-LIST J Q P))) NIL)) LINEAR-LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE UNCHANGING) SDEFN (LAMBDA (K L) (IF (LISTP K) (PLUS (WINS1 (CAR K) L) (WINS (CDR K) L)) (QUOTE 0.))) LISP-CODE 1WINS INDUCTION-MACHINE ((TESTS-AND-CASES ((NLISTP K)) NIL) (TESTS-AND-CASES ((NOT (NLISTP K))) (((CDR K) L)))) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (K) (COUNT K) LESSP (CDR-LESSP NLISTP ZERO CDR-LESSEQP))) IDATE 840118053214. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1WINS) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EQUAL-PLUS-QUOT-LIST-WINS EQUAL-WINS-PLUS-QUOT-LIST A-WINNER-EVERY-TIME EQUAL-LOSSES-WINS WIN-SOME-LOSE-SOME-2) EVENT (DEFN WINS (K L) (IF (NLISTP K) 0. (PLUS (WINS1 (CAR K) L) (WINS (CDR K) L)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 WINS1 . WINS) (DCELL . 1WINS))))) 
(PUT1-LST (QUOTE 1WINS1) (QUOTE NIL)) 
(PUT1-LST (QUOTE WINS1) (QUOTE (TYPE-PRESCRIPTION-LST ((WINS1 4. NIL NIL)) LEMMAS ((REWRITE-RULE EQUAL-QUOT-WINS1 ((PRIME P) (NOT (DIVIDES P Q)) (NOT (LESSP (QUOTIENT P (QUOTE 2.)) J)) (NUMBERP J) (NOT (EQUAL J (QUOTE 0.))) (NUMBERP Q) (NOT (EQUAL Q (QUOTE 0.)))) (EQUAL (WINS1 (TIMES J Q) (MULTS (QUOTIENT Q (QUOTE 2.)) P)) (QUOTIENT (TIMES J Q) P)) NIL)) LINEAR-LEMMAS NIL QUICK-BLOCK-INFO (UNCHANGING SELF-REFLEXIVE) SDEFN (LAMBDA (X L) (IF (LISTP L) (IF (LESSP (CAR L) X) (ADD1 (WINS1 X (CDR L))) (WINS1 X (CDR L))) (QUOTE 0.))) LISP-CODE 1WINS1 INDUCTION-MACHINE ((TESTS-AND-CASES ((NLISTP L)) NIL) (TESTS-AND-CASES ((NOT (NLISTP L)) (LESSP (CAR L) X)) ((X (CDR L)))) (TESTS-AND-CASES ((NOT (NLISTP L)) (NOT (LESSP (CAR L) X))) ((X (CDR L))))) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (L) (COUNT L) LESSP (CDR-LESSP NLISTP ZERO CDR-LESSEQP))) IDATE 840118053211. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (2.) SATELLITES (1WINS1) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EQUAL-QUOT-WINS1 LEQ-WINS1-QUOT LEQ-WINS1 LEQ-WINS1-WINS2 LEQ-WINS1-N LEQ-QUOT-WINS1 MONOTONE-WINS1 LEQ-N-WINS1 EQUAL-LOSSES-WINS WIN-SOME-LOSE-SOME-1 WINS) EVENT (DEFN WINS1 (X L) (IF (NLISTP L) 0. (IF (LESSP (CAR L) X) (ADD1 (WINS1 X (CDR L))) (WINS1 X (CDR L))))) LOCAL-UNDO-TUPLES ((DCELL . 1WINS1))))) 
(PUT1-LST (QUOTE RES1-QUOT-LIST) (QUOTE (IDATE 840118053211. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (RESIDUE-QUOT-LIST) EVENT (PROVE-LEMMA RES1-QUOT-LIST NIL (IMPLIES (AND (PRIME P) (NOT (EVEN3 P)) (NOT (EVEN3 A)) (NOT (DIVIDES P A))) (EQUAL (RES1 (QUOTIENT P 2.) A P) (EVEN3 (PLUS-LIST (QUOT-LIST (QUOTIENT P 2.) A P))))) ((USE (REM-QUOT-LIST (N (QUOTIENT P 2.))) (EQUALS-HAVE-SAME-PARITY (X (TIMES A (PLUS-LIST (POSITIVES (QUOTIENT P 2.))))) (Y (PLUS (TIMES P (PLUS-LIST (QUOT-LIST (QUOTIENT P 2.) A P))) (PLUS-LIST (REM-LIST (QUOTIENT P 2.) A P)))))) (DISABLE PRIME))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . RES1-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 EVEN3-TIMES . RES1-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 PLUS-REFLECT-LIST . RES1-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 IFF . RES1-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 EVEN3-REM-REFLECT . RES1-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 EVEN3-PLUS . RES1-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 REM-QUOT-LIST . RES1-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 EQUALS-HAVE-SAME-PARITY . RES1-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 QUOT-LIST . RES1-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 PLUS-LIST . RES1-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 RES1 . RES1-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 DIVIDES . RES1-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 EVEN3 . RES1-QUOT-LIST) (IMMEDIATE-DEPENDENTS0 PRIME . RES1-QUOT-LIST))))) 
(PUT1-LST (QUOTE EQUALS-HAVE-SAME-PARITY) (QUOTE (IDATE 840118052219. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (RES1-QUOT-LIST) EVENT (PROVE-LEMMA EQUALS-HAVE-SAME-PARITY NIL (IMPLIES (EQUAL X Y) (EQUAL (EVEN3 X) (EVEN3 Y)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EVEN3 . EQUALS-HAVE-SAME-PARITY))))) 
(PUT1-LST (QUOTE PLUS-REFLECT-LIST) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118052219. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (RES1-QUOT-LIST) EVENT (PROVE-LEMMA PLUS-REFLECT-LIST (REWRITE) (IMPLIES (AND (PRIME P) (NOT (DIVIDES P A)) (NOT (EVEN3 P))) (EQUAL (PLUS-LIST (REFLECT-LIST (QUOTIENT P 2.) A P)) (PLUS-LIST (POSITIVES (QUOTIENT P 2.))))) ((USE (PERM-PLUS-LIST (M (REFLECT-LIST (QUOTIENT P 2.) A P)) (L (POSITIVES (QUOTIENT P 2.)))) (PIGEON-HOLE-PRINCIPLE (L (REFLECT-LIST (QUOTIENT P 2.) A P))) (EVEN3-EVEN) (ALL-NON-ZEROP-REFLECT-LIST (B (QUOTIENT P 2.)))) (DISABLE PRIME))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ALL-DISTINCT-REFLECT-LIST . PLUS-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER-DIVISOR . PLUS-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 LENGTH-REFLECT-LIST . PLUS-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 ALL-LESSEQP-REFLECT-LIST . PLUS-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 LESSP-QUOTIENT1 . PLUS-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 REMAINDER-WRT-12 . PLUS-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 PERM-PLUS-LIST . PLUS-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 PIGEON-HOLE-PRINCIPLE . PLUS-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 EVEN3-EVEN . PLUS-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 ALL-NON-ZEROP-REFLECT-LIST . PLUS-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 POSITIVES . PLUS-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 REFLECT-LIST . PLUS-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 PLUS-LIST . PLUS-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 EVEN3 . PLUS-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 DIVIDES . PLUS-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 PRIME . PLUS-REFLECT-LIST) (LEMMAS PLUS-LIST . PLUS-REFLECT-LIST))))) 
(PUT1-LST (QUOTE EVEN3-EVEN) (QUOTE (IDATE 840118050026. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LAW-OF-QUADRATIC-RECIPROCITY RESIDUE-QUOT-LIST PLUS-REFLECT-LIST) EVENT (PROVE-LEMMA EVEN3-EVEN NIL (EQUAL (DIVIDES 2. P) (EVEN3 P))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-2 . EVEN3-EVEN) (IMMEDIATE-DEPENDENTS0 EVEN3-PLUS . EVEN3-EVEN) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . EVEN3-EVEN) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . EVEN3-EVEN) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER-DIVISOR . EVEN3-EVEN) (IMMEDIATE-DEPENDENTS0 EVEN3 . EVEN3-EVEN) (IMMEDIATE-DEPENDENTS0 DIVIDES . EVEN3-EVEN))))) 
(PUT1-LST (QUOTE PERM-PLUS-LIST) (QUOTE (IDATE 840118045926. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PLUS-REFLECT-LIST) EVENT (PROVE-LEMMA PERM-PLUS-LIST NIL (IMPLIES (PERM L M) (EQUAL (PLUS-LIST L) (PLUS-LIST M)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PERM-PLUS-LIST-1 . PERM-PLUS-LIST) (IMMEDIATE-DEPENDENTS0 PERM-MEMBER . PERM-PLUS-LIST) (IMMEDIATE-DEPENDENTS0 PLUS-LIST . PERM-PLUS-LIST) (IMMEDIATE-DEPENDENTS0 PERM . PERM-PLUS-LIST))))) 
(PUT1-LST (QUOTE PERM-PLUS-LIST-1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118045906. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PERM-PLUS-LIST) EVENT (PROVE-LEMMA PERM-PLUS-LIST-1 (REWRITE) (IMPLIES (MEMBER X M) (EQUAL (PLUS X (PLUS-LIST (DELETE X M))) (PLUS-LIST M)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL . PERM-PLUS-LIST-1) (IMMEDIATE-DEPENDENTS0 DELETE . PERM-PLUS-LIST-1) (IMMEDIATE-DEPENDENTS0 PLUS-LIST . PERM-PLUS-LIST-1) (LEMMAS PLUS . PERM-PLUS-LIST-1))))) 
(PUT1-LST (QUOTE EVEN3-REM-REFLECT) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118045900. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (RES1-QUOT-LIST) EVENT (PROVE-LEMMA EVEN3-REM-REFLECT (REWRITE) (IMPLIES (NOT (EVEN3 P)) (EQUAL (RES1 N A P) (IFF (EVEN3 (PLUS-LIST (REM-LIST N A P))) (EVEN3 (PLUS-LIST (REFLECT-LIST N A P))))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EVEN3-PLUS . EVEN3-REM-REFLECT) (IMMEDIATE-DEPENDENTS0 REFLECT . EVEN3-REM-REFLECT) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . EVEN3-REM-REFLECT) (IMMEDIATE-DEPENDENTS0 EVEN3-REM . EVEN3-REM-REFLECT) (IMMEDIATE-DEPENDENTS0 REFLECT-LIST . EVEN3-REM-REFLECT) (IMMEDIATE-DEPENDENTS0 REM-LIST . EVEN3-REM-REFLECT) (IMMEDIATE-DEPENDENTS0 PLUS-LIST . EVEN3-REM-REFLECT) (IMMEDIATE-DEPENDENTS0 IFF . EVEN3-REM-REFLECT) (IMMEDIATE-DEPENDENTS0 RES1 . EVEN3-REM-REFLECT) (IMMEDIATE-DEPENDENTS0 EVEN3 . EVEN3-REM-REFLECT) (LEMMAS RES1 . EVEN3-REM-REFLECT))))) 
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(PUT1-LST (QUOTE EVEN3-PLUS) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118044855. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (RESIDUE-QUOT-LIST RES1-QUOT-LIST EVEN3-EVEN EVEN3-REM-REFLECT EVEN3-REM EVEN3-TIMES EVEN3-DIFF) EVENT (PROVE-LEMMA EVEN3-PLUS (REWRITE) (EQUAL (EVEN3 (PLUS A B)) (EQUAL (EVEN3 A) (EVEN3 B)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EVEN3 . EVEN3-PLUS) (LEMMAS EVEN3 . EVEN3-PLUS))))) 
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(PUT1-LST (QUOTE EVEN3) (QUOTE (TYPE-PRESCRIPTION-LST ((EVEN3 3. NIL)) LEMMAS ((REWRITE-RULE EVEN3-REM ((NOT (EVEN3 P))) (EQUAL (EVEN3 (DIFFERENCE P (REMAINDER X P))) (IF (EVEN3 (REMAINDER X P)) (QUOTE 1FALSE) (QUOTE 1TRUE))) NIL) (REWRITE-RULE EVEN3-TIMES NIL (EQUAL (EVEN3 (TIMES A B)) (IF (EVEN3 A) (QUOTE 1TRUE) (EVEN3 B))) NIL) (REWRITE-RULE EVEN3-DIFF ((NOT (LESSP P X))) (EQUAL (EVEN3 (DIFFERENCE P X)) (EQUAL (EVEN3 P) (EVEN3 X))) NIL) (REWRITE-RULE EVEN3-PLUS NIL (EQUAL (EVEN3 (PLUS A B)) (EQUAL (EVEN3 A) (EVEN3 B))) NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (X) (IF (EQUAL X (QUOTE 0.)) (QUOTE 1TRUE) (IF (NUMBERP X) (IF (EVEN3 (SUB1 X)) (QUOTE 1FALSE) (QUOTE 1TRUE)) (QUOTE 1TRUE)))) LISP-CODE 1EVEN3 INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP X)) NIL) (TESTS-AND-CASES ((NOT (ZEROP X))) (((SUB1 X))))) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (X) (COUNT X) LESSP (ZERO ZEROP COUNT-NUMBERP))) IDATE 840118044847. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1EVEN3) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (RESIDUE-QUOT-LIST RES1-QUOT-LIST EQUALS-HAVE-SAME-PARITY PLUS-REFLECT-LIST EVEN3-EVEN EVEN3-REM-REFLECT EVEN3-REM EVEN3-TIMES EVEN3-DIFF EVEN3-PLUS) EVENT (DEFN EVEN3 (X) (IF (ZEROP X) T (NOT (EVEN3 (SUB1 X))))) LOCAL-UNDO-TUPLES ((DCELL . 1EVEN3))))) 
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(PUT1-LST (QUOTE REM-LIST) (QUOTE (TYPE-PRESCRIPTION-LST ((REM-LIST 24. NIL NIL NIL)) LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE UNCHANGING UNCHANGING) SDEFN (LAMBDA (N A P) (IF (EQUAL N (QUOTE 0.)) (QUOTE NIL) (IF (NUMBERP N) (CONS (REMAINDER (TIMES A N) P) (REM-LIST (SUB1 N) A P)) (QUOTE NIL)))) LISP-CODE 1REM-LIST INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP N)) NIL) (TESTS-AND-CASES ((NOT (ZEROP N))) (((SUB1 N) A P)))) LEVEL-NO 3. JUSTIFICATIONS ((JUSTIFICATION (N) (COUNT N) LESSP (ZERO ZEROP COUNT-NUMBERP))) IDATE 840118044521. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1REM-LIST) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EVEN3-REM-REFLECT REM-QUOT-LIST) EVENT (DEFN REM-LIST (N A P) (IF (ZEROP N) NIL (CONS (REMAINDER (TIMES A N) P) (REM-LIST (SUB1 N) A P)))) LOCAL-UNDO-TUPLES ((DCELL . 1REM-LIST))))) 
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(PUT1-LST (QUOTE QUOT-LIST) (QUOTE (TYPE-PRESCRIPTION-LST ((QUOT-LIST 24. NIL NIL NIL)) LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE UNCHANGING UNCHANGING) SDEFN (LAMBDA (N A P) (IF (EQUAL N (QUOTE 0.)) (QUOTE NIL) (IF (NUMBERP N) (CONS (QUOTIENT (TIMES A N) P) (QUOT-LIST (SUB1 N) A P)) (QUOTE NIL)))) LISP-CODE 1QUOT-LIST INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP N)) NIL) (TESTS-AND-CASES ((NOT (ZEROP N))) (((SUB1 N) A P)))) LEVEL-NO 3. JUSTIFICATIONS ((JUSTIFICATION (N) (COUNT N) LESSP (ZERO ZEROP COUNT-NUMBERP))) IDATE 840118044517. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1QUOT-LIST) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EQUAL-PLUS-QUOT-LIST-WINS RESIDUE-QUOT-LIST EQUAL-WINS-PLUS-QUOT-LIST RES1-QUOT-LIST REM-QUOT-LIST) EVENT (DEFN QUOT-LIST (N A P) (IF (ZEROP N) NIL (CONS (QUOTIENT (TIMES A N) P) (QUOT-LIST (SUB1 N) A P)))) LOCAL-UNDO-TUPLES ((DCELL . 1QUOT-LIST))))) 
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(PUT1-LST (QUOTE PLUS-LIST) (QUOTE (TYPE-PRESCRIPTION-LST ((PLUS-LIST 4. NIL)) LEMMAS ((REWRITE-RULE EQUAL-PLUS-QUOT-LIST-WINS ((PRIME P) (PRIME Q) (NOT (EQUAL P Q))) (EQUAL (PLUS-LIST (QUOT-LIST (QUOTIENT P (QUOTE 2.)) Q P)) (WINS (MULTS (QUOTIENT P (QUOTE 2.)) Q) (MULTS (QUOTIENT Q (QUOTE 2.)) P))) NIL) (REWRITE-RULE PLUS-REFLECT-LIST ((PRIME P) (NOT (DIVIDES P A)) (NOT (EVEN3 P))) (EQUAL (PLUS-LIST (REFLECT-LIST (QUOTIENT P (QUOTE 2.)) A P)) (PLUS-LIST (POSITIVES (QUOTIENT P (QUOTE 2.))))) NIL)) LINEAR-LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (L) (IF (LISTP L) (PLUS (CAR L) (PLUS-LIST (CDR L))) (QUOTE 0.))) LISP-CODE 1PLUS-LIST INDUCTION-MACHINE ((TESTS-AND-CASES ((NLISTP L)) NIL) (TESTS-AND-CASES ((NOT (NLISTP L))) (((CDR L))))) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (L) (COUNT L) LESSP (CDR-LESSP NLISTP ZERO CDR-LESSEQP))) IDATE 840118044503. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1PLUS-LIST) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EQUAL-PLUS-QUOT-LIST-WINS RESIDUE-QUOT-LIST EQUAL-WINS-PLUS-QUOT-LIST RES1-QUOT-LIST PLUS-REFLECT-LIST PERM-PLUS-LIST PERM-PLUS-LIST-1 EVEN3-REM-REFLECT REM-QUOT-LIST) EVENT (DEFN PLUS-LIST (L) (IF (NLISTP L) 0. (PLUS (CAR L) (PLUS-LIST (CDR L))))) LOCAL-UNDO-TUPLES ((DCELL . 1PLUS-LIST))))) 
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(PUT1-LST (QUOTE TIMES-REFLECT-LIST) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118042828. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (RES1-REM-2 RES1-REM-1) EVENT (PROVE-LEMMA TIMES-REFLECT-LIST (REWRITE) (IMPLIES (AND (PRIME P) (NOT (DIVIDES 2. P)) (NOT (DIVIDES P A))) (EQUAL (TIMES-LIST (REFLECT-LIST (QUOTIENT P 2.) A P)) (FACT (QUOTIENT P 2.)))) ((USE (PIGEON-HOLE-PRINCIPLE (L (REFLECT-LIST (QUOTIENT P 2.) A P)))) (HANDS-OFF QUOTIENT REMAINDER) (DISABLE PRIME1 REFLECT-LIST TIMES-LIST FACT))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LESSP-QUOTIENT1 . TIMES-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 ALL-NON-ZEROP-REFLECT-LIST . TIMES-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 ALL-DISTINCT-REFLECT-LIST . TIMES-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 LENGTH-REFLECT-LIST . TIMES-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 ALL-LESSEQP-REFLECT-LIST . TIMES-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 TIMES-LIST-EQUAL-FACT . TIMES-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER-DIVISOR . TIMES-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 PIGEON-HOLE-PRINCIPLE . TIMES-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 FACT . TIMES-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 REFLECT-LIST . TIMES-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 TIMES-LIST . TIMES-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 DIVIDES . TIMES-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 PRIME . TIMES-REFLECT-LIST) (LEMMAS TIMES-LIST . TIMES-REFLECT-LIST))))) 
(PUT1-LST (QUOTE ALL-DISTINCT-REFLECT-LIST) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118042808. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PLUS-REFLECT-LIST TIMES-REFLECT-LIST) EVENT (PROVE-LEMMA ALL-DISTINCT-REFLECT-LIST (REWRITE) (IMPLIES (AND (PRIME P) (NOT (DIVIDES 2. P)) (NOT (DIVIDES P A)) (LEQ I (QUOTIENT P 2.))) (ALL-DISTINCT (REFLECT-LIST I A P))) ((USE (ALL-DISTINCT-REFLECT-LIST-9 (J (SUB1 I))) (ALL-DISTINCT-REFLECT-LIST-10 (J (SUB1 I)))) (INDUCT (REFLECT-LIST I A P)) (HANDS-OFF QUOTIENT REMAINDER TIMES) (DISABLE ALL-DISTINCT-REFLECT-LIST-9 ALL-DISTINCT-REFLECT-LIST-10 PRIME DIVIDES REFLECT))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ALL-DISTINCT-REFLECT-LIST-9 . ALL-DISTINCT-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 ALL-DISTINCT-REFLECT-LIST-10 . ALL-DISTINCT-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 REFLECT-LIST . ALL-DISTINCT-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 ALL-DISTINCT . ALL-DISTINCT-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 DIVIDES . ALL-DISTINCT-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 PRIME . ALL-DISTINCT-REFLECT-LIST) (LEMMAS ALL-DISTINCT . ALL-DISTINCT-REFLECT-LIST))))) 
(PUT1-LST (QUOTE ALL-DISTINCT-REFLECT-LIST-10) (QUOTE (IDATE 840118042522. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (ALL-DISTINCT-REFLECT-LIST) EVENT (PROVE-LEMMA ALL-DISTINCT-REFLECT-LIST-10 (REWRITE) (IMPLIES (AND (PRIME P) (NOT (DIVIDES 2. P)) (NOT (DIVIDES P A)) (LEQ I (QUOTIENT P 2.)) (LESSP J I)) (NOT (MEMBER (REFLECT (REMAINDER (TIMES A I) P) P) (REFLECT-LIST J A P)))) ((USE (ALL-DISTINCT-REFLECT-LIST-3)) (INDUCT (REFLECT-LIST J A P)) (HANDS-OFF QUOTIENT REMAINDER TIMES) (DISABLE PRIME1 REFLECT ALL-DISTINCT-REFLECT-LIST-3))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ALL-DISTINCT-REFLECT-LIST-8 . ALL-DISTINCT-REFLECT-LIST-10) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER-DIVISOR . ALL-DISTINCT-REFLECT-LIST-10) (IMMEDIATE-DEPENDENTS0 ALL-DISTINCT-REFLECT-LIST-3 . ALL-DISTINCT-REFLECT-LIST-10) (IMMEDIATE-DEPENDENTS0 REFLECT-LIST . ALL-DISTINCT-REFLECT-LIST-10) (IMMEDIATE-DEPENDENTS0 REFLECT . ALL-DISTINCT-REFLECT-LIST-10) (IMMEDIATE-DEPENDENTS0 DIVIDES . ALL-DISTINCT-REFLECT-LIST-10) (IMMEDIATE-DEPENDENTS0 PRIME . ALL-DISTINCT-REFLECT-LIST-10) (LEMMAS MEMBER . ALL-DISTINCT-REFLECT-LIST-10))))) 
(PUT1-LST (QUOTE ALL-DISTINCT-REFLECT-LIST-9) (QUOTE (IDATE 840118042113. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (ALL-DISTINCT-REFLECT-LIST) EVENT (PROVE-LEMMA ALL-DISTINCT-REFLECT-LIST-9 (REWRITE) (IMPLIES (AND (PRIME P) (NOT (DIVIDES 2. P)) (NOT (DIVIDES P A)) (LEQ I (QUOTIENT P 2.)) (LESSP J I)) (NOT (MEMBER (REMAINDER (TIMES A I) P) (REFLECT-LIST J A P)))) ((USE (ALL-DISTINCT-REFLECT-LIST-1)) (INDUCT (REFLECT-LIST J A P)) (HANDS-OFF QUOTIENT REMAINDER TIMES) (DISABLE PRIME1 REFLECT ALL-DISTINCT-REFLECT-LIST-1))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ALL-DISTINCT-REFLECT-LIST-7 . ALL-DISTINCT-REFLECT-LIST-9) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . ALL-DISTINCT-REFLECT-LIST-9) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . ALL-DISTINCT-REFLECT-LIST-9) (IMMEDIATE-DEPENDENTS0 THM-55-SPECIALIZED-TO-PRIMES . ALL-DISTINCT-REFLECT-LIST-9) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER-DIVISOR . ALL-DISTINCT-REFLECT-LIST-9) (IMMEDIATE-DEPENDENTS0 ALL-DISTINCT-REFLECT-LIST-1 . ALL-DISTINCT-REFLECT-LIST-9) (IMMEDIATE-DEPENDENTS0 REFLECT-LIST . ALL-DISTINCT-REFLECT-LIST-9) (IMMEDIATE-DEPENDENTS0 DIVIDES . ALL-DISTINCT-REFLECT-LIST-9) (IMMEDIATE-DEPENDENTS0 PRIME . ALL-DISTINCT-REFLECT-LIST-9) (LEMMAS MEMBER . ALL-DISTINCT-REFLECT-LIST-9))))) 
(PUT1-LST (QUOTE ALL-DISTINCT-REFLECT-LIST-8) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118041609. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (ALL-DISTINCT-REFLECT-LIST-10) EVENT (PROVE-LEMMA ALL-DISTINCT-REFLECT-LIST-8 (REWRITE) (IMPLIES (AND (PRIME P) (NOT (DIVIDES P A)) (LEQ I (QUOTIENT P 2.)) (LESSP J I)) (NOT (EQUAL (REFLECT (REMAINDER (TIMES A I) P) P) (REMAINDER (TIMES A J) P)))) ((USE (ALL-DISTINCT-REFLECT-LIST-5 (J I) (I J)) (ALL-DISTINCT-REFLECT-LIST-6)) (HANDS-OFF TIMES DIFFERENCE) (DISABLE PRIME1))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . ALL-DISTINCT-REFLECT-LIST-8) (IMMEDIATE-DEPENDENTS0 PRIME-KEY-REWRITE . ALL-DISTINCT-REFLECT-LIST-8) (IMMEDIATE-DEPENDENTS0 PLUS-EQUAL-0 . ALL-DISTINCT-REFLECT-LIST-8) (IMMEDIATE-DEPENDENTS0 ALL-DISTINCT-REFLECT-LIST-5 . ALL-DISTINCT-REFLECT-LIST-8) (IMMEDIATE-DEPENDENTS0 ALL-DISTINCT-REFLECT-LIST-6 . ALL-DISTINCT-REFLECT-LIST-8) (IMMEDIATE-DEPENDENTS0 REFLECT . ALL-DISTINCT-REFLECT-LIST-8) (IMMEDIATE-DEPENDENTS0 DIVIDES . ALL-DISTINCT-REFLECT-LIST-8) (IMMEDIATE-DEPENDENTS0 PRIME . ALL-DISTINCT-REFLECT-LIST-8) (LEMMAS EQUAL . ALL-DISTINCT-REFLECT-LIST-8))))) 
(PUT1-LST (QUOTE ALL-DISTINCT-REFLECT-LIST-7) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118032035. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (ALL-DISTINCT-REFLECT-LIST-9) EVENT (PROVE-LEMMA ALL-DISTINCT-REFLECT-LIST-7 (REWRITE) (IMPLIES (AND (PRIME P) (NOT (DIVIDES P A)) (LEQ I (QUOTIENT P 2.)) (LESSP J I)) (NOT (EQUAL (REMAINDER (TIMES A I) P) (REFLECT (REMAINDER (TIMES A J) P) P)))) ((USE (ALL-DISTINCT-REFLECT-LIST-5) (ALL-DISTINCT-REFLECT-LIST-6)) (HANDS-OFF DIFFERENCE TIMES PLUS) (DISABLE PRIME1))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PRIME-KEY-REWRITE . ALL-DISTINCT-REFLECT-LIST-7) (IMMEDIATE-DEPENDENTS0 PLUS-EQUAL-0 . ALL-DISTINCT-REFLECT-LIST-7) (IMMEDIATE-DEPENDENTS0 ALL-DISTINCT-REFLECT-LIST-5 . ALL-DISTINCT-REFLECT-LIST-7) (IMMEDIATE-DEPENDENTS0 ALL-DISTINCT-REFLECT-LIST-6 . ALL-DISTINCT-REFLECT-LIST-7) (IMMEDIATE-DEPENDENTS0 REFLECT . ALL-DISTINCT-REFLECT-LIST-7) (IMMEDIATE-DEPENDENTS0 DIVIDES . ALL-DISTINCT-REFLECT-LIST-7) (IMMEDIATE-DEPENDENTS0 PRIME . ALL-DISTINCT-REFLECT-LIST-7) (LEMMAS EQUAL . ALL-DISTINCT-REFLECT-LIST-7))))) 
(PUT1-LST (QUOTE ALL-DISTINCT-REFLECT-LIST-6) (QUOTE (IDATE 840118031827. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (ALL-DISTINCT-REFLECT-LIST-8 ALL-DISTINCT-REFLECT-LIST-7) EVENT (PROVE-LEMMA ALL-DISTINCT-REFLECT-LIST-6 NIL (IMPLIES (AND (LEQ I (QUOTIENT P 2.)) (LESSP J I)) (AND (NOT (ZEROP (PLUS I J))) (LESSP (PLUS I J) P)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . ALL-DISTINCT-REFLECT-LIST-6) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . ALL-DISTINCT-REFLECT-LIST-6) (IMMEDIATE-DEPENDENTS0 PLUS-EQUAL-0 . ALL-DISTINCT-REFLECT-LIST-6))))) 
(PUT1-LST (QUOTE ALL-DISTINCT-REFLECT-LIST-5) (QUOTE (IDATE 840118031814. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (ALL-DISTINCT-REFLECT-LIST-8 ALL-DISTINCT-REFLECT-LIST-7) EVENT (PROVE-LEMMA ALL-DISTINCT-REFLECT-LIST-5 NIL (IMPLIES (AND (EQUAL (REMAINDER (TIMES A I) P) (DIFFERENCE P (REMAINDER (TIMES A J) P))) (NOT (ZEROP P))) (EQUAL (REMAINDER (TIMES A (PLUS I J)) P) 0.)) ((USE (ALL-DISTINCT-REFLECT-LIST-4 (X (REMAINDER (TIMES A I) P)) (Y (REMAINDER (TIMES A J) P)))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . ALL-DISTINCT-REFLECT-LIST-5) (IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-TIMES-OVER-PLUS . ALL-DISTINCT-REFLECT-LIST-5) (IMMEDIATE-DEPENDENTS0 PLUS-MOD-2 . ALL-DISTINCT-REFLECT-LIST-5) (IMMEDIATE-DEPENDENTS0 ALL-DISTINCT-REFLECT-LIST-4 . ALL-DISTINCT-REFLECT-LIST-5))))) 
(PUT1-LST (QUOTE ALL-DISTINCT-REFLECT-LIST-4) (QUOTE (IDATE 840118031350. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (ALL-DISTINCT-REFLECT-LIST-5) EVENT (PROVE-LEMMA ALL-DISTINCT-REFLECT-LIST-4 NIL (IMPLIES (AND (EQUAL X (DIFFERENCE P Y)) (LESSP Y P)) (EQUAL (REMAINDER (PLUS X Y) P) 0.))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . ALL-DISTINCT-REFLECT-LIST-4) (IMMEDIATE-DEPENDENTS0 REMAINDER-0-CROCK . ALL-DISTINCT-REFLECT-LIST-4) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . ALL-DISTINCT-REFLECT-LIST-4))))) 
(PUT1-LST (QUOTE PLUS-MOD-2) (QUOTE (IDATE 840118031344. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (ALL-DISTINCT-REFLECT-LIST-5) EVENT (PROVE-LEMMA PLUS-MOD-2 (REWRITE) (EQUAL (REMAINDER (PLUS Y (REMAINDER X P)) P) (REMAINDER (PLUS X Y) P)) ((USE (PLUS-MOD-1)) (DISABLE PLUS-MOD-1))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . PLUS-MOD-2) (IMMEDIATE-DEPENDENTS0 PLUS-MOD-1 . PLUS-MOD-2) (LEMMAS REMAINDER . PLUS-MOD-2))))) 
(PUT1-LST (QUOTE PLUS-MOD-1) (QUOTE (IDATE 840118031326. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PLUS-MOD-2) EVENT (PROVE-LEMMA PLUS-MOD-1 (REWRITE) (EQUAL (REMAINDER (PLUS (REMAINDER X P) Y) P) (REMAINDER (PLUS X Y) P)) ((USE (REMAINDER-QUOTIENT (Y P)) (REMAINDER-PLUS-TIMES-1 (J P) (X (PLUS (REMAINDER X P) Y)) (I (QUOTIENT X P)))) (DISABLE REMAINDER-QUOTIENT REMAINDER-QUOTIENT-ELIM REMAINDER-PLUS-TIMES-1))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PLUS-RIGHT-ID2 . PLUS-MOD-1) (IMMEDIATE-DEPENDENTS0 REMAINDER-0-CROCK . PLUS-MOD-1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . PLUS-MOD-1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . PLUS-MOD-1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-PLUS . PLUS-MOD-1) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-PLUS . PLUS-MOD-1) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT . PLUS-MOD-1) (IMMEDIATE-DEPENDENTS0 REMAINDER-PLUS-TIMES-1 . PLUS-MOD-1) (LEMMAS REMAINDER . PLUS-MOD-1))))) 
(PUT1-LST (QUOTE ALL-DISTINCT-REFLECT-LIST-3) (QUOTE (IDATE 840118031136. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (ALL-DISTINCT-REFLECT-LIST-10) EVENT (PROVE-LEMMA ALL-DISTINCT-REFLECT-LIST-3 (REWRITE) (IMPLIES (AND (PRIME P) (LESSP J I) (LESSP I P) (NOT (DIVIDES P A))) (NOT (EQUAL (REFLECT (REMAINDER (TIMES A I) P) P) (REFLECT (REMAINDER (TIMES A J) P) P)))) ((USE (ALL-DISTINCT-REFLECT-LIST-1)) (HANDS-OFF DIFFERENCE REMAINDER TIMES) (DISABLE ALL-DISTINCT-REFLECT-LIST-1 PRIME))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PLUS-EQUAL-0 . ALL-DISTINCT-REFLECT-LIST-3) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . ALL-DISTINCT-REFLECT-LIST-3) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER-DIVISOR . ALL-DISTINCT-REFLECT-LIST-3) (IMMEDIATE-DEPENDENTS0 ALL-DISTINCT-REFLECT-LIST-2 . ALL-DISTINCT-REFLECT-LIST-3) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . ALL-DISTINCT-REFLECT-LIST-3) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . ALL-DISTINCT-REFLECT-LIST-3) (IMMEDIATE-DEPENDENTS0 THM-55-SPECIALIZED-TO-PRIMES . ALL-DISTINCT-REFLECT-LIST-3) (IMMEDIATE-DEPENDENTS0 ALL-DISTINCT-REFLECT-LIST-1 . ALL-DISTINCT-REFLECT-LIST-3) (IMMEDIATE-DEPENDENTS0 REFLECT . ALL-DISTINCT-REFLECT-LIST-3) (IMMEDIATE-DEPENDENTS0 DIVIDES . ALL-DISTINCT-REFLECT-LIST-3) (IMMEDIATE-DEPENDENTS0 PRIME . ALL-DISTINCT-REFLECT-LIST-3) (LEMMAS EQUAL . ALL-DISTINCT-REFLECT-LIST-3))))) 
(PUT1-LST (QUOTE NUMBERP-REMAINDER) (QUOTE (IDATE 840118031058. EVENT (PROVE-LEMMA NUMBERP-REMAINDER (REWRITE) (NUMBERP (REMAINDER A P))) LOCAL-UNDO-TUPLES ((LEMMAS NUMBERP . NUMBERP-REMAINDER))))) 
(PUT1-LST (QUOTE ALL-DISTINCT-REFLECT-LIST-2) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118031057. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (ALL-DISTINCT-REFLECT-LIST-3) EVENT (PROVE-LEMMA ALL-DISTINCT-REFLECT-LIST-2 (REWRITE) (IMPLIES (AND (NUMBERP X) (NUMBERP Y) (LESSP X P) (LESSP Y P)) (EQUAL (EQUAL (DIFFERENCE P X) (DIFFERENCE P Y)) (EQUAL X Y)))) LOCAL-UNDO-TUPLES ((LEMMAS EQUAL . ALL-DISTINCT-REFLECT-LIST-2))))) 
(PUT1-LST (QUOTE ALL-DISTINCT-REFLECT-LIST-1) (QUOTE (IDATE 840118031054. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (ALL-DISTINCT-REFLECT-LIST-9 ALL-DISTINCT-REFLECT-LIST-3) EVENT (PROVE-LEMMA ALL-DISTINCT-REFLECT-LIST-1 (REWRITE) (IMPLIES (AND (PRIME P) (LESSP J I) (LESSP I P) (NOT (DIVIDES P A))) (NOT (EQUAL (REMAINDER (TIMES A I) P) (REMAINDER (TIMES A J) P)))) ((DISABLE PRIME))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REMAINDER-0-CROCK . ALL-DISTINCT-REFLECT-LIST-1) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . ALL-DISTINCT-REFLECT-LIST-1) (IMMEDIATE-DEPENDENTS0 THM-55-SPECIALIZED-TO-PRIMES . ALL-DISTINCT-REFLECT-LIST-1) (IMMEDIATE-DEPENDENTS0 DIVIDES . ALL-DISTINCT-REFLECT-LIST-1) (IMMEDIATE-DEPENDENTS0 PRIME . ALL-DISTINCT-REFLECT-LIST-1) (LEMMAS EQUAL . ALL-DISTINCT-REFLECT-LIST-1))))) 
(PUT1-LST (QUOTE ALL-NON-ZEROP-REFLECT-LIST) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118031039. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PLUS-REFLECT-LIST TIMES-REFLECT-LIST) EVENT (PROVE-LEMMA ALL-NON-ZEROP-REFLECT-LIST (REWRITE) (IMPLIES (AND (PRIME P) (NOT (DIVIDES P A)) (LESSP B P)) (ALL-NON-ZEROP (REFLECT-LIST B A P))) ((INDUCT (REFLECT-LIST B A P)) (DISABLE PRIME1))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PRIME-KEY-REWRITE . ALL-NON-ZEROP-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 REFLECT . ALL-NON-ZEROP-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE-0 . ALL-NON-ZEROP-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . ALL-NON-ZEROP-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 REFLECT-LIST . ALL-NON-ZEROP-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 ALL-NON-ZEROP . ALL-NON-ZEROP-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 DIVIDES . ALL-NON-ZEROP-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 PRIME . ALL-NON-ZEROP-REFLECT-LIST) (LEMMAS ALL-NON-ZEROP . ALL-NON-ZEROP-REFLECT-LIST))))) 
(PUT1-LST (QUOTE ALL-LESSEQP-REFLECT-LIST) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118025819. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PLUS-REFLECT-LIST TIMES-REFLECT-LIST) EVENT (PROVE-LEMMA ALL-LESSEQP-REFLECT-LIST (REWRITE) (ALL-LESSEQP (REFLECT-LIST N A P) (QUOTIENT P 2.)) ((DISABLE REFLECT))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ALL-LESSEQP-REFLECT-LIST-1 . ALL-LESSEQP-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 PIGEON-HOLE-PRINCIPLE-LEMMA-2 . ALL-LESSEQP-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . ALL-LESSEQP-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . ALL-LESSEQP-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 REFLECT-LIST . ALL-LESSEQP-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 ALL-LESSEQP . ALL-LESSEQP-REFLECT-LIST) (LEMMAS ALL-LESSEQP . ALL-LESSEQP-REFLECT-LIST))))) 
(PUT1-LST (QUOTE ALL-LESSEQP-REFLECT-LIST-1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118025720. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (ALL-LESSEQP-REFLECT-LIST) EVENT (PROVE-LEMMA ALL-LESSEQP-REFLECT-LIST-1 (REWRITE) (IMPLIES (LESSP (QUOTIENT P 2.) X) (NOT (LESSP (QUOTIENT P 2.) (REFLECT X P))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-2 . ALL-LESSEQP-REFLECT-LIST-1) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . ALL-LESSEQP-REFLECT-LIST-1) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . ALL-LESSEQP-REFLECT-LIST-1) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . ALL-LESSEQP-REFLECT-LIST-1) (IMMEDIATE-DEPENDENTS0 REFLECT . ALL-LESSEQP-REFLECT-LIST-1) (LINEAR-LEMMAS QUOTIENT . ALL-LESSEQP-REFLECT-LIST-1) (LINEAR-LEMMAS REFLECT . ALL-LESSEQP-REFLECT-LIST-1))))) 
(PUT1-LST (QUOTE LENGTH-REFLECT-LIST) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118025713. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PLUS-REFLECT-LIST TIMES-REFLECT-LIST) EVENT (PROVE-LEMMA LENGTH-REFLECT-LIST (REWRITE) (EQUAL (LENGTH (REFLECT-LIST N A P)) (FIX N)) ((INDUCT (POSITIVES N)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REFLECT . LENGTH-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 POSITIVES . LENGTH-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 REFLECT-LIST . LENGTH-REFLECT-LIST) (LEMMAS LENGTH . LENGTH-REFLECT-LIST))))) 
(PUT1-LST (QUOTE REM-REFLECT-LIST) (QUOTE (IDATE 840118025452. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (RES1-REM-2 RES1-REM-1) EVENT (PROVE-LEMMA REM-REFLECT-LIST NIL (IMPLIES (NOT (ZEROP P)) (EQUAL (REMAINDER (TIMES-LIST (REFLECT-LIST N A P)) P) (IF (RES1 N A P) (REMAINDER (TIMES (EXP A N) (FACT N)) P) (REMAINDER (REFLECT (REMAINDER (TIMES (EXP A N) (FACT N)) P) P) P)))) ((HANDS-OFF TIMES-LIST REFLECT-LIST QUOTIENT EXP FACT TIMES) (DISABLE REFLECT))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REM-REFLECT-LIST-3 . REM-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 REM-REFLECT-LIST-1 . REM-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 REM-REFLECT-LIST-4 . REM-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 REM-REFLECT-LIST-2 . REM-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 REM-REFLECT-LIST-BASE-CASE . REM-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 REFLECT . REM-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 FACT . REM-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 EXP . REM-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 RES1 . REM-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 REFLECT-LIST . REM-REFLECT-LIST) (IMMEDIATE-DEPENDENTS0 TIMES-LIST . REM-REFLECT-LIST))))) 
(PUT1-LST (QUOTE REM-REFLECT-LIST-BASE-CASE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118024814. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (REM-REFLECT-LIST) EVENT (PROVE-LEMMA REM-REFLECT-LIST-BASE-CASE (REWRITE) (IMPLIES (ZEROP N) (EQUAL (REMAINDER (TIMES-LIST (REFLECT-LIST N A P)) P) (REMAINDER (TIMES (EXP A N) (FACT N)) P)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REMAINDER-OF-1 . REM-REFLECT-LIST-BASE-CASE) (IMMEDIATE-DEPENDENTS0 EXP-BY-0 . REM-REFLECT-LIST-BASE-CASE) (IMMEDIATE-DEPENDENTS0 FACT . REM-REFLECT-LIST-BASE-CASE) (IMMEDIATE-DEPENDENTS0 EXP . REM-REFLECT-LIST-BASE-CASE) (IMMEDIATE-DEPENDENTS0 REFLECT-LIST . REM-REFLECT-LIST-BASE-CASE) (IMMEDIATE-DEPENDENTS0 TIMES-LIST . REM-REFLECT-LIST-BASE-CASE) (LEMMAS REMAINDER . REM-REFLECT-LIST-BASE-CASE))))) 
(PUT1-LST (QUOTE REM-REFLECT-LIST-4) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118024807. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (REM-REFLECT-LIST) EVENT (PROVE-LEMMA REM-REFLECT-LIST-4 (REWRITE) (IMPLIES (AND (NOT (ZEROP P)) (NOT (ZEROP N)) (LESSP (QUOTIENT P 2.) (REMAINDER (TIMES A N) P)) (EQUAL (REMAINDER (TIMES-LIST (REFLECT-LIST (SUB1 N) A P)) P) (REMAINDER (REFLECT (REMAINDER (TIMES (EXP A (SUB1 N)) (FACT (SUB1 N))) P) P) P))) (EQUAL (REMAINDER (TIMES-LIST (REFLECT-LIST N A P)) P) (REMAINDER (TIMES (EXP A N) (FACT N)) P))) ((USE (REMAINDER-EXP-LEMMA (A P) (X (TIMES A N)) (Y (TIMES-LIST (REFLECT-LIST (SUB1 N) A P))) (Z (REFLECT (REMAINDER (TIMES (EXP A (SUB1 N)) (FACT (SUB1 N))) P) P)))) (HANDS-OFF TIMES DIFFERENCE QUOTIENT EXP FACT) (DISABLE REMAINDER-EXP-LEMMA REFLECT))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER-DIVISOR . REM-REFLECT-LIST-4) (IMMEDIATE-DEPENDENTS0 TIMES-EXP-FACT . REM-REFLECT-LIST-4) (IMMEDIATE-DEPENDENTS0 TIMES-MOD-1 . REM-REFLECT-LIST-4) (IMMEDIATE-DEPENDENTS0 REFLECT-COMMUTES-WITH-TIMES-2 . REM-REFLECT-LIST-4) (IMMEDIATE-DEPENDENTS0 TIMES-MOD-3 . REM-REFLECT-LIST-4) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . REM-REFLECT-LIST-4) (IMMEDIATE-DEPENDENTS0 DOUBLE-REFLECT . REM-REFLECT-LIST-4) (IMMEDIATE-DEPENDENTS0 REFLECT-COMMUTES-WITH-TIMES-1 . REM-REFLECT-LIST-4) (IMMEDIATE-DEPENDENTS0 REMAINDER-EXP-LEMMA . REM-REFLECT-LIST-4) (IMMEDIATE-DEPENDENTS0 FACT . REM-REFLECT-LIST-4) (IMMEDIATE-DEPENDENTS0 EXP . REM-REFLECT-LIST-4) (IMMEDIATE-DEPENDENTS0 REFLECT . REM-REFLECT-LIST-4) (IMMEDIATE-DEPENDENTS0 REFLECT-LIST . REM-REFLECT-LIST-4) (IMMEDIATE-DEPENDENTS0 TIMES-LIST . REM-REFLECT-LIST-4) (LEMMAS REMAINDER . REM-REFLECT-LIST-4))))) 
(PUT1-LST (QUOTE DOUBLE-REFLECT) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118024438. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (REM-REFLECT-LIST-4) EVENT (PROVE-LEMMA DOUBLE-REFLECT (REWRITE) (IMPLIES (LEQ A P) (EQUAL (REMAINDER (REFLECT (REMAINDER (REFLECT A P) P) P) P) (REMAINDER A P)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REMAINDER-WRT-12 . DOUBLE-REFLECT) (IMMEDIATE-DEPENDENTS0 REMAINDER-0-CROCK . DOUBLE-REFLECT) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . DOUBLE-REFLECT) (IMMEDIATE-DEPENDENTS0 REFLECT . DOUBLE-REFLECT) (LEMMAS REMAINDER . DOUBLE-REFLECT))))) 
(PUT1-LST (QUOTE REM-REFLECT-LIST-3) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118024407. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (REM-REFLECT-LIST) EVENT (PROVE-LEMMA REM-REFLECT-LIST-3 (REWRITE) (IMPLIES (AND (NOT (ZEROP P)) (NOT (ZEROP N)) (NOT (LESSP (QUOTIENT P 2.) (REMAINDER (TIMES A N) P))) (EQUAL (REMAINDER (TIMES-LIST (REFLECT-LIST (SUB1 N) A P)) P) (REMAINDER (REFLECT (REMAINDER (TIMES (EXP A (SUB1 N)) (FACT (SUB1 N))) P) P) P))) (EQUAL (REMAINDER (TIMES-LIST (REFLECT-LIST N A P)) P) (REMAINDER (REFLECT (REMAINDER (TIMES (EXP A N) (FACT N)) P) P) P))) ((USE (REMAINDER-EXP-LEMMA (A P) (X (TIMES A N)) (Y (TIMES-LIST (REFLECT-LIST (SUB1 N) A P))) (Z (REFLECT (REMAINDER (TIMES (EXP A (SUB1 N)) (FACT (SUB1 N))) P) P)))) (HANDS-OFF TIMES DIFFERENCE QUOTIENT EXP FACT) (DISABLE REMAINDER-EXP-LEMMA REFLECT))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER-DIVISOR . REM-REFLECT-LIST-3) (IMMEDIATE-DEPENDENTS0 TIMES-EXP-FACT . REM-REFLECT-LIST-3) (IMMEDIATE-DEPENDENTS0 TIMES-MOD-1 . REM-REFLECT-LIST-3) (IMMEDIATE-DEPENDENTS0 REFLECT-COMMUTES-WITH-TIMES-2 . REM-REFLECT-LIST-3) (IMMEDIATE-DEPENDENTS0 TIMES-MOD-3 . REM-REFLECT-LIST-3) (IMMEDIATE-DEPENDENTS0 REMAINDER-EXP-LEMMA . REM-REFLECT-LIST-3) (IMMEDIATE-DEPENDENTS0 FACT . REM-REFLECT-LIST-3) (IMMEDIATE-DEPENDENTS0 EXP . REM-REFLECT-LIST-3) (IMMEDIATE-DEPENDENTS0 REFLECT . REM-REFLECT-LIST-3) (IMMEDIATE-DEPENDENTS0 REFLECT-LIST . REM-REFLECT-LIST-3) (IMMEDIATE-DEPENDENTS0 TIMES-LIST . REM-REFLECT-LIST-3) (LEMMAS REMAINDER . REM-REFLECT-LIST-3))))) 
(PUT1-LST (QUOTE REM-REFLECT-LIST-2) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118024039. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (REM-REFLECT-LIST) EVENT (PROVE-LEMMA REM-REFLECT-LIST-2 (REWRITE) (IMPLIES (AND (NOT (ZEROP P)) (NOT (ZEROP N)) (LESSP (QUOTIENT P 2.) (REMAINDER (TIMES A N) P)) (EQUAL (REMAINDER (TIMES-LIST (REFLECT-LIST (SUB1 N) A P)) P) (REMAINDER (TIMES (EXP A (SUB1 N)) (FACT (SUB1 N))) P))) (EQUAL (REMAINDER (TIMES-LIST (REFLECT-LIST N A P)) P) (REMAINDER (REFLECT (REMAINDER (TIMES (EXP A N) (FACT N)) P) P) P))) ((USE (REMAINDER-EXP-LEMMA (A P) (X (TIMES A N)) (Y (TIMES-LIST (REFLECT-LIST (SUB1 N) A P))) (Z (TIMES (EXP A (SUB1 N)) (FACT (SUB1 N)))))) (HANDS-OFF TIMES DIFFERENCE QUOTIENT EXP FACT) (DISABLE REMAINDER-EXP-LEMMA REFLECT))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-EXP-FACT . REM-REFLECT-LIST-2) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER-DIVISOR . REM-REFLECT-LIST-2) (IMMEDIATE-DEPENDENTS0 TIMES-MOD-3 . REM-REFLECT-LIST-2) (IMMEDIATE-DEPENDENTS0 REFLECT-COMMUTES-WITH-TIMES-1 . REM-REFLECT-LIST-2) (IMMEDIATE-DEPENDENTS0 REMAINDER-EXP-LEMMA . REM-REFLECT-LIST-2) (IMMEDIATE-DEPENDENTS0 REFLECT . REM-REFLECT-LIST-2) (IMMEDIATE-DEPENDENTS0 FACT . REM-REFLECT-LIST-2) (IMMEDIATE-DEPENDENTS0 EXP . REM-REFLECT-LIST-2) (IMMEDIATE-DEPENDENTS0 REFLECT-LIST . REM-REFLECT-LIST-2) (IMMEDIATE-DEPENDENTS0 TIMES-LIST . REM-REFLECT-LIST-2) (LEMMAS REMAINDER . REM-REFLECT-LIST-2))))) 
(PUT1-LST (QUOTE REM-REFLECT-LIST-1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118023755. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (REM-REFLECT-LIST) EVENT (PROVE-LEMMA REM-REFLECT-LIST-1 (REWRITE) (IMPLIES (AND (NOT (ZEROP P)) (NOT (ZEROP N)) (NOT (LESSP (QUOTIENT P 2.) (REMAINDER (TIMES A N) P))) (EQUAL (REMAINDER (TIMES-LIST (REFLECT-LIST (SUB1 N) A P)) P) (REMAINDER (TIMES (EXP A (SUB1 N)) (FACT (SUB1 N))) P))) (EQUAL (REMAINDER (TIMES-LIST (REFLECT-LIST N A P)) P) (REMAINDER (TIMES (EXP A N) (FACT N)) P))) ((USE (REMAINDER-EXP-LEMMA (A P) (X (TIMES A N)) (Y (TIMES-LIST (REFLECT-LIST (SUB1 N) A P))) (Z (TIMES (EXP A (SUB1 N)) (FACT (SUB1 N)))))) (HANDS-OFF TIMES DIFFERENCE QUOTIENT EXP FACT) (DISABLE REMAINDER-EXP-LEMMA REFLECT))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-EXP-FACT . REM-REFLECT-LIST-1) (IMMEDIATE-DEPENDENTS0 TIMES-MOD-3 . REM-REFLECT-LIST-1) (IMMEDIATE-DEPENDENTS0 REMAINDER-EXP-LEMMA . REM-REFLECT-LIST-1) (IMMEDIATE-DEPENDENTS0 FACT . REM-REFLECT-LIST-1) (IMMEDIATE-DEPENDENTS0 EXP . REM-REFLECT-LIST-1) (IMMEDIATE-DEPENDENTS0 REFLECT-LIST . REM-REFLECT-LIST-1) (IMMEDIATE-DEPENDENTS0 TIMES-LIST . REM-REFLECT-LIST-1) (LEMMAS REMAINDER . REM-REFLECT-LIST-1))))) 
(PUT1-LST (QUOTE TIMES-EXP-FACT) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118023533. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (REM-REFLECT-LIST-4 REM-REFLECT-LIST-3 REM-REFLECT-LIST-2 REM-REFLECT-LIST-1) EVENT (PROVE-LEMMA TIMES-EXP-FACT (REWRITE) (IMPLIES (NOT (ZEROP N)) (EQUAL (REMAINDER (TIMES (TIMES A N) (TIMES (EXP A (SUB1 N)) (FACT (SUB1 N)))) P) (REMAINDER (TIMES (EXP A N) (FACT N)) P)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . TIMES-EXP-FACT) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-TIMES . TIMES-EXP-FACT) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-TIMES . TIMES-EXP-FACT) (IMMEDIATE-DEPENDENTS0 FACT . TIMES-EXP-FACT) (IMMEDIATE-DEPENDENTS0 EXP . TIMES-EXP-FACT) (LEMMAS REMAINDER . TIMES-EXP-FACT))))) 
(PUT1-LST (QUOTE REFLECT-COMMUTES-WITH-TIMES-2) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118023517. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (REM-REFLECT-LIST-4 REM-REFLECT-LIST-3) EVENT (PROVE-LEMMA REFLECT-COMMUTES-WITH-TIMES-2 (REWRITE) (IMPLIES (LEQ Y P) (EQUAL (REMAINDER (TIMES X (REFLECT Y P)) P) (REMAINDER (REFLECT (REMAINDER (TIMES X Y) P) P) P))) ((USE (REFLECT-COMMUTES-WITH-TIMES-1)) (DISABLE REFLECT-COMMUTES-WITH-TIMES-1 REFLECT))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . REFLECT-COMMUTES-WITH-TIMES-2) (IMMEDIATE-DEPENDENTS0 REFLECT-COMMUTES-WITH-TIMES-1 . REFLECT-COMMUTES-WITH-TIMES-2) (IMMEDIATE-DEPENDENTS0 REFLECT . REFLECT-COMMUTES-WITH-TIMES-2) (LEMMAS REMAINDER . REFLECT-COMMUTES-WITH-TIMES-2))))) 
(PUT1-LST (QUOTE REFLECT-COMMUTES-WITH-TIMES-1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118023504. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (REM-REFLECT-LIST-4 REM-REFLECT-LIST-2 REFLECT-COMMUTES-WITH-TIMES-2) EVENT (PROVE-LEMMA REFLECT-COMMUTES-WITH-TIMES-1 (REWRITE) (IMPLIES (LEQ Y P) (EQUAL (REMAINDER (TIMES (REFLECT Y P) X) P) (REMAINDER (REFLECT (REMAINDER (TIMES Y X) P) P) P))) ((USE (DIFF-MOD-1 (A (TIMES P X)) (B (TIMES Y X))) (LESSP-TIMES-CANCELLATION (Z X) (X Y) (Y P)) (REM-DIFF-TIMES (B X) (X (REMAINDER (TIMES Y X) P)))) (DISABLE LESSP-TIMES-CANCELLATION REM-DIFF-TIMES DIFF-MOD-1))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REMAINDER-X-X . REFLECT-COMMUTES-WITH-TIMES-1) (IMMEDIATE-DEPENDENTS0 DIVIDES-TIMES . REFLECT-COMMUTES-WITH-TIMES-1) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER-DIVISOR . REFLECT-COMMUTES-WITH-TIMES-1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . REFLECT-COMMUTES-WITH-TIMES-1) (IMMEDIATE-DEPENDENTS0 EQUAL-LESSP . REFLECT-COMMUTES-WITH-TIMES-1) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . REFLECT-COMMUTES-WITH-TIMES-1) (IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES . REFLECT-COMMUTES-WITH-TIMES-1) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . REFLECT-COMMUTES-WITH-TIMES-1) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO2 . REFLECT-COMMUTES-WITH-TIMES-1) (IMMEDIATE-DEPENDENTS0 REMAINDER-WRT-12 . REFLECT-COMMUTES-WITH-TIMES-1) (IMMEDIATE-DEPENDENTS0 REMAINDER-0-CROCK . REFLECT-COMMUTES-WITH-TIMES-1) (IMMEDIATE-DEPENDENTS0 TIMES-IDENTITY . REFLECT-COMMUTES-WITH-TIMES-1) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . REFLECT-COMMUTES-WITH-TIMES-1) (IMMEDIATE-DEPENDENTS0 TIMES-DIFFERENCE . REFLECT-COMMUTES-WITH-TIMES-1) (IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE-0 . REFLECT-COMMUTES-WITH-TIMES-1) (IMMEDIATE-DEPENDENTS0 DIFF-MOD-1 . REFLECT-COMMUTES-WITH-TIMES-1) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES-CANCELLATION . REFLECT-COMMUTES-WITH-TIMES-1) (IMMEDIATE-DEPENDENTS0 REM-DIFF-TIMES . REFLECT-COMMUTES-WITH-TIMES-1) (IMMEDIATE-DEPENDENTS0 REFLECT . REFLECT-COMMUTES-WITH-TIMES-1) (LEMMAS REMAINDER . REFLECT-COMMUTES-WITH-TIMES-1))))) 
(PUT1-LST (QUOTE REM-DIFF-TIMES) (QUOTE (IDATE 840118021815. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (REFLECT-COMMUTES-WITH-TIMES-1) EVENT (PROVE-LEMMA REM-DIFF-TIMES (REWRITE) (IMPLIES (AND (LESSP X P) (NOT (ZEROP X)) (NOT (ZEROP B))) (EQUAL (REMAINDER (DIFFERENCE (TIMES B P) X) P) (DIFFERENCE P X))) ((USE (REMAINDER-PLUS-TIMES-1 (X (DIFFERENCE P X)) (I (SUB1 B)) (J P))) (DISABLE REMAINDER-PLUS-TIMES-1 REMAINDER-PLUS-TIMES-2))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-ADD1 . REM-DIFF-TIMES) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-PLUS . REM-DIFF-TIMES) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-PLUS . REM-DIFF-TIMES) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-PLUS1 . REM-DIFF-TIMES) (IMMEDIATE-DEPENDENTS0 LESSP-PLUS-CANCELLATION3 . REM-DIFF-TIMES) (IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-TIMES-OVER-PLUS . REM-DIFF-TIMES) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-ELIM . REM-DIFF-TIMES) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . REM-DIFF-TIMES) (IMMEDIATE-DEPENDENTS0 REMAINDER-0-CROCK . REM-DIFF-TIMES) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . REM-DIFF-TIMES) (IMMEDIATE-DEPENDENTS0 REMAINDER-PLUS-TIMES-1 . REM-DIFF-TIMES) (LEMMAS REMAINDER . REM-DIFF-TIMES))))) 
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(PUT1-LST (QUOTE REFLECT-LIST) (QUOTE (TYPE-PRESCRIPTION-LST ((REFLECT-LIST 24. NIL NIL NIL)) LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE UNCHANGING UNCHANGING) SDEFN (LAMBDA (N A P) (IF (EQUAL N (QUOTE 0.)) (QUOTE NIL) (IF (NUMBERP N) (IF (LESSP (QUOTIENT P (QUOTE 2.)) (REMAINDER (TIMES A N) P)) (CONS (REFLECT (REMAINDER (TIMES A N) P) P) (REFLECT-LIST (SUB1 N) A P)) (CONS (REMAINDER (TIMES A N) P) (REFLECT-LIST (SUB1 N) A P))) (QUOTE NIL)))) LISP-CODE 1REFLECT-LIST INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP N)) NIL) (TESTS-AND-CASES ((NOT (ZEROP N)) (LESSP (QUOTIENT P (QUOTE 2.)) (REMAINDER (TIMES A N) P))) (((SUB1 N) A P))) (TESTS-AND-CASES ((NOT (ZEROP N)) (NOT (LESSP (QUOTIENT P (QUOTE 2.)) (REMAINDER (TIMES A N) P)))) (((SUB1 N) A P)))) LEVEL-NO 3. JUSTIFICATIONS ((JUSTIFICATION (N) (COUNT N) LESSP (ZERO ZEROP COUNT-NUMBERP))) IDATE 840118020838. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1REFLECT-LIST) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PLUS-REFLECT-LIST EVEN3-REM-REFLECT TIMES-REFLECT-LIST ALL-DISTINCT-REFLECT-LIST ALL-DISTINCT-REFLECT-LIST-10 ALL-DISTINCT-REFLECT-LIST-9 ALL-NON-ZEROP-REFLECT-LIST ALL-LESSEQP-REFLECT-LIST LENGTH-REFLECT-LIST REM-REFLECT-LIST REM-REFLECT-LIST-BASE-CASE REM-REFLECT-LIST-4 REM-REFLECT-LIST-3 REM-REFLECT-LIST-2 REM-REFLECT-LIST-1) EVENT (DEFN REFLECT-LIST (N A P) (IF (ZEROP N) NIL (IF (LESSP (QUOTIENT P 2.) (REMAINDER (TIMES A N) P)) (CONS (REFLECT (REMAINDER (TIMES A N) P) P) (REFLECT-LIST (SUB1 N) A P)) (CONS (REMAINDER (TIMES A N) P) (REFLECT-LIST (SUB1 N) A P))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REFLECT . REFLECT-LIST) (DCELL . 1REFLECT-LIST))))) 
(PUT1-LST (QUOTE 1REFLECT) (QUOTE NIL)) 
(PUT1-LST (QUOTE REFLECT) (QUOTE (TYPE-PRESCRIPTION-LST ((REFLECT 4. NIL NIL)) LEMMAS NIL LINEAR-LEMMAS ((LINEAR-LEMMA ALL-LESSEQP-REFLECT-LIST-1 ((LESSP (QUOTIENT P (QUOTE 2.)) X)) (NOT (LESSP (QUOTIENT P (QUOTE 2.)) (REFLECT X P))) (REFLECT X P))) QUICK-BLOCK-INFO NIL SDEFN (LAMBDA (X P) (DIFFERENCE P X)) LISP-CODE 1REFLECT INDUCTION-MACHINE NIL LEVEL-NO 1. JUSTIFICATIONS NIL IDATE 840118020836. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS NIL SATELLITES (1REFLECT) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EVEN3-REM-REFLECT RES1-REM-2 RES1-REM-1 ALL-DISTINCT-REFLECT-LIST-10 ALL-DISTINCT-REFLECT-LIST-8 ALL-DISTINCT-REFLECT-LIST-7 ALL-DISTINCT-REFLECT-LIST-3 ALL-NON-ZEROP-REFLECT-LIST ALL-LESSEQP-REFLECT-LIST-1 LENGTH-REFLECT-LIST REM-REFLECT-LIST REM-REFLECT-LIST-4 DOUBLE-REFLECT REM-REFLECT-LIST-3 REM-REFLECT-LIST-2 REFLECT-COMMUTES-WITH-TIMES-2 REFLECT-COMMUTES-WITH-TIMES-1 REFLECT-LIST) EVENT (DEFN REFLECT (X P) (DIFFERENCE P X)) LOCAL-UNDO-TUPLES ((DCELL . 1REFLECT))))) 
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(PUT1-LST (QUOTE EULER-2) (QUOTE (IDATE 840118020819. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (GAUSS-LEMMA) EVENT (PROVE-LEMMA EULER-2 (REWRITE) (IMPLIES (AND (PRIME P) (NOT (DIVIDES 2. P)) (NOT (DIVIDES P A)) (NOT (RESIDUE A P))) (EQUAL (REMAINDER (EXP A (QUOTIENT P 2.)) P) (SUB1 P))) ((USE (EULER-2-1)) (DISABLE EULER-2-1 PRIME DIVIDES RESIDUE EXP QUOTIENT LENGTH COMP-LIST))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EULER-2-2 . EULER-2) (IMMEDIATE-DEPENDENTS0 EULER-2-4 . EULER-2) (IMMEDIATE-DEPENDENTS0 EULER-2-1 . EULER-2) (IMMEDIATE-DEPENDENTS0 EXP . EULER-2) (IMMEDIATE-DEPENDENTS0 RESIDUE . EULER-2) (IMMEDIATE-DEPENDENTS0 DIVIDES . EULER-2) (IMMEDIATE-DEPENDENTS0 PRIME . EULER-2) (LEMMAS REMAINDER . EULER-2))))) 
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(PUT1-LST (QUOTE EULER-2-2) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118020431. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EULER-2) EVENT (PROVE-LEMMA EULER-2-2 (REWRITE) (IMPLIES (AND (PRIME P) (NOT (DIVIDES P A)) (NOT (RESIDUE A P))) (EQUAL (LENGTH (COMP-LIST (SUB1 P) A P)) (SUB1 P))) ((USE (EQUAL-LENGTH-PERM (A (POSITIVES (SUB1 P))) (B (COMP-LIST (SUB1 P) A P))) (PERM-POSITIVES-COMP-LIST)) (DISABLE EQUAL-LENGTH-PERM PERM-POSITIVES-COMP-LIST))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SUBSETP-POSITIVES-COMP-LIST . EULER-2-2) (IMMEDIATE-DEPENDENTS0 BOUNDED-COMP-LIST . EULER-2-2) (IMMEDIATE-DEPENDENTS0 ALL-NON-ZEROP-COMP-LIST . EULER-2-2) (IMMEDIATE-DEPENDENTS0 ALL-DISTINCT-COMP-LIST . EULER-2-2) (IMMEDIATE-DEPENDENTS0 PIGEONHOLE2 . EULER-2-2) (IMMEDIATE-DEPENDENTS0 LENGTH-POSITIVES . EULER-2-2) (IMMEDIATE-DEPENDENTS0 EQUAL-LENGTH-PERM . EULER-2-2) (IMMEDIATE-DEPENDENTS0 PERM-POSITIVES-COMP-LIST . EULER-2-2) (IMMEDIATE-DEPENDENTS0 COMP-LIST . EULER-2-2) (IMMEDIATE-DEPENDENTS0 RESIDUE . EULER-2-2) (IMMEDIATE-DEPENDENTS0 DIVIDES . EULER-2-2) (IMMEDIATE-DEPENDENTS0 PRIME . EULER-2-2) (LEMMAS LENGTH . EULER-2-2))))) 
(PUT1-LST (QUOTE EULER-2-1) (QUOTE (IDATE 840118020401. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EULER-2) EVENT (PROVE-LEMMA EULER-2-1 NIL (IMPLIES (AND (PRIME P) (NOT (DIVIDES P A)) (NOT (RESIDUE A P))) (EQUAL (REMAINDER (EXP A (QUOTIENT (LENGTH (COMP-LIST (SUB1 P) A P)) 2.)) P) (SUB1 P))) ((USE (TIMES-COMP-LIST (I (SUB1 P))) (COMP-LIST-FACT) (WILSON-THM)) (DISABLE TIMES-COMP-LIST COMP-LIST-FACT))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-COMP-LIST . EULER-2-1) (IMMEDIATE-DEPENDENTS0 COMP-LIST-FACT . EULER-2-1) (IMMEDIATE-DEPENDENTS0 WILSON-THM . EULER-2-1) (IMMEDIATE-DEPENDENTS0 COMP-LIST . EULER-2-1) (IMMEDIATE-DEPENDENTS0 EXP . EULER-2-1) (IMMEDIATE-DEPENDENTS0 RESIDUE . EULER-2-1) (IMMEDIATE-DEPENDENTS0 DIVIDES . EULER-2-1) (IMMEDIATE-DEPENDENTS0 PRIME . EULER-2-1))))) 
(PUT1-LST (QUOTE LENGTH-POSITIVES) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118015613. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EULER-2-2) EVENT (PROVE-LEMMA LENGTH-POSITIVES (REWRITE) (EQUAL (LENGTH (POSITIVES N)) (FIX N)) ((INDUCT (POSITIVES N)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 POSITIVES . LENGTH-POSITIVES) (LEMMAS LENGTH . LENGTH-POSITIVES))))) 
(PUT1-LST (QUOTE EQUAL-LENGTH-PERM) (QUOTE (IDATE 840118015608. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EULER-2-2) EVENT (PROVE-LEMMA EQUAL-LENGTH-PERM NIL (IMPLIES (PERM A B) (EQUAL (LENGTH A) (LENGTH B))) ((INDUCT (PERM A B)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQUAL-LENGTH-0 . EQUAL-LENGTH-PERM) (IMMEDIATE-DEPENDENTS0 PERM-MEMBER . EQUAL-LENGTH-PERM) (IMMEDIATE-DEPENDENTS0 SUB1-LENGTH-DELETE . EQUAL-LENGTH-PERM) (IMMEDIATE-DEPENDENTS0 PERM . EQUAL-LENGTH-PERM))))) 
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(PUT1-LST (QUOTE TIMES-COMP-LIST) (QUOTE (IDATE 840118015550. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EULER-2-1) EVENT (PROVE-LEMMA TIMES-COMP-LIST (REWRITE) (IMPLIES (AND (PRIME P) (LESSP I P)) (EQUAL (REMAINDER (TIMES-LIST (COMP-LIST I A P)) P) (REMAINDER (EXP A (QUOTIENT (LENGTH (COMP-LIST I A P)) 2.)) P))) ((USE (TIMES-COMP-LIST-4) (TIMES-COMP-LIST-5)) (INDUCT (POSITIVES I)) (DISABLE PRIME REMAINDER TIMES-LIST COMP-LIST QUOTIENT LENGTH))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 POSITIVES . TIMES-COMP-LIST) (IMMEDIATE-DEPENDENTS0 TIMES-COMP-LIST-4 . TIMES-COMP-LIST) (IMMEDIATE-DEPENDENTS0 TIMES-COMP-LIST-5 . TIMES-COMP-LIST) (IMMEDIATE-DEPENDENTS0 EXP . TIMES-COMP-LIST) (IMMEDIATE-DEPENDENTS0 COMP-LIST . TIMES-COMP-LIST) (IMMEDIATE-DEPENDENTS0 TIMES-LIST . TIMES-COMP-LIST) (IMMEDIATE-DEPENDENTS0 PRIME . TIMES-COMP-LIST) (LEMMAS REMAINDER . TIMES-COMP-LIST))))) 
(PUT1-LST (QUOTE TIMES-COMP-LIST-5) (QUOTE (IDATE 840118015511. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (TIMES-COMP-LIST) EVENT (PROVE-LEMMA TIMES-COMP-LIST-5 NIL (IMPLIES (ZEROP I) (EQUAL (REMAINDER (TIMES-LIST (COMP-LIST I A P)) P) (REMAINDER (EXP A (QUOTIENT (LENGTH (COMP-LIST I A P)) 2.)) P)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REMAINDER-OF-1 . TIMES-COMP-LIST-5) (IMMEDIATE-DEPENDENTS0 EXP-BY-0 . TIMES-COMP-LIST-5) (IMMEDIATE-DEPENDENTS0 EXP . TIMES-COMP-LIST-5) (IMMEDIATE-DEPENDENTS0 COMP-LIST . TIMES-COMP-LIST-5) (IMMEDIATE-DEPENDENTS0 TIMES-LIST . TIMES-COMP-LIST-5))))) 
(PUT1-LST (QUOTE TIMES-COMP-LIST-4) (QUOTE (IDATE 840118015503. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (TIMES-COMP-LIST) EVENT (PROVE-LEMMA TIMES-COMP-LIST-4 NIL (IMPLIES (AND (PRIME P) (NOT (ZEROP I)) (LESSP I P) (EQUAL (REMAINDER (TIMES-LIST (COMP-LIST (SUB1 I) A P)) P) (REMAINDER (EXP A (QUOTIENT (LENGTH (COMP-LIST (SUB1 I) A P)) 2.)) P))) (EQUAL (REMAINDER (TIMES-LIST (COMP-LIST I A P)) P) (REMAINDER (EXP A (QUOTIENT (LENGTH (COMP-LIST I A P)) 2.)) P))) ((USE (TIMES-COMP-LIST-2) (TIMES-COMP-LIST-3) (TIMES-MOD-1 (X A) (Y (EXP A (QUOTIENT (LENGTH (COMP-LIST (SUB1 I) A P)) 2.))) (N P))) (DISABLE PRIME TIMES-MOD-1 TIMES-LIST))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIFFERENCE-2 . TIMES-COMP-LIST-4) (IMMEDIATE-DEPENDENTS0 EQUAL-MODS-TRICK-2 . TIMES-COMP-LIST-4) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . TIMES-COMP-LIST-4) (IMMEDIATE-DEPENDENTS0 REMAINDER-EXP-LEMMA . TIMES-COMP-LIST-4) (IMMEDIATE-DEPENDENTS0 EQUAL-MODS-TRICK-1 . TIMES-COMP-LIST-4) (IMMEDIATE-DEPENDENTS0 DIVIDES . TIMES-COMP-LIST-4) (IMMEDIATE-DEPENDENTS0 TIMES-COMP-LIST-2 . TIMES-COMP-LIST-4) (IMMEDIATE-DEPENDENTS0 TIMES-COMP-LIST-3 . TIMES-COMP-LIST-4) (IMMEDIATE-DEPENDENTS0 TIMES-MOD-1 . TIMES-COMP-LIST-4) (IMMEDIATE-DEPENDENTS0 EXP . TIMES-COMP-LIST-4) (IMMEDIATE-DEPENDENTS0 COMP-LIST . TIMES-COMP-LIST-4) (IMMEDIATE-DEPENDENTS0 TIMES-LIST . TIMES-COMP-LIST-4) (IMMEDIATE-DEPENDENTS0 PRIME . TIMES-COMP-LIST-4))))) 
(PUT1-LST (QUOTE TIMES-COMP-LIST-3) (QUOTE (IDATE 840118014505. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (TIMES-COMP-LIST-4) EVENT (PROVE-LEMMA TIMES-COMP-LIST-3 NIL (IMPLIES (AND (NOT (ZEROP I)) (NOT (MEMBER I (COMP-LIST (SUB1 I) A P)))) (EQUAL (QUOTIENT (LENGTH (COMP-LIST I A P)) 2.) (ADD1 (QUOTIENT (LENGTH (COMP-LIST (SUB1 I) A P)) 2.)))) ((USE (QUOTIENT-PLUS-1 (X (LENGTH (COMP-LIST (SUB1 I) A P))) (Y (LENGTH (COMP-LIST I A P))) (N 2.))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . TIMES-COMP-LIST-3) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-2 . TIMES-COMP-LIST-3) (IMMEDIATE-DEPENDENTS0 QUOTIENT-PLUS-1 . TIMES-COMP-LIST-3) (IMMEDIATE-DEPENDENTS0 COMP-LIST . TIMES-COMP-LIST-3))))) 
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(PUT1-LST (QUOTE TIMES-COMP-LIST-1) (QUOTE (IDATE 840118014323. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (TIMES-COMP-LIST-2) EVENT (PROVE-LEMMA TIMES-COMP-LIST-1 NIL (IMPLIES (AND (EQUAL (REMAINDER (TIMES I (COMPLEMENT I A P)) P) (REMAINDER A P)) (NOT (ZEROP I)) (NOT (MEMBER I (COMP-LIST (SUB1 I) A P)))) (EQUAL (REMAINDER (TIMES-LIST (COMP-LIST I A P)) P) (REMAINDER (TIMES A (REMAINDER (TIMES-LIST (COMP-LIST (SUB1 I) A P)) P)) P))) ((USE (TIMES-MOD-4 (J (COMPLEMENT I A P)) (K (TIMES-LIST (COMP-LIST (SUB1 I) A P))))) (DISABLE COMPLEMENT-WORKS))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-MOD-1 . TIMES-COMP-LIST-1) (IMMEDIATE-DEPENDENTS0 TIMES-MOD-4 . TIMES-COMP-LIST-1) (IMMEDIATE-DEPENDENTS0 TIMES-LIST . TIMES-COMP-LIST-1) (IMMEDIATE-DEPENDENTS0 COMP-LIST . TIMES-COMP-LIST-1) (IMMEDIATE-DEPENDENTS0 COMPLEMENT . TIMES-COMP-LIST-1))))) 
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(PUT1-LST (QUOTE PERM-POSITIVES-COMP-LIST) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118014047. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EULER-2-2 COMP-LIST-FACT) EVENT (PROVE-LEMMA PERM-POSITIVES-COMP-LIST (REWRITE) (IMPLIES (AND (PRIME P) (NOT (DIVIDES P A)) (NOT (RESIDUE A P))) (PERM (POSITIVES (SUB1 P)) (COMP-LIST (SUB1 P) A P)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SUBSETP-POSITIVES-COMP-LIST . PERM-POSITIVES-COMP-LIST) (IMMEDIATE-DEPENDENTS0 BOUNDED-COMP-LIST . PERM-POSITIVES-COMP-LIST) (IMMEDIATE-DEPENDENTS0 ALL-NON-ZEROP-COMP-LIST . PERM-POSITIVES-COMP-LIST) (IMMEDIATE-DEPENDENTS0 ALL-DISTINCT-COMP-LIST . PERM-POSITIVES-COMP-LIST) (IMMEDIATE-DEPENDENTS0 PIGEONHOLE2 . PERM-POSITIVES-COMP-LIST) (IMMEDIATE-DEPENDENTS0 COMP-LIST . PERM-POSITIVES-COMP-LIST) (IMMEDIATE-DEPENDENTS0 POSITIVES . PERM-POSITIVES-COMP-LIST) (IMMEDIATE-DEPENDENTS0 PERM . PERM-POSITIVES-COMP-LIST) (IMMEDIATE-DEPENDENTS0 RESIDUE . PERM-POSITIVES-COMP-LIST) (IMMEDIATE-DEPENDENTS0 DIVIDES . PERM-POSITIVES-COMP-LIST) (IMMEDIATE-DEPENDENTS0 PRIME . PERM-POSITIVES-COMP-LIST) (LEMMAS PERM . PERM-POSITIVES-COMP-LIST))))) 
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(PUT1-LST (QUOTE COMPLEMENT-OFF) (QUOTE (IDATE 840118003235. EVENT (TOGGLE COMPLEMENT-OFF COMPLEMENT T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMPLEMENT . COMPLEMENT-OFF) (DISABLED-LEMMAS NIL COMPLEMENT COMPLEMENT-OFF . T))))) 
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(PUT1-LST (QUOTE G0219) (QUOTE (IDATE 840118002722. EVENT (TOGGLE G0219 INVERSE T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 INVERSE . G0219) (DISABLED-LEMMAS NIL INVERSE G0219 . T))))) 
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(PUT1-LST (QUOTE EULER-1-7) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840118002655. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EULER-1) EVENT (PROVE-LEMMA EULER-1-7 (REWRITE) (IMPLIES (AND (PRIME P) (NOT (DIVIDES 2. P)) (NOT (DIVIDES P A)) (MEMBER (REMAINDER A P) (SQUARES I P))) (EQUAL (REMAINDER (EXP A (QUOTIENT P 2.)) P) 1.)) ((USE (EULER-1-6)) (INDUCT (SQUARES I P)) (DISABLE PRIME REMAINDER LESSP-REMAINDER-DIVISOR))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-ZERO2 . EULER-1-7) (IMMEDIATE-DEPENDENTS0 REMAINDER-0-CROCK . EULER-1-7) (IMMEDIATE-DEPENDENTS0 EULER-1-6 . EULER-1-7) (IMMEDIATE-DEPENDENTS0 EXP . EULER-1-7) (IMMEDIATE-DEPENDENTS0 SQUARES . EULER-1-7) (IMMEDIATE-DEPENDENTS0 DIVIDES . EULER-1-7) (IMMEDIATE-DEPENDENTS0 PRIME . EULER-1-7) (LEMMAS REMAINDER . EULER-1-7))))) 
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(PUT1-LST (QUOTE EULER-1-4) (QUOTE (IDATE 840118002452. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EULER-1-6) EVENT (PROVE-LEMMA EULER-1-4 NIL (IMPLIES (AND (PRIME P) (NOT (DIVIDES 2. P)) (NOT (DIVIDES P I))) (EQUAL (REMAINDER (EXP (TIMES I I) (QUOTIENT P 2.)) P) 1.)) ((USE (EULER-1-2)) (DISABLE LESSP-REMAINDER-DIVISOR PRIME))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EXP-TIMES . EULER-1-4) (IMMEDIATE-DEPENDENTS0 FERMAT-THM . EULER-1-4) (IMMEDIATE-DEPENDENTS0 EULER-1-2 . EULER-1-4) (IMMEDIATE-DEPENDENTS0 EXP . EULER-1-4) (IMMEDIATE-DEPENDENTS0 DIVIDES . EULER-1-4) (IMMEDIATE-DEPENDENTS0 PRIME . EULER-1-4))))) 
(PUT1-LST (QUOTE EULER-1-3) (QUOTE (IDATE 840118002431. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EULER-1-6) EVENT (PROVE-LEMMA EULER-1-3 NIL (IMPLIES (EQUAL (REMAINDER A P) (REMAINDER B P)) (EQUAL (REMAINDER (EXP A C) P) (REMAINDER (EXP B C) P))) ((USE (REMAINDER-EXP (I C) (N P)) (REMAINDER-EXP (A B) (I C) (N P))) (DISABLE REMAINDER-EXP))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REMAINDER-EXP . EULER-1-3) (IMMEDIATE-DEPENDENTS0 EXP . EULER-1-3))))) 
(PUT1-LST (QUOTE EULER-1-2) (QUOTE (IDATE 840118002357. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EULER-1-4) EVENT (PROVE-LEMMA EULER-1-2 NIL (IMPLIES (NOT (DIVIDES 2. P)) (EQUAL (EXP (TIMES I I) (QUOTIENT P 2.)) (EXP I (SUB1 P)))) ((USE (EXP-EXP (J 2.) (K (QUOTIENT P 2.))) (EULER-1-1)) (DISABLE EXP-EXP))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . EULER-1-2) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . EULER-1-2) (IMMEDIATE-DEPENDENTS0 TIMES-2 . EULER-1-2) (IMMEDIATE-DEPENDENTS0 EXP-PLUS . EULER-1-2) (IMMEDIATE-DEPENDENTS0 EXP-TIMES . EULER-1-2) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER-DIVISOR . EULER-1-2) (IMMEDIATE-DEPENDENTS0 EXP-EXP . EULER-1-2) (IMMEDIATE-DEPENDENTS0 EULER-1-1 . EULER-1-2) (IMMEDIATE-DEPENDENTS0 EXP . EULER-1-2) (IMMEDIATE-DEPENDENTS0 DIVIDES . EULER-1-2))))) 
(PUT1-LST (QUOTE EULER-1-1) (QUOTE (IDATE 840118002321. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EULER-1-2) EVENT (PROVE-LEMMA EULER-1-1 NIL (IMPLIES (NOT (DIVIDES 2. P)) (EQUAL (TIMES 2. (QUOTIENT P 2.)) (SUB1 P)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . EULER-1-1) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . EULER-1-1) (IMMEDIATE-DEPENDENTS0 TIMES-2 . EULER-1-1) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER-DIVISOR . EULER-1-1) (IMMEDIATE-DEPENDENTS0 DIVIDES . EULER-1-1))))) 
(PUT1-LST (QUOTE ALL-SQUARES) (QUOTE (IDATE 840118002256. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (NO-SELF-COMPLEMENT) EVENT (PROVE-LEMMA ALL-SQUARES (REWRITE) (IMPLIES (AND (NOT (ZEROP P)) (NOT (MEMBER X (SQUARES P P)))) (NOT (EQUAL X (REMAINDER (TIMES Y Y) P)))) ((USE (ALL-SQUARES-1 (N P) (M (REMAINDER Y P))) (ALL-SQUARES-2)) (DISABLE TIMES-MOD-1 TIMES-MOD-3))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER-DIVISOR . ALL-SQUARES) (IMMEDIATE-DEPENDENTS0 ALL-SQUARES-1 . ALL-SQUARES) (IMMEDIATE-DEPENDENTS0 ALL-SQUARES-2 . ALL-SQUARES) (IMMEDIATE-DEPENDENTS0 SQUARES . ALL-SQUARES) (LEMMAS EQUAL . ALL-SQUARES))))) 
(PUT1-LST (QUOTE ALL-SQUARES-2) (QUOTE (IDATE 840118002119. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (ALL-SQUARES) EVENT (PROVE-LEMMA ALL-SQUARES-2 NIL (EQUAL (REMAINDER (TIMES Y Y) P) (REMAINDER (TIMES (REMAINDER Y P) (REMAINDER Y P)) P)) ((USE (TIMES-MOD-1 (X Y) (N P)) (TIMES-MOD-3 (B (REMAINDER Y P)) (A Y) (N P))) (DISABLE TIMES-MOD-1 TIMES-MOD-3))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-MOD-1 . ALL-SQUARES-2) (IMMEDIATE-DEPENDENTS0 TIMES-MOD-3 . ALL-SQUARES-2))))) 
(PUT1-LST (QUOTE ALL-SQUARES-1) (QUOTE (IDATE 840118002111. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (ALL-SQUARES) EVENT (PROVE-LEMMA ALL-SQUARES-1 NIL (IMPLIES (AND (NOT (ZEROP P)) (LEQ M N)) (MEMBER (REMAINDER (TIMES M M) P) (SQUARES N P)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REMAINDER-OF-1 . ALL-SQUARES-1) (IMMEDIATE-DEPENDENTS0 TIMES-ADD1 . ALL-SQUARES-1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . ALL-SQUARES-1) (IMMEDIATE-DEPENDENTS0 PLUS-ADD1 . ALL-SQUARES-1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-PLUS . ALL-SQUARES-1) (IMMEDIATE-DEPENDENTS0 REMAINDER-0-CROCK . ALL-SQUARES-1) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO2 . ALL-SQUARES-1) (IMMEDIATE-DEPENDENTS0 SQUARES . ALL-SQUARES-1))))) 
(PUT1-LST (QUOTE 1RESIDUE) (QUOTE NIL)) 
(PUT1-LST (QUOTE RESIDUE) (QUOTE (TYPE-PRESCRIPTION-LST ((RESIDUE 3. NIL NIL)) LEMMAS NIL SDEFN (LAMBDA (A P) (IF (DIVIDES P A) (QUOTE 1FALSE) (MEMBER (REMAINDER A P) (SQUARES P P)))) LISP-CODE 1RESIDUE INDUCTION-MACHINE NIL LEVEL-NO 3. JUSTIFICATIONS NIL IDATE 840118001901. CONTROLLER-POCKETS NIL SATELLITES (1RESIDUE) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LAW-OF-QUADRATIC-RECIPROCITY RESIDUE-QUOT-LIST GAUSS-COROLLARY GAUSS-LEMMA EULER-2 EULER-2-2 EULER-2-1 COMP-LIST-FACT PERM-POSITIVES-COMP-LIST ALL-DISTINCT-COMP-LIST ALL-DISTINCT-COMP-LIST-1 NO-SELF-COMPLEMENT EULER-1) EVENT (DEFN RESIDUE (A P) (AND (NOT (DIVIDES P A)) (MEMBER (REMAINDER A P) (SQUARES P P)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SQUARES . RESIDUE) (IMMEDIATE-DEPENDENTS0 DIVIDES . RESIDUE) (DCELL . 1RESIDUE))))) 
(PUT1-LST (QUOTE 1SQUARES) (QUOTE NIL)) 
(PUT1-LST (QUOTE SQUARES) (QUOTE (TYPE-PRESCRIPTION-LST ((SQUARES 16. NIL NIL)) LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE UNCHANGING) SDEFN (LAMBDA (N P) (IF (EQUAL N (QUOTE 0.)) (QUOTE (0.)) (IF (NUMBERP N) (CONS (REMAINDER (TIMES N N) P) (SQUARES (SUB1 N) P)) (QUOTE (0.))))) LISP-CODE 1SQUARES INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP N)) NIL) (TESTS-AND-CASES ((NOT (ZEROP N))) (((SUB1 N) P)))) LEVEL-NO 3. JUSTIFICATIONS ((JUSTIFICATION (N) (COUNT N) LESSP (ZERO ZEROP COUNT-NUMBERP))) IDATE 840118001843. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1SQUARES) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (SQUARES-OFF EULER-1-7 ALL-SQUARES ALL-SQUARES-1 RESIDUE) EVENT (DEFN SQUARES (N P) (IF (ZEROP N) (LIST 0.) (CONS (REMAINDER (TIMES N N) P) (SQUARES (SUB1 N) P)))) LOCAL-UNDO-TUPLES ((DCELL . 1SQUARES))))) 
(PUT1-LST (QUOTE WILSON-THM) (QUOTE (IDATE 840118000127. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EULER-2-1) EVENT (PROVE-LEMMA WILSON-THM NIL (IMPLIES (PRIME P) (EQUAL (REMAINDER (FACT (SUB1 P)) P) (SUB1 P))) ((USE (W-T-LEMMA (I (SUB1 (SUB1 P)))) (THM-55-SPECIALIZED-TO-PRIMES (M (SUB1 P)) (X (FACT (SUB1 (SUB1 P)))) (Y 1.))) (DISABLE W-T-LEMMA THM-55-SPECIALIZED-TO-PRIMES))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PRIME1 . WILSON-THM) (IMMEDIATE-DEPENDENTS0 DIVIDES . WILSON-THM) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-1 . WILSON-THM) (IMMEDIATE-DEPENDENTS0 REMAINDER-0-CROCK . WILSON-THM) (IMMEDIATE-DEPENDENTS0 REMAINDER-OF-1 . WILSON-THM) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . WILSON-THM) (IMMEDIATE-DEPENDENTS0 TIMES-1 . WILSON-THM) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . WILSON-THM) (IMMEDIATE-DEPENDENTS0 INVERSE-1 . WILSON-THM) (IMMEDIATE-DEPENDENTS0 B-I-LEMMA2 . WILSON-THM) (IMMEDIATE-DEPENDENTS0 W-T-LEMMA . WILSON-THM) (IMMEDIATE-DEPENDENTS0 THM-55-SPECIALIZED-TO-PRIMES . WILSON-THM) (IMMEDIATE-DEPENDENTS0 FACT . WILSON-THM) (IMMEDIATE-DEPENDENTS0 PRIME . WILSON-THM))))) 
(PUT1-LST (QUOTE W-T-LEMMA) (QUOTE (IDATE 840117235613. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (WILSON-THM) EVENT (PROVE-LEMMA W-T-LEMMA (REWRITE) (IMPLIES (AND (PRIME P) (EQUAL I (DIFFERENCE P 2.))) (EQUAL (REMAINDER (FACT I) P) 1.)) ((USE (TIMES-INVERSE-LIST)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIFFERENCE-1 . W-T-LEMMA) (IMMEDIATE-DEPENDENTS0 INVERSE-LIST-FACT . W-T-LEMMA) (IMMEDIATE-DEPENDENTS0 TIMES-INVERSE-LIST . W-T-LEMMA) (IMMEDIATE-DEPENDENTS0 FACT . W-T-LEMMA) (IMMEDIATE-DEPENDENTS0 PRIME . W-T-LEMMA) (LEMMAS REMAINDER . W-T-LEMMA))))) 
(PUT1-LST (QUOTE INVERSE-LIST-FACT) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117235351. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (W-T-LEMMA) EVENT (PROVE-LEMMA INVERSE-LIST-FACT (REWRITE) (IMPLIES (AND (PRIME P) (EQUAL I (DIFFERENCE P 2.))) (EQUAL (TIMES-LIST (INVERSE-LIST I P)) (FACT I))) ((USE (TIMES-LIST-EQUAL-FACT (N I) (L (INVERSE-LIST I P)))) (DISABLE INVERSE-LIST))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIFFERENCE-1 . INVERSE-LIST-FACT) (IMMEDIATE-DEPENDENTS0 PERM-POSITIVES-INVERSE-LIST . INVERSE-LIST-FACT) (IMMEDIATE-DEPENDENTS0 TIMES-LIST-EQUAL-FACT . INVERSE-LIST-FACT) (IMMEDIATE-DEPENDENTS0 FACT . INVERSE-LIST-FACT) (IMMEDIATE-DEPENDENTS0 INVERSE-LIST . INVERSE-LIST-FACT) (IMMEDIATE-DEPENDENTS0 TIMES-LIST . INVERSE-LIST-FACT) (IMMEDIATE-DEPENDENTS0 PRIME . INVERSE-LIST-FACT) (LEMMAS TIMES-LIST . INVERSE-LIST-FACT))))) 
(PUT1-LST (QUOTE PERM-POSITIVES-INVERSE-LIST) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117235342. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (INVERSE-LIST-FACT) EVENT (PROVE-LEMMA PERM-POSITIVES-INVERSE-LIST (REWRITE) (IMPLIES (AND (PRIME P) (EQUAL I (DIFFERENCE P 2.))) (PERM (POSITIVES I) (INVERSE-LIST I P)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIFFERENCE-1 . PERM-POSITIVES-INVERSE-LIST) (IMMEDIATE-DEPENDENTS0 SUBSETP-POSITIVES . PERM-POSITIVES-INVERSE-LIST) (IMMEDIATE-DEPENDENTS0 BOUNDED-INVERSE-LIST . PERM-POSITIVES-INVERSE-LIST) (IMMEDIATE-DEPENDENTS0 ALL-NON-ZEROP-INVERSE-LIST . PERM-POSITIVES-INVERSE-LIST) (IMMEDIATE-DEPENDENTS0 ALL-DISTINCT-INVERSE-LIST . PERM-POSITIVES-INVERSE-LIST) (IMMEDIATE-DEPENDENTS0 PIGEONHOLE2 . PERM-POSITIVES-INVERSE-LIST) (IMMEDIATE-DEPENDENTS0 INVERSE-LIST . PERM-POSITIVES-INVERSE-LIST) (IMMEDIATE-DEPENDENTS0 POSITIVES . PERM-POSITIVES-INVERSE-LIST) (IMMEDIATE-DEPENDENTS0 PERM . PERM-POSITIVES-INVERSE-LIST) (IMMEDIATE-DEPENDENTS0 PRIME . PERM-POSITIVES-INVERSE-LIST) (LEMMAS PERM . PERM-POSITIVES-INVERSE-LIST))))) 
(PUT1-LST (QUOTE PIGEONHOLE2) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117235330. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EULER-2-2 PERM-POSITIVES-COMP-LIST PERM-POSITIVES-INVERSE-LIST) EVENT (PROVE-LEMMA PIGEONHOLE2 (REWRITE) (IMPLIES (AND (ALL-DISTINCT L) (ALL-NON-ZEROP L) (ALL-LESSEQP L N) (SUBSETP (POSITIVES N) L)) (PERM (POSITIVES N) L)) ((INDUCT (PIGEONHOLE2-INDUCTION L N)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ALL-DISTINCT-DELETE . PIGEONHOLE2) (IMMEDIATE-DEPENDENTS0 ALL-NON-ZEROP-DELETE . PIGEONHOLE2) (IMMEDIATE-DEPENDENTS0 ALL-LESSEQP-DELETE . PIGEONHOLE2) (IMMEDIATE-DEPENDENTS0 SUBSETP-POSITIVES-DELETE . PIGEONHOLE2) (IMMEDIATE-DEPENDENTS0 PIGEONHOLE2-INDUCTION . PIGEONHOLE2) (IMMEDIATE-DEPENDENTS0 PERM . PIGEONHOLE2) (IMMEDIATE-DEPENDENTS0 POSITIVES . PIGEONHOLE2) (IMMEDIATE-DEPENDENTS0 ALL-LESSEQP . PIGEONHOLE2) (IMMEDIATE-DEPENDENTS0 ALL-NON-ZEROP . PIGEONHOLE2) (IMMEDIATE-DEPENDENTS0 ALL-DISTINCT . PIGEONHOLE2) (LEMMAS PERM . PIGEONHOLE2))))) 
(PUT1-LST (QUOTE 1PIGEONHOLE2-INDUCTION) (QUOTE NIL)) 
(PUT1-LST (QUOTE PIGEONHOLE2-INDUCTION) (QUOTE (TYPE-PRESCRIPTION-LST ((PIGEONHOLE2-INDUCTION 2. NIL NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE SELF-REFLEXIVE) SDEFN (LAMBDA (L N) (IF (EQUAL N (QUOTE 0.)) (QUOTE 1TRUE) (IF (NUMBERP N) (PIGEONHOLE2-INDUCTION (DELETE N L) (SUB1 N)) (QUOTE 1TRUE)))) LISP-CODE 1PIGEONHOLE2-INDUCTION INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP N)) NIL) (TESTS-AND-CASES ((NOT (ZEROP N))) (((DELETE N L) (SUB1 N))))) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (N) (COUNT N) LESSP (ZERO ZEROP COUNT-NUMBERP))) IDATE 840117235314. CONTROLLER-POCKETS (2.) SATELLITES (1PIGEONHOLE2-INDUCTION) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PIGEONHOLE2) EVENT (DEFN PIGEONHOLE2-INDUCTION (L N) (IF (ZEROP N) T (PIGEONHOLE2-INDUCTION (DELETE N L) (SUB1 N)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DELETE . PIGEONHOLE2-INDUCTION) (DCELL . 1PIGEONHOLE2-INDUCTION))))) 
(PUT1-LST (QUOTE NONZEROP-LESSEQP-ZERO) (QUOTE (IDATE 840117235314. EVENT (PROVE-LEMMA NONZEROP-LESSEQP-ZERO (REWRITE) (IMPLIES (AND (ZEROP N) (ALL-LESSEQP L N) (ALL-NON-ZEROP L)) (NOT (LISTP L)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ALL-NON-ZEROP . NONZEROP-LESSEQP-ZERO) (IMMEDIATE-DEPENDENTS0 ALL-LESSEQP . NONZEROP-LESSEQP-ZERO) (LEMMAS LISTP . NONZEROP-LESSEQP-ZERO))))) 
(PUT1-LST (QUOTE SUBSETP-POSITIVES-DELETE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117235305. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PIGEONHOLE2) EVENT (PROVE-LEMMA SUBSETP-POSITIVES-DELETE (REWRITE) (IMPLIES (SUBSETP (POSITIVES N) L) (SUBSETP (POSITIVES (SUB1 N)) (DELETE N L)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 POSITIVES-BOUNDED . SUBSETP-POSITIVES-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE-MEMBER-LEAVE-SUBSET . SUBSETP-POSITIVES-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE . SUBSETP-POSITIVES-DELETE) (IMMEDIATE-DEPENDENTS0 POSITIVES . SUBSETP-POSITIVES-DELETE) (LEMMAS SUBSETP . SUBSETP-POSITIVES-DELETE))))) 
(PUT1-LST (QUOTE POSITIVES-BOUNDED) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117235301. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (SUBSETP-POSITIVES-DELETE) EVENT (PROVE-LEMMA POSITIVES-BOUNDED (REWRITE) (IMPLIES (LESSP N M) (NOT (MEMBER M (POSITIVES N))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 MEMBER-POSITIVES . POSITIVES-BOUNDED) (IMMEDIATE-DEPENDENTS0 POSITIVES . POSITIVES-BOUNDED) (LEMMAS MEMBER . POSITIVES-BOUNDED))))) 
(PUT1-LST (QUOTE ALL-LESSEQP-DELETE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117235300. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PIGEONHOLE2) EVENT (PROVE-LEMMA ALL-LESSEQP-DELETE (REWRITE) (IMPLIES (AND (ALL-DISTINCT L) (ALL-LESSEQP L N)) (ALL-LESSEQP (DELETE N L) (SUB1 N)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PIGEON-HOLE-PRINCIPLE-LEMMA-2 . ALL-LESSEQP-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE-NON-MEMBER . ALL-LESSEQP-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE . ALL-LESSEQP-DELETE) (IMMEDIATE-DEPENDENTS0 ALL-LESSEQP . ALL-LESSEQP-DELETE) (IMMEDIATE-DEPENDENTS0 ALL-DISTINCT . ALL-LESSEQP-DELETE) (LEMMAS ALL-LESSEQP . ALL-LESSEQP-DELETE))))) 
(PUT1-LST (QUOTE DELETE-MEMBER-LEAVE-SUBSET) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117235243. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (SUBSETP-POSITIVES-DELETE) EVENT (PROVE-LEMMA DELETE-MEMBER-LEAVE-SUBSET (REWRITE) (IMPLIES (AND (SUBSETP R S) (NOT (MEMBER X R))) (SUBSETP R (DELETE X S)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DELETE-X-LEAVE-A . DELETE-MEMBER-LEAVE-SUBSET) (IMMEDIATE-DEPENDENTS0 DELETE . DELETE-MEMBER-LEAVE-SUBSET) (LEMMAS SUBSETP . DELETE-MEMBER-LEAVE-SUBSET))))) 
(PUT1-LST (QUOTE DELETE-X-LEAVE-A) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117235237. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (DELETE-MEMBER-LEAVE-SUBSET) EVENT (PROVE-LEMMA DELETE-X-LEAVE-A (REWRITE) (IMPLIES (AND (MEMBER A S) (NOT (EQUAL A X))) (MEMBER A (DELETE X S)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DELETE . DELETE-X-LEAVE-A) (LEMMAS MEMBER . DELETE-X-LEAVE-A))))) 
(PUT1-LST (QUOTE TIMES-INVERSE-LIST) (QUOTE (IDATE 840117235230. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (W-T-LEMMA) EVENT (PROVE-LEMMA TIMES-INVERSE-LIST (REWRITE) (IMPLIES (AND (PRIME P) (LESSP I P)) (EQUAL (REMAINDER (TIMES-LIST (INVERSE-LIST I P)) P) 1.)) ((USE (T-I-L-LEMMA3) (T-I-L-LEMMA4)) (INDUCT (POSITIVES I)) (DISABLE INVERSE INVERSE-LIST TIMES-LIST T-I-L-LEMMA3 T-I-L-LEMMA4))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REMAINDER-WRT-12 . TIMES-INVERSE-LIST) (IMMEDIATE-DEPENDENTS0 REMAINDER-OF-1 . TIMES-INVERSE-LIST) (IMMEDIATE-DEPENDENTS0 REMAINDER-WRT-1 . TIMES-INVERSE-LIST) (IMMEDIATE-DEPENDENTS0 POSITIVES . TIMES-INVERSE-LIST) (IMMEDIATE-DEPENDENTS0 T-I-L-LEMMA3 . TIMES-INVERSE-LIST) (IMMEDIATE-DEPENDENTS0 T-I-L-LEMMA4 . TIMES-INVERSE-LIST) (IMMEDIATE-DEPENDENTS0 INVERSE-LIST . TIMES-INVERSE-LIST) (IMMEDIATE-DEPENDENTS0 TIMES-LIST . TIMES-INVERSE-LIST) (IMMEDIATE-DEPENDENTS0 PRIME . TIMES-INVERSE-LIST) (LEMMAS REMAINDER . TIMES-INVERSE-LIST))))) 
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(PUT1-LST (QUOTE CRYPT-INVERTS-STEP-2) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117222538. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CRYPT-INVERTS) EVENT (PROVE-LEMMA CRYPT-INVERTS-STEP-2 (REWRITE) (IMPLIES (AND (PRIME P) (PRIME Q) (NOT (EQUAL P Q)) (NUMBERP M) (LESSP M (TIMES P Q)) (EQUAL (REMAINDER ED (TIMES (SUB1 P) (SUB1 Q))) 1.)) (EQUAL (REMAINDER (EXP M ED) (TIMES P Q)) M))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQUAL-LESSP . CRYPT-INVERTS-STEP-2) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . CRYPT-INVERTS-STEP-2) (IMMEDIATE-DEPENDENTS0 TIMES-IDENTITY . CRYPT-INVERTS-STEP-2) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-TIMES . CRYPT-INVERTS-STEP-2) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-TIMES . CRYPT-INVERTS-STEP-2) (IMMEDIATE-DEPENDENTS0 TIMES-1 . CRYPT-INVERTS-STEP-2) (IMMEDIATE-DEPENDENTS0 EXP-BY-0 . CRYPT-INVERTS-STEP-2) (IMMEDIATE-DEPENDENTS0 EXP-PLUS . CRYPT-INVERTS-STEP-2) (IMMEDIATE-DEPENDENTS0 CRYPT-INVERTS-STEP-1B . CRYPT-INVERTS-STEP-2) (IMMEDIATE-DEPENDENTS0 CRYPT-INVERTS-STEP-1A . CRYPT-INVERTS-STEP-2) (IMMEDIATE-DEPENDENTS0 COROLLARY-53 . CRYPT-INVERTS-STEP-2) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES-2 . CRYPT-INVERTS-STEP-2) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . CRYPT-INVERTS-STEP-2) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . CRYPT-INVERTS-STEP-2) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . CRYPT-INVERTS-STEP-2) (IMMEDIATE-DEPENDENTS0 EXP . CRYPT-INVERTS-STEP-2) (IMMEDIATE-DEPENDENTS0 PRIME . CRYPT-INVERTS-STEP-2) (LEMMAS REMAINDER . CRYPT-INVERTS-STEP-2))))) 
(PUT1-LST (QUOTE CRYPT-INVERTS-STEP-1B) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117222245. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CRYPT-INVERTS-STEP-2) EVENT (PROVE-LEMMA CRYPT-INVERTS-STEP-1B (REWRITE) (IMPLIES (PRIME Q) (EQUAL (REMAINDER (TIMES M (EXP M (TIMES K (SUB1 P) (SUB1 Q)))) Q) (REMAINDER M Q))) ((USE (CRYPT-INVERTS-STEP-1 (P Q) (K (TIMES K (SUB1 P))))) (DISABLE CRYPT-INVERTS-STEP-1))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EXP-MOD-IS-1 . CRYPT-INVERTS-STEP-1B) (IMMEDIATE-DEPENDENTS0 FERMAT-THM . CRYPT-INVERTS-STEP-1B) (IMMEDIATE-DEPENDENTS0 COROLLARY-55 . CRYPT-INVERTS-STEP-1B) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-TIMES . CRYPT-INVERTS-STEP-1B) (IMMEDIATE-DEPENDENTS0 CRYPT-INVERTS-STEP-1 . CRYPT-INVERTS-STEP-1B) (IMMEDIATE-DEPENDENTS0 EXP . CRYPT-INVERTS-STEP-1B) (IMMEDIATE-DEPENDENTS0 PRIME . CRYPT-INVERTS-STEP-1B) (LEMMAS REMAINDER . CRYPT-INVERTS-STEP-1B))))) 
(PUT1-LST (QUOTE CRYPT-INVERTS-STEP-1A) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117222159. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CRYPT-INVERTS-STEP-2) EVENT (PROVE-LEMMA CRYPT-INVERTS-STEP-1A (REWRITE) (IMPLIES (PRIME P) (EQUAL (REMAINDER (TIMES M (EXP M (TIMES K (SUB1 P) (SUB1 Q)))) P) (REMAINDER M P))) ((USE (CRYPT-INVERTS-STEP-1 (K (TIMES K (SUB1 Q))))) (DISABLE CRYPT-INVERTS-STEP-1))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . CRYPT-INVERTS-STEP-1A) (IMMEDIATE-DEPENDENTS0 COROLLARY-55 . CRYPT-INVERTS-STEP-1A) (IMMEDIATE-DEPENDENTS0 PRIME-KEY-REWRITE . CRYPT-INVERTS-STEP-1A) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-TIMES . CRYPT-INVERTS-STEP-1A) (IMMEDIATE-DEPENDENTS0 CRYPT-INVERTS-STEP-1 . CRYPT-INVERTS-STEP-1A) (IMMEDIATE-DEPENDENTS0 EXP . CRYPT-INVERTS-STEP-1A) (IMMEDIATE-DEPENDENTS0 PRIME . CRYPT-INVERTS-STEP-1A) (LEMMAS REMAINDER . CRYPT-INVERTS-STEP-1A))))) 
(PUT1-LST (QUOTE CRYPT-INVERTS-STEP-1) (QUOTE (IDATE 840117222054. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CRYPT-INVERTS-STEP-1B CRYPT-INVERTS-STEP-1A) EVENT (PROVE-LEMMA CRYPT-INVERTS-STEP-1 NIL (IMPLIES (PRIME P) (EQUAL (REMAINDER (TIMES M (EXP M (TIMES K (SUB1 P)))) P) (REMAINDER M P)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 FERMAT-THM . CRYPT-INVERTS-STEP-1) (IMMEDIATE-DEPENDENTS0 EXP-MOD-IS-1 . CRYPT-INVERTS-STEP-1) (IMMEDIATE-DEPENDENTS0 COROLLARY-55 . CRYPT-INVERTS-STEP-1) (IMMEDIATE-DEPENDENTS0 EXP . CRYPT-INVERTS-STEP-1) (IMMEDIATE-DEPENDENTS0 PRIME . CRYPT-INVERTS-STEP-1))))) 
(PUT1-LST (QUOTE FERMAT-THM) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117222032. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EULER-1-4 INVERSE-OF-INVERSE INVERSE-INVERTS CRYPT-INVERTS-STEP-1B CRYPT-INVERTS-STEP-1) EVENT (PROVE-LEMMA FERMAT-THM (REWRITE) (IMPLIES (AND (PRIME P) (NOT (EQUAL (REMAINDER M P) 0.))) (EQUAL (REMAINDER (EXP M (SUB1 P)) P) 1.)) ((USE (PIGEON-HOLE-PRINCIPLE (L (S (SUB1 P) M P))) (REMAINDER-TIMES-LIST-S (N (SUB1 P)))) (DISABLE PIGEON-HOLE-PRINCIPLE REMAINDER-TIMES-LIST-S))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ALL-NON-ZEROP-S . FERMAT-THM) (IMMEDIATE-DEPENDENTS0 ALL-DISTINCT-S . FERMAT-THM) (IMMEDIATE-DEPENDENTS0 LENGTH-S . FERMAT-THM) (IMMEDIATE-DEPENDENTS0 ALL-LESSEQP-S . FERMAT-THM) (IMMEDIATE-DEPENDENTS0 TIMES-LIST-EQUAL-FACT . FERMAT-THM) (IMMEDIATE-DEPENDENTS0 PRIME-FACT . FERMAT-THM) (IMMEDIATE-DEPENDENTS0 COROLLARY-55 . FERMAT-THM) (IMMEDIATE-DEPENDENTS0 PIGEON-HOLE-PRINCIPLE . FERMAT-THM) (IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES-LIST-S . FERMAT-THM) (IMMEDIATE-DEPENDENTS0 EXP . FERMAT-THM) (IMMEDIATE-DEPENDENTS0 PRIME . FERMAT-THM) (LEMMAS REMAINDER . FERMAT-THM))))) 
(PUT1-LST (QUOTE LENGTH-S) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117221948. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (FERMAT-THM) EVENT (PROVE-LEMMA LENGTH-S (REWRITE) (EQUAL (LENGTH (S N M P)) (FIX N))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 S . LENGTH-S) (LEMMAS LENGTH . LENGTH-S))))) 
(PUT1-LST (QUOTE ALL-LESSEQP-S) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117221940. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (FERMAT-THM) EVENT (PROVE-LEMMA ALL-LESSEQP-S (REWRITE) (IMPLIES (NOT (ZEROP P)) (ALL-LESSEQP (S N M P) (SUB1 P)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER-DIVISOR . ALL-LESSEQP-S) (IMMEDIATE-DEPENDENTS0 PIGEON-HOLE-PRINCIPLE-LEMMA-2 . ALL-LESSEQP-S) (IMMEDIATE-DEPENDENTS0 S . ALL-LESSEQP-S) (IMMEDIATE-DEPENDENTS0 ALL-LESSEQP . ALL-LESSEQP-S) (LEMMAS ALL-LESSEQP . ALL-LESSEQP-S))))) 
(PUT1-LST (QUOTE ALL-NON-ZEROP-S) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117221919. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (FERMAT-THM) EVENT (PROVE-LEMMA ALL-NON-ZEROP-S (REWRITE) (IMPLIES (AND (PRIME P) (NOT (EQUAL (REMAINDER M P) 0.)) (LESSP N P)) (ALL-NON-ZEROP (S N M P)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PRIME-KEY-REWRITE . ALL-NON-ZEROP-S) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-PLUS . ALL-NON-ZEROP-S) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-PLUS . ALL-NON-ZEROP-S) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-TIMES . ALL-NON-ZEROP-S) (IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-TIMES-OVER-PLUS . ALL-NON-ZEROP-S) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . ALL-NON-ZEROP-S) (IMMEDIATE-DEPENDENTS0 TIMES-ADD1 . ALL-NON-ZEROP-S) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . ALL-NON-ZEROP-S) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . ALL-NON-ZEROP-S) (IMMEDIATE-DEPENDENTS0 S . ALL-NON-ZEROP-S) (IMMEDIATE-DEPENDENTS0 ALL-NON-ZEROP . ALL-NON-ZEROP-S) (IMMEDIATE-DEPENDENTS0 PRIME . ALL-NON-ZEROP-S) (LEMMAS ALL-NON-ZEROP . ALL-NON-ZEROP-S))))) 
(PUT1-LST (QUOTE ALL-DISTINCT-S) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117215942. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (FERMAT-THM) EVENT (PROVE-LEMMA ALL-DISTINCT-S (REWRITE) (IMPLIES (AND (PRIME P) (NOT (EQUAL (REMAINDER M P) 0.)) (LESSP N P)) (ALL-DISTINCT (S N M P)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ALL-DISTINCT-S-LEMMA . ALL-DISTINCT-S) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-PLUS . ALL-DISTINCT-S) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-PLUS . ALL-DISTINCT-S) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-TIMES . ALL-DISTINCT-S) (IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-TIMES-OVER-PLUS . ALL-DISTINCT-S) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . ALL-DISTINCT-S) (IMMEDIATE-DEPENDENTS0 TIMES-ADD1 . ALL-DISTINCT-S) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . ALL-DISTINCT-S) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . ALL-DISTINCT-S) (IMMEDIATE-DEPENDENTS0 S . ALL-DISTINCT-S) (IMMEDIATE-DEPENDENTS0 ALL-DISTINCT . ALL-DISTINCT-S) (IMMEDIATE-DEPENDENTS0 PRIME . ALL-DISTINCT-S) (LEMMAS ALL-DISTINCT . ALL-DISTINCT-S))))) 
(PUT1-LST (QUOTE ALL-DISTINCT-S-LEMMA) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117215542. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (ALL-DISTINCT-S) EVENT (PROVE-LEMMA ALL-DISTINCT-S-LEMMA (REWRITE) (IMPLIES (AND (PRIME P) (NOT (EQUAL (REMAINDER M P) 0.)) (NUMBERP N1) (LESSP N2 N1) (LESSP N1 P)) (NOT (MEMBER (REMAINDER (TIMES M N1) P) (S N2 M P)))) ((INDUCT (S N2 M P)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 THM-55-SPECIALIZED-TO-PRIMES . ALL-DISTINCT-S-LEMMA) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . ALL-DISTINCT-S-LEMMA) (IMMEDIATE-DEPENDENTS0 REMAINDER-0-CROCK . ALL-DISTINCT-S-LEMMA) (IMMEDIATE-DEPENDENTS0 S . ALL-DISTINCT-S-LEMMA) (IMMEDIATE-DEPENDENTS0 PRIME . ALL-DISTINCT-S-LEMMA) (LEMMAS MEMBER . ALL-DISTINCT-S-LEMMA))))) 
(PUT1-LST (QUOTE REMAINDER-TIMES-LIST-S) (QUOTE (IDATE 840117215417. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (FERMAT-THM) EVENT (PROVE-LEMMA REMAINDER-TIMES-LIST-S NIL (EQUAL (REMAINDER (TIMES-LIST (S N M P)) P) (REMAINDER (TIMES (FACT N) (EXP M N)) P))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-TIMES . REMAINDER-TIMES-LIST-S) (IMMEDIATE-DEPENDENTS0 TIMES-MOD-3 . REMAINDER-TIMES-LIST-S) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-TIMES . REMAINDER-TIMES-LIST-S) (IMMEDIATE-DEPENDENTS0 EQUAL-MODS-TRICK-2 . REMAINDER-TIMES-LIST-S) (IMMEDIATE-DEPENDENTS0 REMAINDER-EXP-LEMMA . REMAINDER-TIMES-LIST-S) (IMMEDIATE-DEPENDENTS0 EQUAL-MODS-TRICK-1 . REMAINDER-TIMES-LIST-S) (IMMEDIATE-DEPENDENTS0 REMAINDER-OF-1 . REMAINDER-TIMES-LIST-S) (IMMEDIATE-DEPENDENTS0 EXP-BY-0 . REMAINDER-TIMES-LIST-S) (IMMEDIATE-DEPENDENTS0 EXP . REMAINDER-TIMES-LIST-S) (IMMEDIATE-DEPENDENTS0 FACT . REMAINDER-TIMES-LIST-S) (IMMEDIATE-DEPENDENTS0 S . REMAINDER-TIMES-LIST-S) (IMMEDIATE-DEPENDENTS0 TIMES-LIST . REMAINDER-TIMES-LIST-S))))) 
(PUT1-LST (QUOTE 1S) (QUOTE NIL)) 
(PUT1-LST (QUOTE S) (QUOTE (TYPE-PRESCRIPTION-LST ((S 24. NIL NIL NIL)) LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE UNCHANGING UNCHANGING) SDEFN (LAMBDA (N M P) (IF (EQUAL N (QUOTE 0.)) (QUOTE NIL) (IF (NUMBERP N) (CONS (REMAINDER (TIMES M N) P) (S (SUB1 N) M P)) (QUOTE NIL)))) LISP-CODE 1S INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP N)) NIL) (TESTS-AND-CASES ((NOT (ZEROP N))) (((SUB1 N) M P)))) LEVEL-NO 3. JUSTIFICATIONS ((JUSTIFICATION (N) (COUNT N) LESSP (ZERO ZEROP COUNT-NUMBERP))) IDATE 840117215254. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1S) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LENGTH-S ALL-LESSEQP-S ALL-NON-ZEROP-S ALL-DISTINCT-S ALL-DISTINCT-S-LEMMA REMAINDER-TIMES-LIST-S) EVENT (DEFN S (N M P) (IF (ZEROP N) NIL (CONS (REMAINDER (TIMES M N) P) (S (SUB1 N) M P)))) LOCAL-UNDO-TUPLES ((DCELL . 1S))))) 
(PUT1-LST (QUOTE PRIME-FACT) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117215254. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (RES1-REM-2 RES1-REM-1 FERMAT-THM) EVENT (PROVE-LEMMA PRIME-FACT (REWRITE) (IMPLIES (AND (PRIME P) (LESSP N P)) (NOT (EQUAL (REMAINDER (FACT N) P) 0.))) ((INDUCT (FACT N)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PRIME-KEY-REWRITE . PRIME-FACT) (IMMEDIATE-DEPENDENTS0 REMAINDER-OF-1 . PRIME-FACT) (IMMEDIATE-DEPENDENTS0 FACT . PRIME-FACT) (IMMEDIATE-DEPENDENTS0 PRIME . PRIME-FACT) (LEMMAS EQUAL . PRIME-FACT))))) 
(PUT1-LST (QUOTE TIMES-LIST-EQUAL-FACT) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117215214. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (TIMES-REFLECT-LIST COMP-LIST-FACT INVERSE-LIST-FACT FERMAT-THM) EVENT (PROVE-LEMMA TIMES-LIST-EQUAL-FACT (REWRITE) (IMPLIES (PERM (POSITIVES N) L) (EQUAL (TIMES-LIST L) (FACT N))) ((USE (PERM-TIMES-LIST (L1 (POSITIVES N)) (L2 L))) (DISABLE PERM-TIMES-LIST))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-LIST-POSITIVES . TIMES-LIST-EQUAL-FACT) (IMMEDIATE-DEPENDENTS0 PERM-TIMES-LIST . TIMES-LIST-EQUAL-FACT) (IMMEDIATE-DEPENDENTS0 FACT . TIMES-LIST-EQUAL-FACT) (IMMEDIATE-DEPENDENTS0 TIMES-LIST . TIMES-LIST-EQUAL-FACT) (IMMEDIATE-DEPENDENTS0 POSITIVES . TIMES-LIST-EQUAL-FACT) (IMMEDIATE-DEPENDENTS0 PERM . TIMES-LIST-EQUAL-FACT) (LEMMAS TIMES-LIST . TIMES-LIST-EQUAL-FACT))))) 
(PUT1-LST (QUOTE TIMES-LIST-POSITIVES) (QUOTE (IDATE 840117215211. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (TIMES-LIST-EQUAL-FACT) EVENT (PROVE-LEMMA TIMES-LIST-POSITIVES (REWRITE) (EQUAL (TIMES-LIST (POSITIVES N)) (FACT N))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 FACT . TIMES-LIST-POSITIVES) (IMMEDIATE-DEPENDENTS0 POSITIVES . TIMES-LIST-POSITIVES) (IMMEDIATE-DEPENDENTS0 TIMES-LIST . TIMES-LIST-POSITIVES) (LEMMAS TIMES-LIST . TIMES-LIST-POSITIVES))))) 
(PUT1-LST (QUOTE PERM-TIMES-LIST) (QUOTE (IDATE 840117215206. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (TIMES-LIST-EQUAL-FACT) EVENT (PROVE-LEMMA PERM-TIMES-LIST NIL (IMPLIES (PERM L1 L2) (EQUAL (TIMES-LIST L1) (TIMES-LIST L2)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-TIMES-LIST-DELETE . PERM-TIMES-LIST) (IMMEDIATE-DEPENDENTS0 PERM-MEMBER . PERM-TIMES-LIST) (IMMEDIATE-DEPENDENTS0 TIMES-LIST . PERM-TIMES-LIST) (IMMEDIATE-DEPENDENTS0 PERM . PERM-TIMES-LIST))))) 
(PUT1-LST (QUOTE PIGEON-HOLE-PRINCIPLE) (QUOTE (IDATE 840117215146. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PLUS-REFLECT-LIST TIMES-REFLECT-LIST FERMAT-THM) EVENT (PROVE-LEMMA PIGEON-HOLE-PRINCIPLE NIL (IMPLIES (AND (ALL-NON-ZEROP L) (ALL-DISTINCT L) (ALL-LESSEQP L (LENGTH L))) (PERM (POSITIVES (LENGTH L)) L)) ((INDUCT (PIGEON-HOLE-INDUCTION L)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 MEMBER-POSITIVES . PIGEON-HOLE-PRINCIPLE) (IMMEDIATE-DEPENDENTS0 PERM-MEMBER . PIGEON-HOLE-PRINCIPLE) (IMMEDIATE-DEPENDENTS0 PIGEON-HOLE-PRINCIPLE-LEMMA-2 . PIGEON-HOLE-PRINCIPLE) (IMMEDIATE-DEPENDENTS0 PIGEON-HOLE-PRINCIPLE-LEMMA-1 . PIGEON-HOLE-PRINCIPLE) (IMMEDIATE-DEPENDENTS0 ALL-NON-ZEROP-DELETE . PIGEON-HOLE-PRINCIPLE) (IMMEDIATE-DEPENDENTS0 ALL-DISTINCT-DELETE . PIGEON-HOLE-PRINCIPLE) (IMMEDIATE-DEPENDENTS0 LENGTH-DELETE . PIGEON-HOLE-PRINCIPLE) (IMMEDIATE-DEPENDENTS0 PIGEON-HOLE-INDUCTION . PIGEON-HOLE-PRINCIPLE) (IMMEDIATE-DEPENDENTS0 POSITIVES . PIGEON-HOLE-PRINCIPLE) (IMMEDIATE-DEPENDENTS0 PERM . PIGEON-HOLE-PRINCIPLE) (IMMEDIATE-DEPENDENTS0 ALL-LESSEQP . PIGEON-HOLE-PRINCIPLE) (IMMEDIATE-DEPENDENTS0 ALL-DISTINCT . PIGEON-HOLE-PRINCIPLE) (IMMEDIATE-DEPENDENTS0 ALL-NON-ZEROP . PIGEON-HOLE-PRINCIPLE))))) 
(PUT1-LST (QUOTE 1PIGEON-HOLE-INDUCTION) (QUOTE NIL)) 
(PUT1-LST (QUOTE PIGEON-HOLE-INDUCTION) (QUOTE (TYPE-PRESCRIPTION-LST ((PIGEON-HOLE-INDUCTION 2. NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (L) (IF (LISTP L) (IF (MEMBER (LENGTH L) L) (PIGEON-HOLE-INDUCTION (DELETE (LENGTH L) L)) (PIGEON-HOLE-INDUCTION (CDR L))) (QUOTE 1TRUE))) LISP-CODE 1PIGEON-HOLE-INDUCTION INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP L) (MEMBER (LENGTH L) L)) (((DELETE (LENGTH L) L)))) (TESTS-AND-CASES ((LISTP L) (NOT (MEMBER (LENGTH L) L))) (((CDR L)))) (TESTS-AND-CASES ((NOT (LISTP L))) NIL)) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (L) (COUNT L) LESSP (CDR-LESSP ZERO LESSP-COUNT-DELETE))) IDATE 840117215007. CONTROLLER-POCKETS (1.) SATELLITES (1PIGEON-HOLE-INDUCTION) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PIGEON-HOLE-PRINCIPLE) EVENT (DEFN PIGEON-HOLE-INDUCTION (L) (IF (LISTP L) (IF (MEMBER (LENGTH L) L) (PIGEON-HOLE-INDUCTION (DELETE (LENGTH L) L)) (PIGEON-HOLE-INDUCTION (CDR L))) T)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DELETE . PIGEON-HOLE-INDUCTION) (IMMEDIATE-DEPENDENTS0 LESSP-COUNT-DELETE . PIGEON-HOLE-INDUCTION) (DCELL . 1PIGEON-HOLE-INDUCTION))))) 
(PUT1-LST (QUOTE PERM-MEMBER) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117215006. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PERM-PLUS-LIST EQUAL-LENGTH-PERM PERM-TIMES-LIST PIGEON-HOLE-PRINCIPLE) EVENT (PROVE-LEMMA PERM-MEMBER (REWRITE) (IMPLIES (AND (PERM A B) (MEMBER X A)) (MEMBER X B))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 MEMBER-DELETE . PERM-MEMBER) (IMMEDIATE-DEPENDENTS0 PERM . PERM-MEMBER) (LEMMAS MEMBER . PERM-MEMBER))))) 
(PUT1-LST (QUOTE PIGEON-HOLE-PRINCIPLE-LEMMA-2) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117215000. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (ALL-LESSEQP-REFLECT-LIST BOUNDED-COMP-LIST ALL-LESSEQP-DELETE BOUNDED-INVERSE-LIST ALL-LESSEQP-S PIGEON-HOLE-PRINCIPLE) EVENT (PROVE-LEMMA PIGEON-HOLE-PRINCIPLE-LEMMA-2 (REWRITE) (IMPLIES (AND (NOT (MEMBER (ADD1 N) X)) (ALL-LESSEQP X (ADD1 N))) (ALL-LESSEQP X N))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ALL-LESSEQP . PIGEON-HOLE-PRINCIPLE-LEMMA-2) (LEMMAS ALL-LESSEQP . PIGEON-HOLE-PRINCIPLE-LEMMA-2))))) 
(PUT1-LST (QUOTE PIGEON-HOLE-PRINCIPLE-LEMMA-1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117214949. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PIGEON-HOLE-PRINCIPLE) EVENT (PROVE-LEMMA PIGEON-HOLE-PRINCIPLE-LEMMA-1 (REWRITE) (IMPLIES (AND (ALL-DISTINCT L) (ALL-LESSEQP L (ADD1 N))) (ALL-LESSEQP (DELETE (ADD1 N) L) N))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DELETE-NON-MEMBER . PIGEON-HOLE-PRINCIPLE-LEMMA-1) (IMMEDIATE-DEPENDENTS0 DELETE . PIGEON-HOLE-PRINCIPLE-LEMMA-1) (IMMEDIATE-DEPENDENTS0 ALL-LESSEQP . PIGEON-HOLE-PRINCIPLE-LEMMA-1) (IMMEDIATE-DEPENDENTS0 ALL-DISTINCT . PIGEON-HOLE-PRINCIPLE-LEMMA-1) (LEMMAS ALL-LESSEQP . PIGEON-HOLE-PRINCIPLE-LEMMA-1))))) 
(PUT1-LST (QUOTE ALL-DISTINCT-DELETE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117214916. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PIGEONHOLE2 PIGEON-HOLE-PRINCIPLE) EVENT (PROVE-LEMMA ALL-DISTINCT-DELETE (REWRITE) (IMPLIES (ALL-DISTINCT L) (ALL-DISTINCT (DELETE X L)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 MEMBER-DELETE . ALL-DISTINCT-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE-NON-MEMBER . ALL-DISTINCT-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE . ALL-DISTINCT-DELETE) (IMMEDIATE-DEPENDENTS0 ALL-DISTINCT . ALL-DISTINCT-DELETE) (LEMMAS ALL-DISTINCT . ALL-DISTINCT-DELETE))))) 
(PUT1-LST (QUOTE ALL-NON-ZEROP-DELETE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117214911. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PIGEONHOLE2 PIGEON-HOLE-PRINCIPLE) EVENT (PROVE-LEMMA ALL-NON-ZEROP-DELETE (REWRITE) (IMPLIES (ALL-NON-ZEROP L) (ALL-NON-ZEROP (DELETE X L)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DELETE-NON-MEMBER . ALL-NON-ZEROP-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE . ALL-NON-ZEROP-DELETE) (IMMEDIATE-DEPENDENTS0 ALL-NON-ZEROP . ALL-NON-ZEROP-DELETE) (LEMMAS ALL-NON-ZEROP . ALL-NON-ZEROP-DELETE))))) 
(PUT1-LST (QUOTE MEMBER-POSITIVES) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117214905. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (POSITIVES-BOUNDED PIGEON-HOLE-PRINCIPLE) EVENT (PROVE-LEMMA MEMBER-POSITIVES (REWRITE) (EQUAL (MEMBER X (POSITIVES N)) (IF (ZEROP X) F (LESSP X (ADD1 N))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQUAL-LESSP . MEMBER-POSITIVES) (IMMEDIATE-DEPENDENTS0 POSITIVES . MEMBER-POSITIVES) (LEMMAS MEMBER . MEMBER-POSITIVES))))) 
(PUT1-LST (QUOTE CAR-POSITIVES) (QUOTE (IDATE 840117214847. EVENT (PROVE-LEMMA CAR-POSITIVES (REWRITE) (EQUAL (CAR (POSITIVES N)) (IF (ZEROP N) 0. N))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 POSITIVES . CAR-POSITIVES) (LEMMAS CAR . CAR-POSITIVES))))) 
(PUT1-LST (QUOTE LISTP-POSITIVES) (QUOTE (IDATE 840117214838. EVENT (PROVE-LEMMA LISTP-POSITIVES (REWRITE) (EQUAL (LISTP (POSITIVES N)) (NOT (ZEROP N)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 POSITIVES . LISTP-POSITIVES) (LEMMAS LISTP . LISTP-POSITIVES))))) 
(PUT1-LST (QUOTE 1POSITIVES) (QUOTE NIL)) 
(PUT1-LST (QUOTE POSITIVES) (QUOTE (TYPE-PRESCRIPTION-LST ((POSITIVES 24. NIL)) LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (N) (IF (EQUAL N (QUOTE 0.)) (QUOTE NIL) (IF (NUMBERP N) (CONS N (POSITIVES (SUB1 N))) (QUOTE NIL)))) LISP-CODE 1POSITIVES INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP N)) NIL) (TESTS-AND-CASES ((NOT (ZEROP N))) (((SUB1 N))))) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (N) (COUNT N) LESSP (ZERO ZEROP COUNT-NUMBERP))) IDATE 840117214833. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1POSITIVES) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PLUS-REFLECT-LIST REM-QUOT-LIST LENGTH-REFLECT-LIST LENGTH-POSITIVES TIMES-COMP-LIST PERM-POSITIVES-COMP-LIST ALL-DISTINCT-COMP-LIST SUBSETP-POSITIVES-COMP-LIST PERM-POSITIVES-INVERSE-LIST PIGEONHOLE2 SUBSETP-POSITIVES-DELETE POSITIVES-BOUNDED TIMES-INVERSE-LIST ALL-DISTINCT-INVERSE-LIST SUBSETP-POSITIVES TIMES-LIST-EQUAL-FACT TIMES-LIST-POSITIVES PIGEON-HOLE-PRINCIPLE MEMBER-POSITIVES CAR-POSITIVES LISTP-POSITIVES) EVENT (DEFN POSITIVES (N) (IF (ZEROP N) NIL (CONS N (POSITIVES (SUB1 N))))) LOCAL-UNDO-TUPLES ((DCELL . 1POSITIVES))))) 
(PUT1-LST (QUOTE 1ALL-NON-ZEROP) (QUOTE NIL)) 
(PUT1-LST (QUOTE ALL-NON-ZEROP) (QUOTE (TYPE-PRESCRIPTION-LST ((ALL-NON-ZEROP 3. NIL)) LEMMAS ((REWRITE-RULE ALL-NON-ZEROP-MULTS ((NUMBERP P) (NOT (EQUAL P (QUOTE 0.)))) (ALL-NON-ZEROP (MULTS N P)) NIL) (REWRITE-RULE ALL-NON-ZEROP-REFLECT-LIST ((PRIME P) (NOT (DIVIDES P A)) (LESSP B P)) (ALL-NON-ZEROP (REFLECT-LIST B A P)) NIL) (REWRITE-RULE ALL-NON-ZEROP-COMP-LIST ((PRIME P) (LESSP I P) (NOT (DIVIDES P A))) (ALL-NON-ZEROP (COMP-LIST I A P)) NIL) (REWRITE-RULE ALL-NON-ZEROP-INVERSE-LIST ((PRIME P) (LESSP I (SUB1 P))) (ALL-NON-ZEROP (INVERSE-LIST I P)) NIL) (REWRITE-RULE ALL-NON-ZEROP-S ((PRIME P) (NOT (EQUAL (REMAINDER M P) (QUOTE 0.))) (LESSP N P)) (ALL-NON-ZEROP (S N M P)) NIL) (REWRITE-RULE ALL-NON-ZEROP-DELETE ((ALL-NON-ZEROP L)) (ALL-NON-ZEROP (DELETE X L)) NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (L) (IF (LISTP L) (IF (EQUAL (CAR L) (QUOTE 0.)) (QUOTE 1FALSE) (IF (NUMBERP (CAR L)) (IF (ALL-NON-ZEROP (CDR L)) (QUOTE 1TRUE) (QUOTE 1FALSE)) (QUOTE 1FALSE))) (QUOTE 1TRUE))) LISP-CODE 1ALL-NON-ZEROP INDUCTION-MACHINE ((TESTS-AND-CASES ((NLISTP L)) NIL) (TESTS-AND-CASES ((NOT (NLISTP L))) (((CDR L))))) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (L) (COUNT L) LESSP (CDR-LESSP NLISTP ZERO CDR-LESSEQP))) IDATE 840117214832. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1ALL-NON-ZEROP) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (ALL-NON-ZEROP-MULTS A-WINNER-EVERY-TIME WIN-SOME-LOSE-SOME-2 WIN-SOME-LOSE-SOME-1 ALL-NON-ZEROP-REFLECT-LIST ALL-NON-ZEROP-COMP-LIST PIGEONHOLE2 NONZEROP-LESSEQP-ZERO ALL-NON-ZEROP-INVERSE-LIST ALL-NON-ZEROP-S PIGEON-HOLE-PRINCIPLE ALL-NON-ZEROP-DELETE) EVENT (DEFN ALL-NON-ZEROP (L) (IF (NLISTP L) T (AND (NOT (ZEROP (CAR L))) (ALL-NON-ZEROP (CDR L))))) LOCAL-UNDO-TUPLES ((DCELL . 1ALL-NON-ZEROP))))) 
(PUT1-LST (QUOTE 1ALL-LESSEQP) (QUOTE NIL)) 
(PUT1-LST (QUOTE ALL-LESSEQP) (QUOTE (TYPE-PRESCRIPTION-LST ((ALL-LESSEQP 3. NIL NIL)) LEMMAS ((REWRITE-RULE ALL-LESSEQP-REFLECT-LIST NIL (ALL-LESSEQP (REFLECT-LIST N A P) (QUOTIENT P (QUOTE 2.))) NIL) (REWRITE-RULE BOUNDED-COMP-LIST ((LESSP I P)) (ALL-LESSEQP (COMP-LIST I A P) (SUB1 P)) NIL) (REWRITE-RULE ALL-LESSEQP-DELETE ((ALL-DISTINCT L) (ALL-LESSEQP L N)) (ALL-LESSEQP (DELETE N L) (SUB1 N)) NIL) (REWRITE-RULE BOUNDED-INVERSE-LIST ((PRIME P) (LESSP I (SUB1 P)) (EQUAL J (DIFFERENCE P (QUOTE 2.)))) (ALL-LESSEQP (INVERSE-LIST I P) J) NIL) (REWRITE-RULE ALL-LESSEQP-S ((NUMBERP P) (NOT (EQUAL P (QUOTE 0.)))) (ALL-LESSEQP (S N M P) (SUB1 P)) NIL) (REWRITE-RULE PIGEON-HOLE-PRINCIPLE-LEMMA-2 ((NOT (MEMBER (ADD1 N) X)) (ALL-LESSEQP X (ADD1 N))) (ALL-LESSEQP X N) NIL) (REWRITE-RULE PIGEON-HOLE-PRINCIPLE-LEMMA-1 ((ALL-DISTINCT L) (ALL-LESSEQP L (ADD1 N))) (ALL-LESSEQP (DELETE (ADD1 N) L) N) NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE UNCHANGING) SDEFN (LAMBDA (L N) (IF (LISTP L) (IF (LESSP N (CAR L)) (QUOTE 1FALSE) (IF (ALL-LESSEQP (CDR L) N) (QUOTE 1TRUE) (QUOTE 1FALSE))) (QUOTE 1TRUE))) LISP-CODE 1ALL-LESSEQP INDUCTION-MACHINE ((TESTS-AND-CASES ((NLISTP L)) NIL) (TESTS-AND-CASES ((NOT (NLISTP L))) (((CDR L) N)))) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (L) (COUNT L) LESSP (CDR-LESSP NLISTP ZERO CDR-LESSEQP))) IDATE 840117214831. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1ALL-LESSEQP) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (ALL-LESSEQP-REFLECT-LIST BOUNDED-COMP-LIST PIGEONHOLE2 NONZEROP-LESSEQP-ZERO ALL-LESSEQP-DELETE BOUNDED-INVERSE-LIST ALL-LESSEQP-S PIGEON-HOLE-PRINCIPLE PIGEON-HOLE-PRINCIPLE-LEMMA-2 PIGEON-HOLE-PRINCIPLE-LEMMA-1) EVENT (DEFN ALL-LESSEQP (L N) (IF (NLISTP L) T (AND (NOT (LESSP N (CAR L))) (ALL-LESSEQP (CDR L) N)))) LOCAL-UNDO-TUPLES ((DCELL . 1ALL-LESSEQP))))) 
(PUT1-LST (QUOTE 1ALL-DISTINCT) (QUOTE NIL)) 
(PUT1-LST (QUOTE ALL-DISTINCT) (QUOTE (TYPE-PRESCRIPTION-LST ((ALL-DISTINCT 3. NIL)) LEMMAS ((REWRITE-RULE ALL-DISTINCT-REFLECT-LIST ((PRIME P) (NOT (DIVIDES (QUOTE 2.) P)) (NOT (DIVIDES P A)) (NOT (LESSP (QUOTIENT P (QUOTE 2.)) I))) (ALL-DISTINCT (REFLECT-LIST I A P)) NIL) (REWRITE-RULE ALL-DISTINCT-COMP-LIST ((PRIME P) (LESSP I P) (NOT (DIVIDES P A)) (NOT (RESIDUE A P))) (ALL-DISTINCT (COMP-LIST I A P)) NIL) (REWRITE-RULE ALL-DISTINCT-INVERSE-LIST ((PRIME P) (LESSP I (SUB1 P))) (ALL-DISTINCT (INVERSE-LIST I P)) NIL) (REWRITE-RULE A-D-I-L-LEMMA3 ((PRIME P) (LESSP I (SUB1 P)) (ALL-DISTINCT (INVERSE-LIST (SUB1 I) P))) (ALL-DISTINCT (INVERSE-LIST I P)) NIL) (REWRITE-RULE ALL-DISTINCT-S ((PRIME P) (NOT (EQUAL (REMAINDER M P) (QUOTE 0.))) (LESSP N P)) (ALL-DISTINCT (S N M P)) NIL) (REWRITE-RULE ALL-DISTINCT-DELETE ((ALL-DISTINCT L)) (ALL-DISTINCT (DELETE X L)) NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (L) (IF (LISTP L) (IF (MEMBER (CAR L) (CDR L)) (QUOTE 1FALSE) (IF (ALL-DISTINCT (CDR L)) (QUOTE 1TRUE) (QUOTE 1FALSE))) (QUOTE 1TRUE))) LISP-CODE 1ALL-DISTINCT INDUCTION-MACHINE ((TESTS-AND-CASES ((NLISTP L)) NIL) (TESTS-AND-CASES ((NOT (NLISTP L))) (((CDR L))))) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (L) (COUNT L) LESSP (CDR-LESSP NLISTP ZERO CDR-LESSEQP))) IDATE 840117214826. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1ALL-DISTINCT) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (ALL-DISTINCT-REFLECT-LIST ALL-DISTINCT-COMP-LIST ALL-DISTINCT-COMP-LIST-1 PIGEONHOLE2 ALL-LESSEQP-DELETE ALL-DISTINCT-INVERSE-LIST A-D-I-L-LEMMA3 ALL-DISTINCT-S PIGEON-HOLE-PRINCIPLE PIGEON-HOLE-PRINCIPLE-LEMMA-1 ALL-DISTINCT-DELETE) EVENT (DEFN ALL-DISTINCT (L) (IF (NLISTP L) T (AND (NOT (MEMBER (CAR L) (CDR L))) (ALL-DISTINCT (CDR L))))) LOCAL-UNDO-TUPLES ((DCELL . 1ALL-DISTINCT))))) 
(PUT1-LST (QUOTE COROLLARY-55) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117214825. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (RES1-REM-1 INVERSE-OF-INVERSE INVERSE-INVERTS-LEMMA CRYPT-INVERTS-STEP-1B CRYPT-INVERTS-STEP-1A CRYPT-INVERTS-STEP-1 FERMAT-THM) EVENT (PROVE-LEMMA COROLLARY-55 (REWRITE) (IMPLIES (PRIME P) (EQUAL (EQUAL (REMAINDER (TIMES M X) P) (REMAINDER M P)) (OR (EQUAL (REMAINDER M P) 0.) (EQUAL (REMAINDER X P) 1.)))) ((USE (THM-55-SPECIALIZED-TO-PRIMES (Y 1.))) (DISABLE THM-55-SPECIALIZED-TO-PRIMES))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-1 . COROLLARY-55) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . COROLLARY-55) (IMMEDIATE-DEPENDENTS0 REMAINDER-OF-1 . COROLLARY-55) (IMMEDIATE-DEPENDENTS0 PRIME-KEY-REWRITE . COROLLARY-55) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . COROLLARY-55) (IMMEDIATE-DEPENDENTS0 EQUAL-MODS-TRICK-2 . COROLLARY-55) (IMMEDIATE-DEPENDENTS0 EQUAL-MODS-TRICK-1 . COROLLARY-55) (IMMEDIATE-DEPENDENTS0 THM-55-SPECIALIZED-TO-PRIMES . COROLLARY-55) (IMMEDIATE-DEPENDENTS0 PRIME . COROLLARY-55) (LEMMAS EQUAL . COROLLARY-55))))) 
(PUT1-LST (QUOTE THM-55-SPECIALIZED-TO-PRIMES) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117214652. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (ALL-DISTINCT-REFLECT-LIST-9 ALL-DISTINCT-REFLECT-LIST-3 ALL-DISTINCT-REFLECT-LIST-1 COMPLEMENT-IS-UNIQUE WILSON-THM INVERSE-IS-UNIQUE ALL-DISTINCT-S-LEMMA COROLLARY-55) EVENT (PROVE-LEMMA THM-55-SPECIALIZED-TO-PRIMES (REWRITE) (IMPLIES (AND (PRIME P) (NOT (EQUAL (REMAINDER M P) 0.))) (EQUAL (EQUAL (REMAINDER (TIMES M X) P) (REMAINDER (TIMES M Y) P)) (EQUAL (REMAINDER X P) (REMAINDER Y P))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQUAL-MODS-TRICK-2 . THM-55-SPECIALIZED-TO-PRIMES) (IMMEDIATE-DEPENDENTS0 REMAINDER-EXP-LEMMA . THM-55-SPECIALIZED-TO-PRIMES) (IMMEDIATE-DEPENDENTS0 EQUAL-MODS-TRICK-1 . THM-55-SPECIALIZED-TO-PRIMES) (IMMEDIATE-DEPENDENTS0 PRIME-KEY-TRICK . THM-55-SPECIALIZED-TO-PRIMES) (IMMEDIATE-DEPENDENTS0 PRIME . THM-55-SPECIALIZED-TO-PRIMES) (LEMMAS EQUAL . THM-55-SPECIALIZED-TO-PRIMES))))) 
(PUT1-LST (QUOTE COROLLARY-53) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117214450. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CRYPT-INVERTS-STEP-2) EVENT (PROVE-LEMMA COROLLARY-53 (REWRITE) (IMPLIES (AND (PRIME P) (PRIME Q) (NOT (EQUAL P Q)) (EQUAL (REMAINDER A P) (REMAINDER B P)) (EQUAL (REMAINDER A Q) (REMAINDER B Q)) (NUMBERP B) (LESSP B (TIMES P Q))) (EQUAL (EQUAL (REMAINDER A (TIMES P Q)) B) T)) ((USE (THM-53-SPECIALIZED-TO-PRIMES)) (DISABLE THM-53-SPECIALIZED-TO-PRIMES))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . COROLLARY-53) (IMMEDIATE-DEPENDENTS0 THM-53-SPECIALIZED-TO-PRIMES . COROLLARY-53) (IMMEDIATE-DEPENDENTS0 PRIME . COROLLARY-53) (LEMMAS EQUAL . COROLLARY-53))))) 
(PUT1-LST (QUOTE THM-53-SPECIALIZED-TO-PRIMES) (QUOTE (IDATE 840117214412. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (COROLLARY-53) EVENT (PROVE-LEMMA THM-53-SPECIALIZED-TO-PRIMES NIL (IMPLIES (AND (PRIME P) (PRIME Q) (NOT (EQUAL P Q)) (EQUAL (REMAINDER A P) (REMAINDER B P)) (EQUAL (REMAINDER A Q) (REMAINDER B Q))) (EQUAL (REMAINDER A (TIMES P Q)) (REMAINDER B (TIMES P Q))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PRODUCT-DIVIDES . THM-53-SPECIALIZED-TO-PRIMES) (IMMEDIATE-DEPENDENTS0 EQUAL-MODS-TRICK-2 . THM-53-SPECIALIZED-TO-PRIMES) (IMMEDIATE-DEPENDENTS0 EQUAL-MODS-TRICK-1 . THM-53-SPECIALIZED-TO-PRIMES) (IMMEDIATE-DEPENDENTS0 PRIME . THM-53-SPECIALIZED-TO-PRIMES))))) 
(PUT1-LST (QUOTE PRODUCT-DIVIDES) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117214256. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (THM-53-SPECIALIZED-TO-PRIMES) EVENT (PROVE-LEMMA PRODUCT-DIVIDES (REWRITE) (IMPLIES (AND (EQUAL (REMAINDER X P) 0.) (EQUAL (REMAINDER X Q) 0.) (PRIME P) (PRIME Q) (NOT (EQUAL P Q))) (EQUAL (REMAINDER X (TIMES P Q)) 0.))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LITTLE-STEP . PRODUCT-DIVIDES) (IMMEDIATE-DEPENDENTS0 PRIME-KEY-REWRITE . PRODUCT-DIVIDES) (IMMEDIATE-DEPENDENTS0 PRODUCT-DIVIDES-LEMMA . PRODUCT-DIVIDES) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . PRODUCT-DIVIDES) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . PRODUCT-DIVIDES) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . PRODUCT-DIVIDES) (IMMEDIATE-DEPENDENTS0 PRIME . PRODUCT-DIVIDES) (LEMMAS REMAINDER . PRODUCT-DIVIDES))))) 
(PUT1-LST (QUOTE PRODUCT-DIVIDES-LEMMA) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117214038. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PRODUCT-DIVIDES) EVENT (PROVE-LEMMA PRODUCT-DIVIDES-LEMMA (REWRITE) (IMPLIES (EQUAL (REMAINDER X Z) 0.) (EQUAL (REMAINDER (TIMES Y X) (TIMES Y Z)) 0.))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-TIMES . PRODUCT-DIVIDES-LEMMA) (IMMEDIATE-DEPENDENTS0 DIVIDES-TIMES . PRODUCT-DIVIDES-LEMMA) (IMMEDIATE-DEPENDENTS0 REMAINDER-WRT-12 . PRODUCT-DIVIDES-LEMMA) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO2 . PRODUCT-DIVIDES-LEMMA) (IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES . PRODUCT-DIVIDES-LEMMA) (IMMEDIATE-DEPENDENTS0 REMAINDER-X-X . PRODUCT-DIVIDES-LEMMA) (IMMEDIATE-DEPENDENTS0 TIMES-IDENTITY . PRODUCT-DIVIDES-LEMMA) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . PRODUCT-DIVIDES-LEMMA) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . PRODUCT-DIVIDES-LEMMA) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . PRODUCT-DIVIDES-LEMMA) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . PRODUCT-DIVIDES-LEMMA) (LEMMAS REMAINDER . PRODUCT-DIVIDES-LEMMA))))) 
(PUT1-LST (QUOTE PRIME-KEY-TRICK) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117214012. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (RES1-REM-1 THM-55-SPECIALIZED-TO-PRIMES) EVENT (PROVE-LEMMA PRIME-KEY-TRICK (REWRITE) (IMPLIES (AND (EQUAL (REMAINDER (TIMES M A) P) (REMAINDER (TIMES M B) P)) (NOT (EQUAL (REMAINDER M P) 0.)) (PRIME P)) (EQUAL (EQUAL (REMAINDER A P) (REMAINDER B P)) T)) ((USE (PRIME-KEY-REWRITE (A M) (B (PDIFFERENCE A B))) (EQUAL-MODS-TRICK-2 (A (TIMES M A)) (B (TIMES M B)))) (DISABLE PRIME-KEY-REWRITE EQUAL-MODS-TRICK-2))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . PRIME-KEY-TRICK) (IMMEDIATE-DEPENDENTS0 TIMES-DISTRIBUTES-OVER-PDIFFERENCE . PRIME-KEY-TRICK) (IMMEDIATE-DEPENDENTS0 EQUAL-MODS-TRICK-1 . PRIME-KEY-TRICK) (IMMEDIATE-DEPENDENTS0 PRIME-KEY-REWRITE . PRIME-KEY-TRICK) (IMMEDIATE-DEPENDENTS0 EQUAL-MODS-TRICK-2 . PRIME-KEY-TRICK) (IMMEDIATE-DEPENDENTS0 PRIME . PRIME-KEY-TRICK) (LEMMAS EQUAL . PRIME-KEY-TRICK))))) 
(PUT1-LST (QUOTE G0006) (QUOTE (IDATE 840117213853. EVENT (TOGGLE G0006 PDIFFERENCE T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PDIFFERENCE . G0006) (DISABLED-LEMMAS NIL PDIFFERENCE G0006 . T))))) 
(PUT1-LST (QUOTE EQUAL-MODS-TRICK-2) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117213852. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (TIMES-COMP-LIST-4 N-O-I-LEMMA3 REMAINDER-TIMES-LIST-S COROLLARY-55 THM-55-SPECIALIZED-TO-PRIMES THM-53-SPECIALIZED-TO-PRIMES PRIME-KEY-TRICK) EVENT (PROVE-LEMMA EQUAL-MODS-TRICK-2 (REWRITE) (IMPLIES (EQUAL (REMAINDER A P) (REMAINDER B P)) (EQUAL (REMAINDER (PDIFFERENCE A B) P) 0.)) ((DISABLE DIFFERENCE-ELIM))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIFFERENCE-X-X . EQUAL-MODS-TRICK-2) (IMMEDIATE-DEPENDENTS0 LESSP-PLUS-CANCELATION . EQUAL-MODS-TRICK-2) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-PLUS-CANCELATION . EQUAL-MODS-TRICK-2) (IMMEDIATE-DEPENDENTS0 REMAINDER-DIFFERENCE-TIMES . EQUAL-MODS-TRICK-2) (IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES . EQUAL-MODS-TRICK-2) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . EQUAL-MODS-TRICK-2) (IMMEDIATE-DEPENDENTS0 REMAINDER-WRT-12 . EQUAL-MODS-TRICK-2) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . EQUAL-MODS-TRICK-2) (IMMEDIATE-DEPENDENTS0 REMAINDER-0-CROCK . EQUAL-MODS-TRICK-2) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . EQUAL-MODS-TRICK-2) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . EQUAL-MODS-TRICK-2) (IMMEDIATE-DEPENDENTS0 PDIFFERENCE . EQUAL-MODS-TRICK-2) (LEMMAS REMAINDER . EQUAL-MODS-TRICK-2))))) 
(PUT1-LST (QUOTE EQUAL-MODS-TRICK-1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117213619. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (TIMES-COMP-LIST-4 REMAINDER-TIMES-LIST-S COROLLARY-55 THM-55-SPECIALIZED-TO-PRIMES THM-53-SPECIALIZED-TO-PRIMES PRIME-KEY-TRICK) EVENT (PROVE-LEMMA EQUAL-MODS-TRICK-1 (REWRITE) (IMPLIES (EQUAL (REMAINDER (PDIFFERENCE A B) P) 0.) (EQUAL (EQUAL (REMAINDER A P) (REMAINDER B P)) T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REMAINDER-PLUS-TIMES-2 . EQUAL-MODS-TRICK-1) (IMMEDIATE-DEPENDENTS0 REMAINDER-WRT-12 . EQUAL-MODS-TRICK-1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . EQUAL-MODS-TRICK-1) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . EQUAL-MODS-TRICK-1) (IMMEDIATE-DEPENDENTS0 REMAINDER-0-CROCK . EQUAL-MODS-TRICK-1) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-ELIM . EQUAL-MODS-TRICK-1) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . EQUAL-MODS-TRICK-1) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . EQUAL-MODS-TRICK-1) (IMMEDIATE-DEPENDENTS0 PDIFFERENCE . EQUAL-MODS-TRICK-1) (LEMMAS EQUAL . EQUAL-MODS-TRICK-1))))) 
(PUT1-LST (QUOTE TIMES-DISTRIBUTES-OVER-PDIFFERENCE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117213516. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PRIME-KEY-TRICK) EVENT (PROVE-LEMMA TIMES-DISTRIBUTES-OVER-PDIFFERENCE (REWRITE) (EQUAL (TIMES M (PDIFFERENCE A B)) (PDIFFERENCE (TIMES M A) (TIMES M B)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . TIMES-DISTRIBUTES-OVER-PDIFFERENCE) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO2 . TIMES-DISTRIBUTES-OVER-PDIFFERENCE) (IMMEDIATE-DEPENDENTS0 TIMES-DIFFERENCE . TIMES-DISTRIBUTES-OVER-PDIFFERENCE) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . TIMES-DISTRIBUTES-OVER-PDIFFERENCE) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES-CANCELLATION . TIMES-DISTRIBUTES-OVER-PDIFFERENCE) (IMMEDIATE-DEPENDENTS0 PDIFFERENCE . TIMES-DISTRIBUTES-OVER-PDIFFERENCE) (LEMMAS TIMES . TIMES-DISTRIBUTES-OVER-PDIFFERENCE))))) 
(PUT1-LST (QUOTE 1PDIFFERENCE) (QUOTE NIL)) 
(PUT1-LST (QUOTE PDIFFERENCE) (QUOTE (TYPE-PRESCRIPTION-LST ((PDIFFERENCE 4. NIL NIL)) LEMMAS NIL LINEAR-LEMMAS NIL QUICK-BLOCK-INFO NIL SDEFN (LAMBDA (A B) (IF (LESSP A B) (DIFFERENCE B A) (DIFFERENCE A B))) LISP-CODE 1PDIFFERENCE INDUCTION-MACHINE NIL LEVEL-NO 1. JUSTIFICATIONS NIL IDATE 840117213455. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS NIL SATELLITES (1PDIFFERENCE) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (N-O-I-LEMMA3 G0006 EQUAL-MODS-TRICK-2 EQUAL-MODS-TRICK-1 TIMES-DISTRIBUTES-OVER-PDIFFERENCE) EVENT (DEFN PDIFFERENCE (A B) (IF (LESSP A B) (DIFFERENCE B A) (DIFFERENCE A B))) LOCAL-UNDO-TUPLES ((DCELL . 1PDIFFERENCE))))) 
(PUT1-LST (QUOTE EXP-MOD-IS-1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117213452. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (INVERSE-OF-INVERSE CRYPT-INVERTS-STEP-1B CRYPT-INVERTS-STEP-1) EVENT (PROVE-LEMMA EXP-MOD-IS-1 (REWRITE) (IMPLIES (EQUAL (REMAINDER (EXP M J) P) 1.) (EQUAL (REMAINDER (EXP M (TIMES I J)) P) 1.)) ((USE (EXP-EXP (I M) (J J) (K I)) (REMAINDER-EXP (A (EXP M J)) (N P))) (DISABLE EXP-EXP REMAINDER-EXP))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . EXP-MOD-IS-1) (IMMEDIATE-DEPENDENTS0 EXP-OF-1 . EXP-MOD-IS-1) (IMMEDIATE-DEPENDENTS0 REMAINDER-OF-1 . EXP-MOD-IS-1) (IMMEDIATE-DEPENDENTS0 REMAINDER-WRT-1 . EXP-MOD-IS-1) (IMMEDIATE-DEPENDENTS0 EXP-EXP . EXP-MOD-IS-1) (IMMEDIATE-DEPENDENTS0 REMAINDER-EXP . EXP-MOD-IS-1) (IMMEDIATE-DEPENDENTS0 EXP . EXP-MOD-IS-1) (LEMMAS REMAINDER . EXP-MOD-IS-1))))) 
(PUT1-LST (QUOTE REMAINDER-EXP) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117213447. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EULER-1-3 INVERSE-OF-INVERSE CRYPT-INVERTS EXP-MOD-IS-1) EVENT (PROVE-LEMMA REMAINDER-EXP (REWRITE) (EQUAL (REMAINDER (EXP (REMAINDER A N) I) N) (REMAINDER (EXP A I) N))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-MOD-3 . REMAINDER-EXP) (IMMEDIATE-DEPENDENTS0 REMAINDER-EXP-LEMMA . REMAINDER-EXP) (IMMEDIATE-DEPENDENTS0 EXP-BY-0 . REMAINDER-EXP) (IMMEDIATE-DEPENDENTS0 REMAINDER-OF-1 . REMAINDER-EXP) (IMMEDIATE-DEPENDENTS0 REMAINDER-0-CROCK . REMAINDER-EXP) (IMMEDIATE-DEPENDENTS0 EXP-OF-0 . REMAINDER-EXP) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . REMAINDER-EXP) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . REMAINDER-EXP) (IMMEDIATE-DEPENDENTS0 EXP . REMAINDER-EXP) (LEMMAS REMAINDER . REMAINDER-EXP))))) 
(PUT1-LST (QUOTE REMAINDER-EXP-LEMMA) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117213425. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (RES1-REM-2 REM-REFLECT-LIST-4 REM-REFLECT-LIST-3 REM-REFLECT-LIST-2 REM-REFLECT-LIST-1 TIMES-COMP-LIST-4 REMAINDER-TIMES-LIST-S THM-55-SPECIALIZED-TO-PRIMES REMAINDER-EXP) EVENT (PROVE-LEMMA REMAINDER-EXP-LEMMA (REWRITE) (IMPLIES (EQUAL (REMAINDER Y A) (REMAINDER Z A)) (EQUAL (EQUAL (REMAINDER (TIMES X Y) A) (REMAINDER (TIMES X Z) A)) T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REMAINDER-PLUS-TIMES-2 . REMAINDER-EXP-LEMMA) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . REMAINDER-EXP-LEMMA) (IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-TIMES-OVER-PLUS . REMAINDER-EXP-LEMMA) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-TIMES . REMAINDER-EXP-LEMMA) (IMMEDIATE-DEPENDENTS0 REMAINDER-WRT-12 . REMAINDER-EXP-LEMMA) (IMMEDIATE-DEPENDENTS0 TIMES-IDENTITY . REMAINDER-EXP-LEMMA) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . REMAINDER-EXP-LEMMA) (IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES . REMAINDER-EXP-LEMMA) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO2 . REMAINDER-EXP-LEMMA) (IMMEDIATE-DEPENDENTS0 REMAINDER-0-CROCK . REMAINDER-EXP-LEMMA) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . REMAINDER-EXP-LEMMA) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . REMAINDER-EXP-LEMMA) (LEMMAS EQUAL . REMAINDER-EXP-LEMMA))))) 
(PUT1-LST (QUOTE TIMES-MOD-3) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117213211. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (REM-REFLECT-LIST-4 REM-REFLECT-LIST-3 REM-REFLECT-LIST-2 REM-REFLECT-LIST-1 TIMES-MOD-4 COMPLEMENT-WORKS ALL-SQUARES-2 T-I-L-LEMMA1 REMAINDER-TIMES-LIST-S REMAINDER-EXP) EVENT (PROVE-LEMMA TIMES-MOD-3 (REWRITE) (EQUAL (REMAINDER (TIMES (REMAINDER A N) B) N) (REMAINDER (TIMES A B) N))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . TIMES-MOD-3) (IMMEDIATE-DEPENDENTS0 TIMES-MOD-1 . TIMES-MOD-3) (LEMMAS REMAINDER . TIMES-MOD-3))))) 
(PUT1-LST (QUOTE CRYPT-CORRECT) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117213154. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CRYPT-INVERTS) EVENT (PROVE-LEMMA CRYPT-CORRECT (REWRITE) (IMPLIES (NOT (EQUAL N 1.)) (EQUAL (CRYPT M E N) (REMAINDER (EXP M E) N)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-ADD1 . CRYPT-CORRECT) (IMMEDIATE-DEPENDENTS0 PLUS-ADD1 . CRYPT-CORRECT) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-PLUS . CRYPT-CORRECT) (IMMEDIATE-DEPENDENTS0 TIMES-MOD-2 . CRYPT-CORRECT) (IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-TIMES-OVER-PLUS . CRYPT-CORRECT) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-PLUS . CRYPT-CORRECT) (IMMEDIATE-DEPENDENTS0 REMAINDER-WRT-12 . CRYPT-CORRECT) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO2 . CRYPT-CORRECT) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . CRYPT-CORRECT) (IMMEDIATE-DEPENDENTS0 TIMES-IDENTITY . CRYPT-CORRECT) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-TIMES . CRYPT-CORRECT) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER-DIVISOR . CRYPT-CORRECT) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . CRYPT-CORRECT) (IMMEDIATE-DEPENDENTS0 TIMES-MOD-1 . CRYPT-CORRECT) (IMMEDIATE-DEPENDENTS0 TIMES-2 . CRYPT-CORRECT) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL . CRYPT-CORRECT) (IMMEDIATE-DEPENDENTS0 PLUS-EQUAL-0 . CRYPT-CORRECT) (IMMEDIATE-DEPENDENTS0 EXP-PLUS . CRYPT-CORRECT) (IMMEDIATE-DEPENDENTS0 TIMES-1 . CRYPT-CORRECT) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . CRYPT-CORRECT) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . CRYPT-CORRECT) (IMMEDIATE-DEPENDENTS0 SQUARE . CRYPT-CORRECT) (IMMEDIATE-DEPENDENTS0 EXP-BY-0 . CRYPT-CORRECT) (IMMEDIATE-DEPENDENTS0 REMAINDER-OF-1 . CRYPT-CORRECT) (IMMEDIATE-DEPENDENTS0 EVEN . CRYPT-CORRECT) (IMMEDIATE-DEPENDENTS0 LESSP-QUOTIENT1 . CRYPT-CORRECT) (IMMEDIATE-DEPENDENTS0 EXP . CRYPT-CORRECT) (IMMEDIATE-DEPENDENTS0 CRYPT . CRYPT-CORRECT) (LEMMAS CRYPT . CRYPT-CORRECT))))) 
(PUT1-LST (QUOTE TIMES-MOD-2) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117212006. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (COMPLEMENT-WORKS CRYPT-CORRECT) EVENT (PROVE-LEMMA TIMES-MOD-2 (REWRITE) (EQUAL (REMAINDER (TIMES A (TIMES B (REMAINDER Y N))) N) (REMAINDER (TIMES A B Y) N)) ((USE (TIMES-MOD-1 (X (TIMES A B)))) (DISABLE TIMES-MOD-1))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-TIMES . TIMES-MOD-2) (IMMEDIATE-DEPENDENTS0 TIMES-MOD-1 . TIMES-MOD-2) (LEMMAS REMAINDER . TIMES-MOD-2))))) 
(PUT1-LST (QUOTE TIMES-MOD-1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117212001. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (REM-REFLECT-LIST-4 REM-REFLECT-LIST-3 TIMES-COMP-LIST-4 TIMES-COMP-LIST-2 TIMES-COMP-LIST-1 TIMES-MOD-4 COMPLEMENT-WORKS ALL-SQUARES-2 INVERSE-IS-UNIQUE INVERSE-INVERTS-LEMMA TIMES-MOD-3 CRYPT-CORRECT TIMES-MOD-2) EVENT (PROVE-LEMMA TIMES-MOD-1 (REWRITE) (EQUAL (REMAINDER (TIMES X (REMAINDER Y N)) N) (REMAINDER (TIMES X Y) N))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-TIMES . TIMES-MOD-1) (IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-TIMES-OVER-PLUS . TIMES-MOD-1) (IMMEDIATE-DEPENDENTS0 REMAINDER-PLUS-TIMES-2 . TIMES-MOD-1) (IMMEDIATE-DEPENDENTS0 REMAINDER-WRT-12 . TIMES-MOD-1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . TIMES-MOD-1) (IMMEDIATE-DEPENDENTS0 TIMES-IDENTITY . TIMES-MOD-1) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO2 . TIMES-MOD-1) (IMMEDIATE-DEPENDENTS0 REMAINDER-0-CROCK . TIMES-MOD-1) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . TIMES-MOD-1) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . TIMES-MOD-1) (LEMMAS REMAINDER . TIMES-MOD-1))))) 
(PUT1-LST (QUOTE 1CRYPT) (QUOTE NIL)) 
(PUT1-LST (QUOTE CRYPT) (QUOTE (TYPE-PRESCRIPTION-LST ((CRYPT 4. NIL NIL NIL)) LEMMAS ((REWRITE-RULE CRYPT-CORRECT ((NOT (EQUAL N (QUOTE 1.)))) (EQUAL (CRYPT M E N) (REMAINDER (EXP M E) N)) NIL)) LINEAR-LEMMAS NIL QUICK-BLOCK-INFO (UNCHANGING SELF-REFLEXIVE UNCHANGING) SDEFN (LAMBDA (M E N) (IF (EQUAL E (QUOTE 0.)) (QUOTE 1.) (IF (NUMBERP E) (IF (EVEN E) (REMAINDER (SQUARE (CRYPT M (QUOTIENT E (QUOTE 2.)) N)) N) (REMAINDER (TIMES M (REMAINDER (SQUARE (CRYPT M (QUOTIENT E (QUOTE 2.)) N)) N)) N)) (QUOTE 1.)))) LISP-CODE 1CRYPT INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP E)) NIL) (TESTS-AND-CASES ((NOT (ZEROP E)) (EVEN E)) ((M (QUOTIENT E (QUOTE 2.)) N))) (TESTS-AND-CASES ((NOT (ZEROP E)) (NOT (EVEN E))) ((M (QUOTIENT E (QUOTE 2.)) N)))) LEVEL-NO 3. JUSTIFICATIONS ((JUSTIFICATION (E) (COUNT E) LESSP (ZEROP EVEN COUNT-NUMBERP EQUAL NUMBERP LESSP-QUOTIENT1))) IDATE 840117211825. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (2.) SATELLITES (1CRYPT) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CRYPT-INVERTS CRYPT-CORRECT) EVENT (DEFN CRYPT (M E N) (IF (ZEROP E) 1. (IF (EVEN E) (REMAINDER (SQUARE (CRYPT M (QUOTIENT E 2.) N)) N) (REMAINDER (TIMES M (REMAINDER (SQUARE (CRYPT M (QUOTIENT E 2.) N)) N)) N)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SQUARE . CRYPT) (IMMEDIATE-DEPENDENTS0 EVEN . CRYPT) (IMMEDIATE-DEPENDENTS0 LESSP-QUOTIENT1 . CRYPT) (DCELL . 1CRYPT))))) 
(PUT1-LST (QUOTE G0005) (QUOTE (IDATE 840117211821. EVENT (TOGGLE G0005 TIMES T) LOCAL-UNDO-TUPLES ((DISABLED-LEMMAS NIL TIMES G0005 . T))))) 
(PUT1-LST (QUOTE G0004) (QUOTE (IDATE 840117211819. EVENT (TOGGLE G0004 IF-TIMES-THEN-DIVIDES T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 IF-TIMES-THEN-DIVIDES . G0004) (DISABLED-LEMMAS NIL IF-TIMES-THEN-DIVIDES G0004 . T))))) 
(PUT1-LST (QUOTE G0003) (QUOTE (IDATE 840117211818. EVENT (TOGGLE G0003 QUOTIENT-DIVIDES T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 QUOTIENT-DIVIDES . G0003) (DISABLED-LEMMAS NIL QUOTIENT-DIVIDES G0003 . T))))) 
(PUT1-LST (QUOTE G0002) (QUOTE (IDATE 840117211817. EVENT (TOGGLE G0002 EUCLID T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EUCLID . G0002) (DISABLED-LEMMAS NIL EUCLID G0002 . T))))) 
(PUT1-LST (QUOTE SUBST2-OK) (QUOTE (IDATE 840117194047. EVENT (PROVE-LEMMA SUBST2-OK NIL (EQUAL (EVAL2 (SUBST2 NEW OLD TERM) A) (EVAL2 TERM (CONS (CONS OLD (EVAL2 NEW A)) A)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ASSOC . SUBST2-OK) (IMMEDIATE-DEPENDENTS0 SUBST2 . SUBST2-OK) (IMMEDIATE-DEPENDENTS0 EVAL2 . SUBST2-OK))))) 
(PUT1-LST (QUOTE 1SUBST2) (QUOTE NIL)) 
(PUT1-LST (QUOTE SUBST2) (QUOTE (TYPE-PRESCRIPTION-LST ((SUBST2 28. T NIL T)) LEMMAS NIL QUICK-BLOCK-INFO (UNCHANGING UNCHANGING SELF-REFLEXIVE) SDEFN (LAMBDA (NEW OLD TERM) (IF (NUMBERP TERM) TERM (IF (LITATOM TERM) (IF (EQUAL OLD TERM) NEW TERM) (IF (LISTP TERM) (CONS (CAR TERM) (CONS (SUBST2 NEW OLD (CAR (CDR TERM))) (CONS (SUBST2 NEW OLD (CAR (CDR (CDR TERM)))) (QUOTE NIL)))) TERM)))) LISP-CODE 1SUBST2 INDUCTION-MACHINE ((TESTS-AND-CASES ((NUMBERP TERM)) NIL) (TESTS-AND-CASES ((NOT (NUMBERP TERM)) (LITATOM TERM) (EQUAL OLD TERM)) NIL) (TESTS-AND-CASES ((NOT (NUMBERP TERM)) (LITATOM TERM) (NOT (EQUAL OLD TERM))) NIL) (TESTS-AND-CASES ((NOT (NUMBERP TERM)) (NOT (LITATOM TERM)) (LISTP TERM)) ((NEW OLD (CAR (CDR (CDR TERM)))) (NEW OLD (CAR (CDR TERM))))) (TESTS-AND-CASES ((NOT (NUMBERP TERM)) (NOT (LITATOM TERM)) (NOT (LISTP TERM))) NIL)) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (TERM) (COUNT TERM) LESSP (ZERO CDR-LESSP CDR-LESSEQP CAR-LESSEQP))) IDATE 840117194034. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (4.) SATELLITES (1SUBST2) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (SUBST2-OK) EVENT (DEFN SUBST2 (NEW OLD TERM) (IF (NUMBERP TERM) TERM (IF (LITATOM TERM) (IF (EQUAL OLD TERM) NEW TERM) (IF (LISTP TERM) (LIST (CAR TERM) (SUBST2 NEW OLD (CADR TERM)) (SUBST2 NEW OLD (CADDR TERM))) TERM)))) LOCAL-UNDO-TUPLES ((DCELL . 1SUBST2))))) 
(PUT1-LST (QUOTE EVAL2) (QUOTE (TYPE-PRESCRIPTION-LST ((EVAL2 -1. T NIL)) LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE UNCHANGING) SDEFN (LAMBDA (FORM ENVRN) (IF (NUMBERP FORM) FORM (IF (LITATOM FORM) (CDR (ASSOC FORM ENVRN)) (IF (LISTP FORM) (APPLY2 (CAR FORM) (EVAL2 (CAR (CDR FORM)) ENVRN) (EVAL2 (CAR (CDR (CDR FORM))) ENVRN)) FORM)))) INDUCTION-MACHINE ((TESTS-AND-CASES ((NUMBERP FORM)) NIL) (TESTS-AND-CASES ((NOT (NUMBERP FORM)) (LITATOM FORM)) NIL) (TESTS-AND-CASES ((NOT (NUMBERP FORM)) (NOT (LITATOM FORM)) (LISTP FORM)) (((CAR (CDR (CDR FORM))) ENVRN) ((CAR (CDR FORM)) ENVRN))) (TESTS-AND-CASES ((NOT (NUMBERP FORM)) (NOT (LITATOM FORM)) (NOT (LISTP FORM))) NIL)) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (FORM) (COUNT FORM) LESSP (ZERO CDR-LESSP CDR-LESSEQP CAR-LESSEQP))) IDATE 840117194033. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (SUBST2-OK) EVENT (DEFN EVAL2 (FORM ENVRN) (IF (NUMBERP FORM) FORM (IF (LITATOM FORM) (CDR (ASSOC FORM ENVRN)) (IF (LISTP FORM) (APPLY2 (CAR FORM) (EVAL2 (CADR FORM) ENVRN) (EVAL2 (CADDR FORM) ENVRN)) FORM)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 APPLY2 . EVAL2) (IMMEDIATE-DEPENDENTS0 ASSOC . EVAL2))))) 
(PUT1-LST (QUOTE APPLY2) (QUOTE (TYPE-PRESCRIPTION-LST ((APPLY2 -1. NIL NIL NIL)) LEMMAS NIL SDEFN NIL LISP-CODE NIL LEVEL-NO 0. IDATE 840117194032. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EVAL2) EVENT (DCL APPLY2 (FN X Y))))) 
(PUT1-LST (QUOTE LESSP-REMAINDER-DIVISOR) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117194032. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PLUS-REFLECT-LIST EVEN3-EVEN RES1-REM-1-1 PLUS-X-X-EVEN TIMES-REFLECT-LIST ALL-DISTINCT-REFLECT-LIST-10 ALL-DISTINCT-REFLECT-LIST-9 ALL-DISTINCT-REFLECT-LIST-3 REM-REFLECT-LIST-4 REM-REFLECT-LIST-3 REM-REFLECT-LIST-2 REFLECT-COMMUTES-WITH-TIMES-1 EULER-2-4 EULER-1 EULER-1-2 EULER-1-1 ALL-SQUARES B-I-LEMMA1 NON-ZEROP-INVERSE INVERSE-OF-INVERSE INVERSE-IS-UNIQUE INVERSE-INVERTS-LEMMA ALL-LESSEQP-S CRYPT-CORRECT) EVENT (PROVE-LEMMA LESSP-REMAINDER-DIVISOR (REWRITE) (IMPLIES (NOT (ZEROP Y)) (LESSP (REMAINDER X Y) Y))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . LESSP-REMAINDER-DIVISOR) (LINEAR-LEMMAS REMAINDER . LESSP-REMAINDER-DIVISOR))))) 
(PUT1-LST (QUOTE TIMES-TIMES-LIST-DELETE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117194023. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PERM-TIMES-LIST) EVENT (PROVE-LEMMA TIMES-TIMES-LIST-DELETE (REWRITE) (IMPLIES (MEMBER X L) (EQUAL (TIMES X (TIMES-LIST (DELETE X L))) (TIMES-LIST L)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-TIMES . TIMES-TIMES-LIST-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE . TIMES-TIMES-LIST-DELETE) (IMMEDIATE-DEPENDENTS0 TIMES-LIST . TIMES-TIMES-LIST-DELETE) (LEMMAS TIMES . TIMES-TIMES-LIST-DELETE))))) 
(PUT1-LST (QUOTE PRIME-KEY-REWRITE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117193902. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LAW-OF-QUADRATIC-RECIPROCITY LEQ-QUOT-WINS1-2 ALL-DISTINCT-REFLECT-LIST-8 ALL-DISTINCT-REFLECT-LIST-7 ALL-NON-ZEROP-REFLECT-LIST COMPLEMENT-IS-UNIQUE EULER-1-5 N-O-I-LEMMA2 INVERSE-IS-UNIQUE CRYPT-INVERTS-STEP-1A ALL-NON-ZEROP-S PRIME-FACT COROLLARY-55 PRODUCT-DIVIDES PRIME-KEY-TRICK) EVENT (PROVE-LEMMA PRIME-KEY-REWRITE (REWRITE) (IMPLIES (PRIME P) (EQUAL (EQUAL (REMAINDER (TIMES A B) P) 0.) (OR (EQUAL (REMAINDER A P) 0.) (EQUAL (REMAINDER B P) 0.)))) ((USE (PRIME-KEY (X P) (B A) (Z B) (K (QUOTIENT (TIMES A B) P))) (REMAINDER-QUOTIENT (X (TIMES A B)) (Y P))) (DISABLE PRIME-KEY REMAINDER-QUOTIENT))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-TIMES . PRIME-KEY-REWRITE) (IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES-1 . PRIME-KEY-REWRITE) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-TIMES . PRIME-KEY-REWRITE) (IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-DIVIDES . PRIME-KEY-REWRITE) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . PRIME-KEY-REWRITE) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . PRIME-KEY-REWRITE) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO2 . PRIME-KEY-REWRITE) (IMMEDIATE-DEPENDENTS0 REMAINDER-0-CROCK . PRIME-KEY-REWRITE) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . PRIME-KEY-REWRITE) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-PLUS . PRIME-KEY-REWRITE) (IMMEDIATE-DEPENDENTS0 QUOTIENT-DIVIDES . PRIME-KEY-REWRITE) (IMMEDIATE-DEPENDENTS0 DIVIDES . PRIME-KEY-REWRITE) (IMMEDIATE-DEPENDENTS0 PRIME-KEY . PRIME-KEY-REWRITE) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT . PRIME-KEY-REWRITE) (IMMEDIATE-DEPENDENTS0 PRIME . PRIME-KEY-REWRITE) (LEMMAS EQUAL . PRIME-KEY-REWRITE))))) 
(PUT1-LST (QUOTE REMAINDER-DIFFERENCE-TIMES) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117192918. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EQUAL-MODS-TRICK-2) EVENT (PROVE-LEMMA REMAINDER-DIFFERENCE-TIMES (REWRITE) (EQUAL (REMAINDER (DIFFERENCE (TIMES P X) (TIMES P Y)) P) 0.) ((USE (DIVIDES-TIMES (X (DIFFERENCE X Y)) (Z P))) (DISABLE DIVIDES-TIMES))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . REMAINDER-DIFFERENCE-TIMES) (IMMEDIATE-DEPENDENTS0 TIMES-DIFFERENCE . REMAINDER-DIFFERENCE-TIMES) (IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES . REMAINDER-DIFFERENCE-TIMES) (IMMEDIATE-DEPENDENTS0 EUCLID . REMAINDER-DIFFERENCE-TIMES) (IMMEDIATE-DEPENDENTS0 DIVIDES-TIMES . REMAINDER-DIFFERENCE-TIMES) (LEMMAS REMAINDER . REMAINDER-DIFFERENCE-TIMES))))) 
(PUT1-LST (QUOTE LENGTH-DELETE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117192853. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (SUB1-LENGTH-DELETE PIGEON-HOLE-PRINCIPLE) EVENT (PROVE-LEMMA LENGTH-DELETE (REWRITE) (EQUAL (LENGTH (DELETE X L)) (IF (MEMBER X L) (LENGTH (CDR L)) (LENGTH L)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DELETE-NON-MEMBER . LENGTH-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE . LENGTH-DELETE) (LEMMAS LENGTH . LENGTH-DELETE))))) 
(PUT1-LST (QUOTE EQUAL-LENGTH-0) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117192841. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EQUAL-LENGTH-PERM) EVENT (PROVE-LEMMA EQUAL-LENGTH-0 (REWRITE) (EQUAL (EQUAL (LENGTH X) 0.) (NLISTP X))) LOCAL-UNDO-TUPLES ((LEMMAS EQUAL . EQUAL-LENGTH-0))))) 
(PUT1-LST (QUOTE REMAINDER-OF-1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117192839. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (REM-REFLECT-LIST-BASE-CASE TIMES-COMP-LIST-5 ALL-SQUARES-1 WILSON-THM TIMES-INVERSE-LIST T-I-L-LEMMA A-D-I-L-LEMMA1 INVERSE-1 ALL-NON-ZEROP-INVERSE-LIST INVERSE-OF-INVERSE N-O-I-LEMMA3 SUB1-P-IS-INVOLUTION S-P-I-I-LEMMA2 INVERSE-INVERTS-LEMMA REMAINDER-TIMES-LIST-S PRIME-FACT COROLLARY-55 EXP-MOD-IS-1 REMAINDER-EXP CRYPT-CORRECT) EVENT (PROVE-LEMMA REMAINDER-OF-1 (REWRITE) (EQUAL (REMAINDER 1. X) (IF (EQUAL X 1.) 0. 1.))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REMAINDER-0-CROCK . REMAINDER-OF-1) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . REMAINDER-OF-1) (LEMMAS REMAINDER . REMAINDER-OF-1))))) 
(PUT1-LST (QUOTE REMAINDER-TIMES-1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117192838. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PRIME-KEY-REWRITE) EVENT (PROVE-LEMMA REMAINDER-TIMES-1 (REWRITE) (EQUAL (REMAINDER (TIMES B (TIMES A C)) A) 0.)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-TIMES . REMAINDER-TIMES-1) (IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES . REMAINDER-TIMES-1) (LEMMAS REMAINDER . REMAINDER-TIMES-1))))) 
(PUT1-LST (QUOTE REMAINDER-PLUS-TIMES-2) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117192838. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (N-O-I-LEMMA3 SUB1-P-IS-INVOLUTION S-P-I-I-LEMMA2 EQUAL-MODS-TRICK-1 REMAINDER-EXP-LEMMA TIMES-MOD-1) EVENT (PROVE-LEMMA REMAINDER-PLUS-TIMES-2 (REWRITE) (EQUAL (REMAINDER (PLUS X (TIMES J I)) J) (REMAINDER X J))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . REMAINDER-PLUS-TIMES-2) (IMMEDIATE-DEPENDENTS0 REMAINDER-PLUS-TIMES-1 . REMAINDER-PLUS-TIMES-2) (LEMMAS REMAINDER . REMAINDER-PLUS-TIMES-2))))) 
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(PUT1-LST (QUOTE EXP-EXP) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117192800. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EULER-1-2 INVERSE-OF-INVERSE CRYPT-INVERTS EXP-MOD-IS-1) EVENT (PROVE-LEMMA EXP-EXP (REWRITE) (EQUAL (EXP (EXP I J) K) (EXP I (TIMES J K)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EXP-TIMES . EXP-EXP) (IMMEDIATE-DEPENDENTS0 EXP-PLUS . EXP-EXP) (IMMEDIATE-DEPENDENTS0 EXP-BY-0 . EXP-EXP) (IMMEDIATE-DEPENDENTS0 EXP-OF-1 . EXP-EXP) (IMMEDIATE-DEPENDENTS0 EXP . EXP-EXP) (LEMMAS EXP . EXP-EXP))))) 
(PUT1-LST (QUOTE EXP-TIMES) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117192754. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EULER-1-6 EULER-1-4 EULER-1-2 INVERSE-IS-UNIQUE EXP-EXP) EVENT (PROVE-LEMMA EXP-TIMES (REWRITE) (EQUAL (EXP (TIMES I J) K) (TIMES (EXP I K) (EXP J K)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-TIMES . EXP-TIMES) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-TIMES . EXP-TIMES) (IMMEDIATE-DEPENDENTS0 EXP-BY-0 . EXP-TIMES) (IMMEDIATE-DEPENDENTS0 EXP . EXP-TIMES) (LEMMAS EXP . EXP-TIMES))))) 
(PUT1-LST (QUOTE EXP-BY-0) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117192749. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (REM-REFLECT-LIST-BASE-CASE TIMES-COMP-LIST-5 N-Z-I-LEMMA INVERSE-OF-INVERSE INVERSE-INVERTS-LEMMA CRYPT-INVERTS-STEP-2 REMAINDER-TIMES-LIST-S REMAINDER-EXP CRYPT-CORRECT EXP-EXP EXP-TIMES) EVENT (PROVE-LEMMA EXP-BY-0 (REWRITE) (EQUAL (EXP X 0.) 1.)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EXP . EXP-BY-0) (LEMMAS EXP . EXP-BY-0))))) 
(PUT1-LST (QUOTE EXP-OF-1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117192749. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (INVERSE-1 EXP-MOD-IS-1 EXP-EXP) EVENT (PROVE-LEMMA EXP-OF-1 (REWRITE) (EQUAL (EXP 1. K) 1.)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EXP . EXP-OF-1) (LEMMAS EXP . EXP-OF-1))))) 
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(PUT1-LST (QUOTE TIMES-2) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117192745. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LEQ-QUOT-WINS1 LEQ-QUOT-TIMES EVEN3-EVEN RES1-REM-2 ALL-LESSEQP-REFLECT-LIST-1 EULER-2-4 EULER-1-2 EULER-1-1 INVERSE-IS-UNIQUE CRYPT-CORRECT) EVENT (PROVE-LEMMA TIMES-2 (REWRITE) (EQUAL (TIMES 2. X) (PLUS X X))) LOCAL-UNDO-TUPLES ((LEMMAS TIMES . TIMES-2))))) 
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(PUT1-LST (QUOTE 1SQUARE) (QUOTE NIL)) 
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(PUT1-LST (QUOTE 1EVEN) (QUOTE NIL)) 
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(PUT1-LST (QUOTE 1F91) (QUOTE NIL)) 
(PUT1-LST (QUOTE F91) (QUOTE (TYPE-PRESCRIPTION-LST ((F0 4. NIL)) LEMMAS ((REWRITE-RULE F91-IS-F0 NIL (EQUAL (F91 X) (F0 X)) NIL)) LINEAR-LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (X) (IF (LESSP (QUOTE 100.) X) (DIFFERENCE X (QUOTE 10.)) (F91 (F91 (PLUS X (QUOTE 11.)))))) LISP-CODE 1F91 INDUCTION-MACHINE ((TESTS-AND-CASES ((LESSP (QUOTE 100.) X)) NIL) (TESTS-AND-CASES ((NOT (LESSP (QUOTE 100.) X))) (((F91 (PLUS X (QUOTE 11.)))) ((PLUS X (QUOTE 11.)))))) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (X) (DIFFERENCE (QUOTE 101.) X) LESSP (DIFFERENCE-0 EQUAL EQUAL-DIFFERENCE-0 LESSP ZERO COMMUTATIVITY-OF-PLUS F0))) IDATE 840117192733. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1F91) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (F91-IS-F0) EVENT (REFLECT F91 F0-SATISFIES-F91-EQUATION ((LESSP (DIFFERENCE 101. X)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 F0-SATISFIES-F91-EQUATION . F91) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . F91) (IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE-0 . F91) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . F91) (IMMEDIATE-DEPENDENTS0 F0 . F91) (DCELL . 1F91))))) 
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(PUT1-LST (QUOTE 1F0) (QUOTE NIL)) 
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(PUT1-LST (QUOTE CORRECTNESS-OF-GET-SIMPLIFIER) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117191124. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-INTERPRETED-SIGMA INTERPRETER-INPUT-PATH EXECUTE1-OPENED-UP EXECUTE1-4 EXECUTE1-3 EXECUTE1-1) EVENT (PROVE-LEMMA CORRECTNESS-OF-GET-SIMPLIFIER ((META GET)) (IMPLIES (FORMP X) (AND (EQUAL (MEANING X A) (MEANING (GET-SIMPLIFIER X) A)) (FORMP (GET-SIMPLIFIER X))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 GET . CORRECTNESS-OF-GET-SIMPLIFIER) (IMMEDIATE-DEPENDENTS0 GET-SIMPLIFIER . CORRECTNESS-OF-GET-SIMPLIFIER) (LEMMAS GET . CORRECTNESS-OF-GET-SIMPLIFIER))))) 
(PUT1-LST (QUOTE 1GET-SIMPLIFIER) (QUOTE NIL)) 
(PUT1-LST (QUOTE GET-SIMPLIFIER) (QUOTE (TYPE-PRESCRIPTION-LST ((GET-SIMPLIFIER 16. T)) LEMMAS NIL SDEFN (LAMBDA (X) (IF (LISTP X) (IF (EQUAL (CAR X) (QUOTE GET)) (IF (LISTP (CAR (CDR X))) (IF (EQUAL (CAR (CAR (CDR X))) (QUOTE QUOTE)) (IF (EQUAL (CAR (CDR (CAR (CDR X)))) (QUOTE 0.)) (CONS (QUOTE CAR) (CONS (CAR (CDR (CDR X))) (QUOTE NIL))) (IF (NUMBERP (CAR (CDR (CAR (CDR X))))) (CONS (QUOTE GET) (CONS (CONS (QUOTE QUOTE) (CONS (SUB1 (CAR (CDR (CAR (CDR X))))) (QUOTE NIL))) (CONS (CONS (QUOTE CDR) (CONS (CAR (CDR (CDR X))) (QUOTE NIL))) (QUOTE NIL)))) (CONS (QUOTE CAR) (CONS (CAR (CDR (CDR X))) (QUOTE NIL))))) X) X) X) X)) LISP-CODE 1GET-SIMPLIFIER INDUCTION-MACHINE NIL LEVEL-NO 0. JUSTIFICATIONS NIL IDATE 840117191054. CONTROLLER-POCKETS NIL SATELLITES (1GET-SIMPLIFIER) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-GET-SIMPLIFIER) EVENT (DEFN GET-SIMPLIFIER (X) (IF (AND (LISTP X) (EQUAL (CAR X) (QUOTE GET)) (LISTP (CADR X)) (EQUAL (CAR (CADR X)) (QUOTE QUOTE))) (IF (ZEROP (CADR (CADR X))) (LIST (QUOTE CAR) (CADDR X)) (LIST (QUOTE GET) (LIST (QUOTE QUOTE) (SUB1 (CADR (CADR X)))) (LIST (QUOTE CDR) (CADDR X)))) X)) LOCAL-UNDO-TUPLES ((DCELL . 1GET-SIMPLIFIER))))) 
(PUT1-LST (QUOTE 1EXECUTE) (QUOTE NIL)) 
(PUT1-LST (QUOTE EXECUTE) (QUOTE (TYPE-PRESCRIPTION-LST ((EXECUTE -1. NIL T NIL)) LEMMAS ((REWRITE-RULE INTERPRETER-INPUT-PATH NIL (EQUAL (EXECUTE (QUOTE 0.) (CONS (QUOTE (MOVEI 7. 0.)) (CONS (QUOTE (SKIPNE 6.)) (CONS (QUOTE (STOP)) (CONS (QUOTE (ADD 7. 6.)) (CONS (QUOTE (SUBI 6. 1.)) (CONS (QUOTE (JUMPA 1.)) MEM)))))) CLK) (IF (EQUAL CLK (QUOTE 0.)) (CONS (QUOTE (MOVEI 7. 0.)) (CONS (QUOTE (SKIPNE 6.)) (CONS (QUOTE (STOP)) (CONS (QUOTE (ADD 7. 6.)) (CONS (QUOTE (SUBI 6. 1.)) (CONS (QUOTE (JUMPA 1.)) MEM)))))) (IF (NUMBERP CLK) (EXECUTE (QUOTE 1.) (CONS (QUOTE (MOVEI 7. 0.)) (CONS (QUOTE (SKIPNE 6.)) (CONS (QUOTE (STOP)) (CONS (QUOTE (ADD 7. 6.)) (CONS (QUOTE (SUBI 6. 1.)) (CONS (QUOTE (JUMPA 1.)) (CONS (CAR MEM) (CONS (QUOTE 0.) (CDR (CDR MEM)))))))))) CLK) (CONS (QUOTE (MOVEI 7. 0.)) (CONS (QUOTE (SKIPNE 6.)) (CONS (QUOTE (STOP)) (CONS (QUOTE (ADD 7. 6.)) (CONS (QUOTE (SUBI 6. 1.)) (CONS (QUOTE (JUMPA 1.)) MEM))))))))) NIL) (REWRITE-RULE EXECUTE-OPENED-UP ((NUMBERP PC) (NUMBERP CLK) (NOT (EQUAL CLK (QUOTE 0.)))) (EQUAL (EXECUTE PC MEM CLK) (EXECUTE (CAR (EXECUTE1 PC MEM (LENGTH MEM))) (CAR (CDR (EXECUTE1 PC MEM (LENGTH MEM)))) (SUB1 CLK))) NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE SELF-REFLEXIVE SELF-REFLEXIVE) SDEFN (LAMBDA (PC MEM CLK) (IF (EQUAL CLK (QUOTE 0.)) MEM (IF (NUMBERP CLK) (IF (NUMBERP PC) (EXECUTE (CAR (EXECUTE1 PC MEM (LENGTH MEM))) (CAR (CDR (EXECUTE1 PC MEM (LENGTH MEM)))) (SUB1 CLK)) MEM) MEM))) LISP-CODE 1EXECUTE INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP CLK)) NIL) (TESTS-AND-CASES ((NOT (ZEROP CLK)) (NUMBERP PC)) (((CAR (EXECUTE1 PC MEM (LENGTH MEM))) (CAR (CDR (EXECUTE1 PC MEM (LENGTH MEM)))) (SUB1 CLK)))) (TESTS-AND-CASES ((NOT (ZEROP CLK)) (NOT (NUMBERP PC))) NIL)) LEVEL-NO 3. JUSTIFICATIONS ((JUSTIFICATION (CLK) (COUNT CLK) LESSP (ZERO ZEROP COUNT-NUMBERP))) IDATE 840117191050. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (4.) SATELLITES (1EXECUTE) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-INTERPRETED-SIGMA INTERPRETER-INPUT-PATH INTERPRETER-LOOP-INVRT EXECUTE-OPENED-UP) EVENT (DEFN EXECUTE (PC MEM CLK) (IF (ZEROP CLK) MEM (IF (NUMBERP PC) (EXECUTE (CAR (EXECUTE1 PC MEM (LENGTH MEM))) (CADR (EXECUTE1 PC MEM (LENGTH MEM))) (SUB1 CLK)) MEM))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EXECUTE1 . EXECUTE) (DCELL . 1EXECUTE))))) 
(PUT1-LST (QUOTE 1EXECUTE1) (QUOTE NIL)) 
(PUT1-LST (QUOTE EXECUTE1) (QUOTE (TYPE-PRESCRIPTION-LST ((EXECUTE1 16. NIL NIL NIL)) LEMMAS ((REWRITE-RULE EXECUTE1-OPENED-UP ((NOT (LESSP MAX (QUOTE 6.))) (EQUAL (CAR MEM) (QUOTE (MOVEI 7. 0.))) (EQUAL (CAR (CDR MEM)) (QUOTE (SKIPNE 6.))) (EQUAL (CAR (CDR (CDR MEM))) (QUOTE (STOP))) (EQUAL (CAR (CDR (CDR (CDR MEM)))) (QUOTE (ADD 7. 6.))) (EQUAL (CAR (CDR (CDR (CDR (CDR MEM))))) (QUOTE (SUBI 6. 1.))) (EQUAL (CAR (CDR (CDR (CDR (CDR (CDR MEM)))))) (QUOTE (JUMPA 1.)))) (EQUAL (EXECUTE1 (QUOTE 1.) MEM MAX) (IF (EQUAL (CAR (CDR (CDR (CDR (CDR (CDR (CDR MEM))))))) (QUOTE 0.)) (CONS (QUOTE 1FALSE) (CONS (CONS (QUOTE (MOVEI 7. 0.)) (CONS (QUOTE (SKIPNE 6.)) (CONS (QUOTE (STOP)) (CONS (QUOTE (ADD 7. 6.)) (CONS (QUOTE (SUBI 6. 1.)) (CONS (QUOTE (JUMPA 1.)) (CDR (CDR (CDR (CDR (CDR (CDR MEM)))))))))))) (QUOTE NIL))) (IF (NUMBERP (CAR (CDR (CDR (CDR (CDR (CDR (CDR MEM)))))))) (CONS (QUOTE 1.) (CONS (CONS (QUOTE (MOVEI 7. 0.)) (CONS (QUOTE (SKIPNE 6.)) (CONS (QUOTE (STOP)) (CONS (QUOTE (ADD 7. 6.)) (CONS (QUOTE (SUBI 6. 1.)) (CONS (QUOTE (JUMPA 1.)) (CONS (SUB1 (CAR (CDR (CDR (CDR (CDR (CDR (CDR MEM)))))))) (CONS (PLUS (CAR (CDR (CDR (CDR (CDR (CDR (CDR MEM))))))) (CAR (CDR (CDR (CDR (CDR (CDR (CDR (CDR MEM))))))))) (CDR (CDR (CDR (CDR (CDR (CDR (CDR (CDR MEM)))))))))))))))) (QUOTE NIL))) (CONS (QUOTE 1FALSE) (CONS (CONS (QUOTE (MOVEI 7. 0.)) (CONS (QUOTE (SKIPNE 6.)) (CONS (QUOTE (STOP)) (CONS (QUOTE (ADD 7. 6.)) (CONS (QUOTE (SUBI 6. 1.)) (CONS (QUOTE (JUMPA 1.)) (CDR (CDR (CDR (CDR (CDR (CDR MEM)))))))))))) (QUOTE NIL)))))) NIL) (REWRITE-RULE EXECUTE1-4 ((NOT (LESSP MAX (QUOTE 6.)))) (EQUAL (EXECUTE1 (QUOTE 4.) (CONS (QUOTE (MOVEI 7. 0.)) (CONS (QUOTE (SKIPNE 6.)) (CONS (QUOTE (STOP)) (CONS (QUOTE (ADD 7. 6.)) (CONS (QUOTE (SUBI 6. 1.)) (CONS (QUOTE (JUMPA 1.)) L)))))) MAX) (EXECUTE1 (QUOTE 5.) (CONS (QUOTE (MOVEI 7. 0.)) (CONS (QUOTE (SKIPNE 6.)) (CONS (QUOTE (STOP)) (CONS (QUOTE (ADD 7. 6.)) (CONS (QUOTE (SUBI 6. 1.)) (CONS (QUOTE (JUMPA 1.)) (CONS (DIFFERENCE (CAR L) (QUOTE 1.)) (CDR L)))))))) MAX)) NIL) (REWRITE-RULE EXECUTE1-3 ((NOT (LESSP MAX (QUOTE 6.)))) (EQUAL (EXECUTE1 (QUOTE 3.) (CONS (QUOTE (MOVEI 7. 0.)) (CONS (QUOTE (SKIPNE 6.)) (CONS (QUOTE (STOP)) (CONS (QUOTE (ADD 7. 6.)) (CONS (QUOTE (SUBI 6. 1.)) (CONS (QUOTE (JUMPA 1.)) L)))))) MAX) (EXECUTE1 (QUOTE 4.) (CONS (QUOTE (MOVEI 7. 0.)) (CONS (QUOTE (SKIPNE 6.)) (CONS (QUOTE (STOP)) (CONS (QUOTE (ADD 7. 6.)) (CONS (QUOTE (SUBI 6. 1.)) (CONS (QUOTE (JUMPA 1.)) (CONS (CAR L) (CONS (PLUS (CAR L) (CAR (CDR L))) (CDR (CDR L)))))))))) MAX)) NIL) (REWRITE-RULE EXECUTE1-1 ((NOT (LESSP MAX (QUOTE 6.)))) (EQUAL (EXECUTE1 (QUOTE 1.) (CONS (QUOTE (MOVEI 7. 0.)) (CONS (QUOTE (SKIPNE 6.)) (CONS (QUOTE (STOP)) (CONS (QUOTE (ADD 7. 6.)) (CONS (QUOTE (SUBI 6. 1.)) (CONS (QUOTE (JUMPA 1.)) L)))))) MAX) (IF (EQUAL (CAR L) (QUOTE 0.)) (EXECUTE1 (QUOTE 2.) (CONS (QUOTE (MOVEI 7. 0.)) (CONS (QUOTE (SKIPNE 6.)) (CONS (QUOTE (STOP)) (CONS (QUOTE (ADD 7. 6.)) (CONS (QUOTE (SUBI 6. 1.)) (CONS (QUOTE (JUMPA 1.)) L)))))) MAX) (IF (NUMBERP (CAR L)) (EXECUTE1 (QUOTE 3.) (CONS (QUOTE (MOVEI 7. 0.)) (CONS (QUOTE (SKIPNE 6.)) (CONS (QUOTE (STOP)) (CONS (QUOTE (ADD 7. 6.)) (CONS (QUOTE (SUBI 6. 1.)) (CONS (QUOTE (JUMPA 1.)) L)))))) MAX) (EXECUTE1 (QUOTE 2.) (CONS (QUOTE (MOVEI 7. 0.)) (CONS (QUOTE (SKIPNE 6.)) (CONS (QUOTE (STOP)) (CONS (QUOTE (ADD 7. 6.)) (CONS (QUOTE (SUBI 6. 1.)) (CONS (QUOTE (JUMPA 1.)) L)))))) MAX)))) NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE QUESTIONABLE UNCHANGING) SDEFN (LAMBDA (PC MEM MAX) (IF (LESSP PC MAX) (IF (EQUAL (GET PC MEM) (QUOTE (STOP))) (CONS (QUOTE 1FALSE) (CONS MEM (QUOTE NIL))) (IF (EQUAL (CAR (GET PC MEM)) (QUOTE JUMPA)) (CONS (CAR (CDR (GET PC MEM))) (CONS MEM (QUOTE NIL))) (IF (EQUAL (CAR (GET PC MEM)) (QUOTE SKIPNE)) (IF (EQUAL (GET (CAR (CDR (GET PC MEM))) MEM) (QUOTE 0.)) (EXECUTE1 (ADD1 PC) MEM MAX) (IF (NUMBERP (GET (CAR (CDR (GET PC MEM))) MEM)) (EXECUTE1 (ADD1 (ADD1 PC)) MEM MAX) (EXECUTE1 (ADD1 PC) MEM MAX))) (IF (EQUAL (CAR (GET PC MEM)) (QUOTE SUBI)) (EXECUTE1 (ADD1 PC) (SET (CAR (CDR (GET PC MEM))) (DIFFERENCE (GET (CAR (CDR (GET PC MEM))) MEM) (CAR (CDR (CDR (GET PC MEM))))) MEM) MAX) (IF (EQUAL (CAR (GET PC MEM)) (QUOTE ADDI)) (EXECUTE1 (ADD1 PC) (SET (CAR (CDR (GET PC MEM))) (PLUS (CAR (CDR (CDR (GET PC MEM)))) (GET (CAR (CDR (GET PC MEM))) MEM)) MEM) MAX) (IF (EQUAL (CAR (GET PC MEM)) (QUOTE ADD)) (EXECUTE1 (ADD1 PC) (SET (CAR (CDR (GET PC MEM))) (PLUS (GET (CAR (CDR (CDR (GET PC MEM)))) MEM) (GET (CAR (CDR (GET PC MEM))) MEM)) MEM) MAX) (IF (EQUAL (CAR (GET PC MEM)) (QUOTE MOVEI)) (EXECUTE1 (ADD1 PC) (SET (CAR (CDR (GET PC MEM))) (CAR (CDR (CDR (GET PC MEM)))) MEM) MAX) (CONS (QUOTE 1FALSE) (CONS MEM (QUOTE NIL)))))))))) (CONS (QUOTE 1FALSE) (CONS MEM (QUOTE NIL))))) LISP-CODE 1EXECUTE1 INDUCTION-MACHINE ((TESTS-AND-CASES ((NOT (LESSP PC MAX))) NIL) (TESTS-AND-CASES ((LESSP PC MAX) (EQUAL (GET PC MEM) (QUOTE (STOP)))) NIL) (TESTS-AND-CASES ((LESSP PC MAX) (NOT (EQUAL (GET PC MEM) (QUOTE (STOP)))) (EQUAL (CAR (GET PC MEM)) (QUOTE JUMPA))) NIL) (TESTS-AND-CASES ((LESSP PC MAX) (NOT (EQUAL (GET PC MEM) (QUOTE (STOP)))) (NOT (EQUAL (CAR (GET PC MEM)) (QUOTE JUMPA))) (EQUAL (CAR (GET PC MEM)) (QUOTE SKIPNE)) (ZEROP (GET (CAR (CDR (GET PC MEM))) MEM))) (((ADD1 PC) MEM MAX))) (TESTS-AND-CASES ((LESSP PC MAX) (NOT (EQUAL (GET PC MEM) (QUOTE (STOP)))) (NOT (EQUAL (CAR (GET PC MEM)) (QUOTE JUMPA))) (EQUAL (CAR (GET PC MEM)) (QUOTE SKIPNE)) (NOT (ZEROP (GET (CAR (CDR (GET PC MEM))) MEM)))) (((ADD1 (ADD1 PC)) MEM MAX))) (TESTS-AND-CASES ((LESSP PC MAX) (NOT (EQUAL (GET PC MEM) (QUOTE (STOP)))) (NOT (EQUAL (CAR (GET PC MEM)) (QUOTE JUMPA))) (NOT (EQUAL (CAR (GET PC MEM)) (QUOTE SKIPNE))) (EQUAL (CAR (GET PC MEM)) (QUOTE SUBI))) (((ADD1 PC) (SET (CAR (CDR (GET PC MEM))) (DIFFERENCE (GET (CAR (CDR (GET PC MEM))) MEM) (CAR (CDR (CDR (GET PC MEM))))) MEM) MAX))) (TESTS-AND-CASES ((LESSP PC MAX) (NOT (EQUAL (GET PC MEM) (QUOTE (STOP)))) (NOT (EQUAL (CAR (GET PC MEM)) (QUOTE JUMPA))) (NOT (EQUAL (CAR (GET PC MEM)) (QUOTE SKIPNE))) (NOT (EQUAL (CAR (GET PC MEM)) (QUOTE SUBI))) (EQUAL (CAR (GET PC MEM)) (QUOTE ADDI))) (((ADD1 PC) (SET (CAR (CDR (GET PC MEM))) (PLUS (CAR (CDR (CDR (GET PC MEM)))) (GET (CAR (CDR (GET PC MEM))) MEM)) MEM) MAX))) (TESTS-AND-CASES ((LESSP PC MAX) (NOT ( ¬QUAL (GET PC MEM) (QUOTE (STOP)))) (NOT (EQUAL (CAR (GET PC MEM)) (QUOTE JUMPA))) (NOT (EQUAL (CAR (GET PC MEM)) (QUOTE SKIPNE))) (NOT (EQUAL (CAR (GET PC MEM)) (QUOTE SUBI))) (NOT (EQUAL (CAR (GET PC MEM)) (QUOTE ADDI))) (EQUAL (CAR (GET PC MEM)) (QUOTE ADD))) (((ADD1 PC) (SET (CAR (CDR (GET PC MEM))) (PLUS (GET (CAR (CDR (CDR (GET PC MEM)))) MEM) (GET (CAR (CDR (GET PC MEM))) MEM)) MEM) MAX))) (TESTS-AND-CASES ((LESSP PC MAX) (NOT (EQUAL (GET PC MEM) (QUOTE (STOP)))) (NOT (EQUAL (CAR (GET PC MEM)) (QUOTE JUMPA))) (NOT (EQUAL (CAR (GET PC MEM)) (QUOTE SKIPNE))) (NOT (EQUAL (CAR (GET PC MEM)) (QUOTE SUBI))) (NOT (EQUAL (CAR (GET PC MEM)) (QUOTE ADDI))) (NOT (EQUAL (CAR (GET PC MEM)) (QUOTE ADD))) (EQUAL (CAR (GET PC MEM)) (QUOTE MOVEI))) (((ADD1 PC) (SET (CDR (GET PC MEM))) (CAR (CDR (CDR (GET PC MEM)))) MEM) MAX))) (TESTS-AND-CASES ((LESSP PC MAX) (NOT (EQUAL (GET PC MEM) (QUOTE (STOP)))) (NOT (EQUAL (CAR (GET PC MEM)) (QUOTE JUMPA))) (NOT (EQUAL (CAR (GET PC MEM)) (QUOTE SKIPNE))) (NOT (EQUAL (CAR (GET PC MEM)) (QUOTE SUBI))) (NOT (EQUAL (CAR (GET PC MEM)) (QUOTE ADDI))) (NOT (EQUAL (CAR (GET PC MEM)) (QUOTE ADD))) (NOT (EQUAL (CAR (GET PC MEM)) (QUOTE MOVEI)))) NIL)) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (PC MAX) (DIFFERENCE MAX PC) LESSP (SUB1-ADD1 PLUS-EQUAL-0 NUMBERP EQUAL LESSP-PLUS-CANCELLATION3 ZEROP DIFFERENCE-0 DIFFERENCE-PLUS2 PLUS-RIGHT-ID2 GET SUB1-TYPE-RESTRICTION ADD1 DIFFERENCE LESSP ZERO))) IDATE 840117191042. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (5.) SATELLITES (1EXECUTE1) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (INTERPRETER-INPUT-PATH EXECUTE-OPENED-UP EXECUTE1-OPENED-UP EXECUTE1-4 EXECUTE1-3 EXECUTE1-1 EXECUTE) EVENT (DEFN EXECUTE1 (PC MEM MAX) (IF (NOT (LESSP PC MAX)) (LIST F MEM) (IF (EQUAL (GET PC MEM) (QUOTE (STOP))) (LIST F MEM) (IF (EQUAL (CAR (GET PC MEM)) (QUOTE JUMPA)) (LIST (CADR (GET PC MEM)) MEM) (IF (EQUAL (CAR (GET PC MEM)) (QUOTE SKIPNE)) (IF (ZEROP (GET (CADR (GET PC MEM)) MEM)) (EXECUTE1 (ADD1 PC) MEM MAX) (EXECUTE1 (ADD1 (ADD1 PC)) MEM MAX)) (IF (EQUAL (CAR (GET PC MEM)) (QUOTE SUBI)) (EXECUTE1 (ADD1 PC) (SET (CADR (GET PC MEM)) (DIFFERENCE (GET (CADR (GET PC MEM)) MEM) (CADDR (GET PC MEM))) MEM) MAX) (IF (EQUAL (CAR (GET PC MEM)) (QUOTE ADDI)) (EXECUTE1 (ADD1 PC) (SET (CADR (GET PC MEM)) (PLUS (CADDR (GET PC MEM)) (GET (CADR (GET PC MEM)) MEM)) MEM) MAX) (IF (EQUAL (CAR (GET PC MEM)) (QUOTE ADD)) (EXECUTE1 (ADD1 PC) (SET (CADR (GET PC MEM)) (PLUS (GET (CADDR (GET PC MEM)) MEM) (GET (CADR (GET PC MEM)) MEM)) MEM) MAX) (IF (EQUAL (CAR (GET PC MEM)) (QUOTE MOVEI)) (EXECUTE1 (ADD1 PC) (SET (CADR (GET PC MEM)) (CADDR (GET PC MEM)) MEM) MAX) (LIST F MEM))))))))) ((LESSP (DIFFERENCE MAX PC)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SET . EXECUTE1) (IMMEDIATE-DEPENDENTS0 PLUS-EQUAL-0 . EXECUTE1) (IMMEDIATE-DEPENDENTS0 LESSP-PLUS-CANCELLATION3 . EXECUTE1) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . EXECUTE1) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-PLUS2 . EXECUTE1) (IMMEDIATE-DEPENDENTS0 PLUS-RIGHT-ID2 . EXECUTE1) (IMMEDIATE-DEPENDENTS0 GET . EXECUTE1) (DCELL . 1EXECUTE1))))) 
(PUT1-LST (QUOTE GET-SET) (QUOTE (IDATE 840117191041. EVENT (PROVE-LEMMA GET-SET (REWRITE) (EQUAL (GET J (SET I VAL MEM)) (IF (EQP J I) VAL (GET J MEM)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQP . GET-SET) (IMMEDIATE-DEPENDENTS0 SET . GET-SET) (IMMEDIATE-DEPENDENTS0 GET . GET-SET) (LEMMAS GET . GET-SET))))) 
(PUT1-LST (QUOTE 1GET) (QUOTE NIL)) 
(PUT1-LST (QUOTE GET) (QUOTE (TYPE-PRESCRIPTION-LST ((GET -1. NIL NIL)) LEMMAS ((REWRITE-RULE CORRECTNESS-OF-GET-SIMPLIFIER NIL 1GET-SIMPLIFIER NIL) (REWRITE-RULE GET-SET NIL (EQUAL (GET J (SET I VAL MEM)) (IF (EQP J I) VAL (GET J MEM))) NIL)) LINEAR-LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE SELF-REFLEXIVE) SDEFN (LAMBDA (ADDR MEM) (IF (EQUAL ADDR (QUOTE 0.)) (CAR MEM) (IF (NUMBERP ADDR) (GET (SUB1 ADDR) (CDR MEM)) (CAR MEM)))) LISP-CODE 1GET INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP ADDR)) NIL) (TESTS-AND-CASES ((NOT (ZEROP ADDR))) (((SUB1 ADDR) (CDR MEM))))) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (ADDR) (COUNT ADDR) LESSP (ZERO ZEROP COUNT-NUMBERP))) IDATE 840117191027. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1GET) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-INTERPRETED-SIGMA CORRECTNESS-OF-GET-SIMPLIFIER EXECUTE1 GET-SET) EVENT (DEFN GET (ADDR MEM) (IF (ZEROP ADDR) (CAR MEM) (GET (SUB1 ADDR) (CDR MEM)))) LOCAL-UNDO-TUPLES ((DCELL . 1GET))))) 
(PUT1-LST (QUOTE 1SET) (QUOTE NIL)) 
(PUT1-LST (QUOTE SET) (QUOTE (TYPE-PRESCRIPTION-LST ((SET 16. NIL NIL NIL)) LEMMAS ((REWRITE-RULE CORRECTNESS-OF-SET-SIMPLIFIER NIL 1SET-SIMPLIFIER NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE UNCHANGING SELF-REFLEXIVE) SDEFN (LAMBDA (ADDR VAL MEM) (IF (EQUAL ADDR (QUOTE 0.)) (CONS VAL (CDR MEM)) (IF (NUMBERP ADDR) (CONS (CAR MEM) (SET (SUB1 ADDR) VAL (CDR MEM))) (CONS VAL (CDR MEM))))) LISP-CODE 1SET INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP ADDR)) NIL) (TESTS-AND-CASES ((NOT (ZEROP ADDR))) (((SUB1 ADDR) VAL (CDR MEM))))) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (ADDR) (COUNT ADDR) LESSP (ZERO ZEROP COUNT-NUMBERP))) IDATE 840117191027. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1SET) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-SET-SIMPLIFIER EXECUTE1 GET-SET) EVENT (DEFN SET (ADDR VAL MEM) (IF (ZEROP ADDR) (CONS VAL (CDR MEM)) (CONS (CAR MEM) (SET (SUB1 ADDR) VAL (CDR MEM))))) LOCAL-UNDO-TUPLES ((DCELL . 1SET))))) 
(PUT1-LST (QUOTE SIGMA-OUTPUT-PATH) (QUOTE (IDATE 840117191027. EVENT (PROVE-LEMMA SIGMA-OUTPUT-PATH NIL (IMPLIES (AND (ZEROP I) (LEQ I K)) (EQUAL (SIGMA I K) (SIGMA 0. K)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SIGMA . SIGMA-OUTPUT-PATH))))) 
(PUT1-LST (QUOTE SIGMA-LOOP-INVRT) (QUOTE (IDATE 840117191023. EVENT (PROVE-LEMMA SIGMA-LOOP-INVRT NIL (IMPLIES (AND (NOT (ZEROP I)) (LEQ I K)) (AND (EQUAL (PLUS (SIGMA I K) I) (SIGMA (SUB1 I) K)) (LEQ (SUB1 I) K)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-PLUS . SIGMA-LOOP-INVRT) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-PLUS . SIGMA-LOOP-INVRT) (IMMEDIATE-DEPENDENTS0 PLUS-ADD1 . SIGMA-LOOP-INVRT) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . SIGMA-LOOP-INVRT) (IMMEDIATE-DEPENDENTS0 SIGMA . SIGMA-LOOP-INVRT))))) 
(PUT1-LST (QUOTE SIGMA-INPUT-PATH) (QUOTE (IDATE 840117190957. EVENT (PROVE-LEMMA SIGMA-INPUT-PATH NIL (AND (EQUAL 0. (SIGMA K K)) (LEQ K K))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SIGMA . SIGMA-INPUT-PATH))))) 
(PUT1-LST (QUOTE CORRECTNESS-OF-FUNCTIONAL-SIGMA) (QUOTE (IDATE 840117190955. EVENT (PROVE-LEMMA CORRECTNESS-OF-FUNCTIONAL-SIGMA NIL (EQUAL (PROG-TRANS-OF-SIGMA I 0.) (SIGMA 0. I))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 FUNCTIONAL-LOOP-INVRT . CORRECTNESS-OF-FUNCTIONAL-SIGMA) (IMMEDIATE-DEPENDENTS0 SIGMA . CORRECTNESS-OF-FUNCTIONAL-SIGMA) (IMMEDIATE-DEPENDENTS0 PROG-TRANS-OF-SIGMA . CORRECTNESS-OF-FUNCTIONAL-SIGMA))))) 
(PUT1-LST (QUOTE FUNCTIONAL-LOOP-INVRT) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117190955. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-FUNCTIONAL-SIGMA) EVENT (PROVE-LEMMA FUNCTIONAL-LOOP-INVRT (REWRITE) (IMPLIES (NUMBERP AC) (EQUAL (PROG-TRANS-OF-SIGMA I AC) (PLUS AC (SIGMA 0. I))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-PLUS . FUNCTIONAL-LOOP-INVRT) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL . FUNCTIONAL-LOOP-INVRT) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . FUNCTIONAL-LOOP-INVRT) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-1 . FUNCTIONAL-LOOP-INVRT) (IMMEDIATE-DEPENDENTS0 SIGMA . FUNCTIONAL-LOOP-INVRT) (IMMEDIATE-DEPENDENTS0 PROG-TRANS-OF-SIGMA . FUNCTIONAL-LOOP-INVRT) (LEMMAS PROG-TRANS-OF-SIGMA . FUNCTIONAL-LOOP-INVRT))))) 
(PUT1-LST (QUOTE 1PROG-TRANS-OF-SIGMA) (QUOTE NIL)) 
(PUT1-LST (QUOTE PROG-TRANS-OF-SIGMA) (QUOTE (TYPE-PRESCRIPTION-LST ((PROG-TRANS-OF-SIGMA 4. NIL T)) LEMMAS ((REWRITE-RULE FUNCTIONAL-LOOP-INVRT ((NUMBERP AC)) (EQUAL (PROG-TRANS-OF-SIGMA I AC) (PLUS AC (SIGMA (QUOTE 0.) I))) NIL)) LINEAR-LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE SELF-REFLEXIVE) SDEFN (LAMBDA (I AC) (IF (EQUAL I (QUOTE 0.)) AC (IF (NUMBERP I) (PROG-TRANS-OF-SIGMA (DIFFERENCE I (QUOTE 1.)) (PLUS AC I)) AC))) LISP-CODE 1PROG-TRANS-OF-SIGMA INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP I)) NIL) (TESTS-AND-CASES ((NOT (ZEROP I))) (((DIFFERENCE I (QUOTE 1.)) (PLUS AC I))))) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (I) (COUNT I) LESSP (ZERO ZEROP DIFFERENCE-1 COUNT-NUMBERP))) IDATE 840117190944. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1PROG-TRANS-OF-SIGMA) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-FUNCTIONAL-SIGMA FUNCTIONAL-LOOP-INVRT) EVENT (DEFN PROG-TRANS-OF-SIGMA (I AC) (IF (ZEROP I) AC (PROG-TRANS-OF-SIGMA (DIFFERENCE I 1.) (PLUS AC I)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIFFERENCE-1 . PROG-TRANS-OF-SIGMA) (DCELL . 1PROG-TRANS-OF-SIGMA))))) 
(PUT1-LST (QUOTE DIFFERENCE-1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117190944. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EULER-2-3 WILSON-THM W-T-LEMMA INVERSE-LIST-FACT PERM-POSITIVES-INVERSE-LIST T-I-L-LEMMA4 INVERSE-1 SUBSETP-POSITIVES BOUNDED-INVERSE-LIST B-I-LEMMA1 N-Z-I-LEMMA INVERSE-OF-INVERSE I-O-I-LEMMA N-O-I-LEMMA4 N-O-I-LEMMA3 N-O-I-LEMMA1 INVERSE-IS-UNIQUE INVERSE-INVERTS-LEMMA DIFFERENCE-2 EXECUTE1-OPENED-UP EXECUTE1-4 FUNCTIONAL-LOOP-INVRT PROG-TRANS-OF-SIGMA) EVENT (PROVE-LEMMA DIFFERENCE-1 (REWRITE) (EQUAL (DIFFERENCE X 1.) (SUB1 X))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . DIFFERENCE-1) (LEMMAS DIFFERENCE . DIFFERENCE-1))))) 
(PUT1-LST (QUOTE 1SIGMA) (QUOTE NIL)) 
(PUT1-LST (QUOTE SIGMA) (QUOTE (TYPE-PRESCRIPTION-LST ((SIGMA 4. NIL NIL)) LEMMAS ((REWRITE-RULE SIGMA-IS-HALF-PRODUCT NIL (EQUAL (SIGMA (QUOTE 0.) I) (QUOTIENT (TIMES I (ADD1 I)) (QUOTE 2.))) NIL)) LINEAR-LEMMAS NIL QUICK-BLOCK-INFO (UNCHANGING SELF-REFLEXIVE) SDEFN (LAMBDA (M N) (IF (LESSP M N) (PLUS N (SIGMA M (SUB1 N))) (QUOTE 0.))) LISP-CODE 1SIGMA INDUCTION-MACHINE ((TESTS-AND-CASES ((LESSP M N)) ((M (SUB1 N)))) (TESTS-AND-CASES ((NOT (LESSP M N))) NIL)) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (N) (COUNT N) LESSP (ZERO COUNT-NOT-LESSP COUNT-NUMBERP))) IDATE 840117190940. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (2.) SATELLITES (1SIGMA) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (SIGMA-IS-HALF-PRODUCT CORRECTNESS-OF-INTERPRETED-SIGMA INTERPRETER-LOOP-INVRT SIGMA-OUTPUT-PATH SIGMA-LOOP-INVRT SIGMA-INPUT-PATH CORRECTNESS-OF-FUNCTIONAL-SIGMA FUNCTIONAL-LOOP-INVRT) EVENT (DEFN SIGMA (M N) (IF (LESSP M N) (PLUS N (SIGMA M (SUB1 N))) 0.)) LOCAL-UNDO-TUPLES ((DCELL . 1SIGMA))))) 
(PUT1-LST (QUOTE COUNT-LIST-SORT2) (QUOTE (IDATE 840117190939. EVENT (PROVE-LEMMA COUNT-LIST-SORT2 NIL (EQUAL (COUNT-LIST A (SORT2 L)) (COUNT-LIST A L))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ADDTOLIST2 . COUNT-LIST-SORT2) (IMMEDIATE-DEPENDENTS0 PLISTP . COUNT-LIST-SORT2) (IMMEDIATE-DEPENDENTS0 ORDERED2 . COUNT-LIST-SORT2) (IMMEDIATE-DEPENDENTS0 SORT2-GEN . COUNT-LIST-SORT2) (IMMEDIATE-DEPENDENTS0 SORT2 . COUNT-LIST-SORT2) (IMMEDIATE-DEPENDENTS0 COUNT-LIST . COUNT-LIST-SORT2))))) 
(PUT1-LST (QUOTE DSORT-SORT2) (QUOTE (IDATE 840117190833. EVENT (PROVE-LEMMA DSORT-SORT2 (REWRITE) (EQUAL (DSORT X) (SORT2 X))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SORT2-DELETE . DSORT-SORT2) (IMMEDIATE-DEPENDENTS0 SORT2-DELETE-CONS . DSORT-SORT2) (IMMEDIATE-DEPENDENTS0 MEMBER-MAXIMUM . DSORT-SORT2) (IMMEDIATE-DEPENDENTS0 LESSP-DELETE-REWRITE . DSORT-SORT2) (IMMEDIATE-DEPENDENTS0 SORT2 . DSORT-SORT2) (IMMEDIATE-DEPENDENTS0 DSORT . DSORT-SORT2) (LEMMAS DSORT . DSORT-SORT2))))) 
(PUT1-LST (QUOTE SORT2-DELETE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117190829. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (DSORT-SORT2) EVENT (PROVE-LEMMA SORT2-DELETE (REWRITE) (EQUAL (SORT2 (DELETE X L)) (DELETE X (SORT2 L)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DELETE-NON-MEMBER . SORT2-DELETE) (IMMEDIATE-DEPENDENTS0 ADDTOLIST2-DELETE . SORT2-DELETE) (IMMEDIATE-DEPENDENTS0 SORT2-GEN-2 . SORT2-DELETE) (IMMEDIATE-DEPENDENTS0 SORT2-GEN-1 . SORT2-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE-ADDTOLIST2 . SORT2-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE . SORT2-DELETE) (IMMEDIATE-DEPENDENTS0 SORT2 . SORT2-DELETE) (LEMMAS SORT2 . SORT2-DELETE))))) 
(PUT1-LST (QUOTE SORT2-DELETE-CONS) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117190824. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (DSORT-SORT2) EVENT (PROVE-LEMMA SORT2-DELETE-CONS (REWRITE) (IMPLIES (LISTP X) (EQUAL (CONS (MAXIMUM X) (DELETE (MAXIMUM X) (SORT2 X))) (SORT2 X)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DELETE-NON-MEMBER . SORT2-DELETE-CONS) (IMMEDIATE-DEPENDENTS0 PLISTP . SORT2-DELETE-CONS) (IMMEDIATE-DEPENDENTS0 ORDERED2 . SORT2-DELETE-CONS) (IMMEDIATE-DEPENDENTS0 LESSP-MAXIMUM-ADDTOLIST2 . SORT2-DELETE-CONS) (IMMEDIATE-DEPENDENTS0 SORT2-GEN . SORT2-DELETE-CONS) (IMMEDIATE-DEPENDENTS0 ADDTOLIST2 . SORT2-DELETE-CONS) (IMMEDIATE-DEPENDENTS0 SORT2 . SORT2-DELETE-CONS) (IMMEDIATE-DEPENDENTS0 DELETE . SORT2-DELETE-CONS) (IMMEDIATE-DEPENDENTS0 MAXIMUM . SORT2-DELETE-CONS) (LEMMAS CONS . SORT2-DELETE-CONS))))) 
(PUT1-LST (QUOTE LESSP-MAXIMUM-ADDTOLIST2) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117190733. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (SORT2-DELETE-CONS) EVENT (PROVE-LEMMA LESSP-MAXIMUM-ADDTOLIST2 (REWRITE) (IMPLIES (NOT (LESSP V (MAXIMUM Z))) (EQUAL (ADDTOLIST2 V (SORT2 Z)) (CONS V (SORT2 Z))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ADDTOLIST2-KLUDGE . LESSP-MAXIMUM-ADDTOLIST2) (IMMEDIATE-DEPENDENTS0 SORT2 . LESSP-MAXIMUM-ADDTOLIST2) (IMMEDIATE-DEPENDENTS0 ADDTOLIST2 . LESSP-MAXIMUM-ADDTOLIST2) (IMMEDIATE-DEPENDENTS0 MAXIMUM . LESSP-MAXIMUM-ADDTOLIST2) (LEMMAS ADDTOLIST2 . LESSP-MAXIMUM-ADDTOLIST2))))) 
(PUT1-LST (QUOTE ADDTOLIST2-KLUDGE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117190723. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LESSP-MAXIMUM-ADDTOLIST2) EVENT (PROVE-LEMMA ADDTOLIST2-KLUDGE (REWRITE) (IMPLIES (AND (NOT (LESSP V W)) (EQUAL (ADDTOLIST2 V Y) (CONS V Y))) (EQUAL (ADDTOLIST2 V (ADDTOLIST2 W Y)) (CONS V (ADDTOLIST2 W Y))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ADDTOLIST2 . ADDTOLIST2-KLUDGE) (LEMMAS ADDTOLIST2 . ADDTOLIST2-KLUDGE))))) 
(PUT1-LST (QUOTE DELETE-ADDTOLIST2) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117190713. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (SORT2-DELETE) EVENT (PROVE-LEMMA DELETE-ADDTOLIST2 (REWRITE) (IMPLIES (PLISTP Y) (EQUAL (DELETE V (ADDTOLIST2 V Y)) Y))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ADDTOLIST2 . DELETE-ADDTOLIST2) (IMMEDIATE-DEPENDENTS0 DELETE . DELETE-ADDTOLIST2) (IMMEDIATE-DEPENDENTS0 PLISTP . DELETE-ADDTOLIST2) (LEMMAS DELETE . DELETE-ADDTOLIST2))))) 
(PUT1-LST (QUOTE ADDTOLIST2-DELETE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117190710. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (SORT2-DELETE) EVENT (PROVE-LEMMA ADDTOLIST2-DELETE (REWRITE) (IMPLIES (AND (PLISTP Y) (ORDERED2 Y) (NOT (EQUAL X V))) (EQUAL (ADDTOLIST2 V (DELETE X Y)) (DELETE X (ADDTOLIST2 V Y))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DELETE-NON-MEMBER . ADDTOLIST2-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE . ADDTOLIST2-DELETE) (IMMEDIATE-DEPENDENTS0 ADDTOLIST2 . ADDTOLIST2-DELETE) (IMMEDIATE-DEPENDENTS0 ORDERED2 . ADDTOLIST2-DELETE) (IMMEDIATE-DEPENDENTS0 PLISTP . ADDTOLIST2-DELETE) (LEMMAS ADDTOLIST2 . ADDTOLIST2-DELETE))))) 
(PUT1-LST (QUOTE SORT2-GEN) (QUOTE (IDATE 840117190620. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (COUNT-LIST-SORT2 SORT2-DELETE-CONS) EVENT (PROVE-LEMMA SORT2-GEN (GENERALIZE) (AND (PLISTP (SORT2 X)) (ORDERED2 (SORT2 X)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SORT2-GEN-2 . SORT2-GEN) (IMMEDIATE-DEPENDENTS0 SORT2-GEN-1 . SORT2-GEN) (IMMEDIATE-DEPENDENTS0 ORDERED2 . SORT2-GEN) (IMMEDIATE-DEPENDENTS0 SORT2 . SORT2-GEN) (IMMEDIATE-DEPENDENTS0 PLISTP . SORT2-GEN) (GENERALIZE-LEMMAS NIL . SORT2-GEN))))) 
(PUT1-LST (QUOTE SORT2-GEN-2) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117190619. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (SORT2-DELETE SORT2-GEN) EVENT (PROVE-LEMMA SORT2-GEN-2 (REWRITE) (ORDERED2 (SORT2 X))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ADDTOLIST2 . SORT2-GEN-2) (IMMEDIATE-DEPENDENTS0 SORT2 . SORT2-GEN-2) (IMMEDIATE-DEPENDENTS0 ORDERED2 . SORT2-GEN-2) (LEMMAS ORDERED2 . SORT2-GEN-2))))) 
(PUT1-LST (QUOTE SORT2-GEN-1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117190559. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (SORT2-DELETE SORT2-GEN) EVENT (PROVE-LEMMA SORT2-GEN-1 (REWRITE) (PLISTP (SORT2 X))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ADDTOLIST2 . SORT2-GEN-1) (IMMEDIATE-DEPENDENTS0 SORT2 . SORT2-GEN-1) (IMMEDIATE-DEPENDENTS0 PLISTP . SORT2-GEN-1) (LEMMAS PLISTP . SORT2-GEN-1))))) 
(PUT1-LST (QUOTE 1SORT2) (QUOTE NIL)) 
(PUT1-LST (QUOTE SORT2) (QUOTE (TYPE-PRESCRIPTION-LST ((SORT2 24. NIL)) LEMMAS ((REWRITE-RULE SORT2-DELETE NIL (EQUAL (SORT2 (DELETE X L)) (DELETE X (SORT2 L))) NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (L) (IF (LISTP L) (ADDTOLIST2 (CAR L) (SORT2 (CDR L))) (QUOTE NIL))) LISP-CODE 1SORT2 INDUCTION-MACHINE ((TESTS-AND-CASES ((NLISTP L)) NIL) (TESTS-AND-CASES ((NOT (NLISTP L))) (((CDR L))))) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (L) (COUNT L) LESSP (CDR-LESSP NLISTP ZERO CDR-LESSEQP))) IDATE 840117190551. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1SORT2) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (COUNT-LIST-SORT2 DSORT-SORT2 SORT2-DELETE SORT2-DELETE-CONS LESSP-MAXIMUM-ADDTOLIST2 SORT2-GEN SORT2-GEN-2 SORT2-GEN-1) EVENT (DEFN SORT2 (L) (IF (NLISTP L) NIL (ADDTOLIST2 (CAR L) (SORT2 (CDR L))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ADDTOLIST2 . SORT2) (DCELL . 1SORT2))))) 
(PUT1-LST (QUOTE 1ADDTOLIST2) (QUOTE NIL)) 
(PUT1-LST (QUOTE ADDTOLIST2) (QUOTE (TYPE-PRESCRIPTION-LST ((ADDTOLIST2 16. NIL NIL)) LEMMAS ((REWRITE-RULE LESSP-MAXIMUM-ADDTOLIST2 ((NOT (LESSP V (MAXIMUM Z)))) (EQUAL (ADDTOLIST2 V (SORT2 Z)) (CONS V (SORT2 Z))) NIL) (REWRITE-RULE ADDTOLIST2-KLUDGE ((NOT (LESSP V W)) (EQUAL (ADDTOLIST2 V Y) (CONS V Y))) (EQUAL (ADDTOLIST2 V (ADDTOLIST2 W Y)) (CONS V (ADDTOLIST2 W Y))) NIL) (REWRITE-RULE ADDTOLIST2-DELETE ((PLISTP Y) (ORDERED2 Y) (NOT (EQUAL X V))) (EQUAL (ADDTOLIST2 V (DELETE X Y)) (DELETE X (ADDTOLIST2 V Y))) NIL)) QUICK-BLOCK-INFO (UNCHANGING SELF-REFLEXIVE) SDEFN (LAMBDA (X L) (IF (LISTP L) (IF (LESSP X (CAR L)) (CONS (CAR L) (ADDTOLIST2 X (CDR L))) (CONS X L)) (CONS X (QUOTE NIL)))) LISP-CODE 1ADDTOLIST2 INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP L) (LESSP X (CAR L))) ((X (CDR L)))) (TESTS-AND-CASES ((LISTP L) (NOT (LESSP X (CAR L)))) NIL) (TESTS-AND-CASES ((NOT (LISTP L))) NIL)) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (L) (COUNT L) LESSP (ZERO CDR-LESSP))) IDATE 840117190551. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (2.) SATELLITES (1ADDTOLIST2) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (COUNT-LIST-SORT2 SORT2-DELETE-CONS LESSP-MAXIMUM-ADDTOLIST2 ADDTOLIST2-KLUDGE DELETE-ADDTOLIST2 ADDTOLIST2-DELETE SORT2-GEN-2 SORT2-GEN-1 SORT2) EVENT (DEFN ADDTOLIST2 (X L) (IF (LISTP L) (IF (LESSP X (CAR L)) (CONS (CAR L) (ADDTOLIST2 X (CDR L))) (CONS X L)) (CONS X NIL))) LOCAL-UNDO-TUPLES ((DCELL . 1ADDTOLIST2))))) 
(PUT1-LST (QUOTE 1DSORT) (QUOTE NIL)) 
(PUT1-LST (QUOTE DSORT) (QUOTE (TYPE-PRESCRIPTION-LST ((DSORT 24. NIL)) LEMMAS ((REWRITE-RULE DSORT-SORT2 NIL (EQUAL (DSORT X) (SORT2 X)) NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (L) (IF (LISTP L) (CONS (MAXIMUM L) (DSORT (DELETE (MAXIMUM L) L))) (QUOTE NIL))) LISP-CODE 1DSORT INDUCTION-MACHINE ((TESTS-AND-CASES ((NLISTP L)) NIL) (TESTS-AND-CASES ((NOT (NLISTP L))) (((DELETE (MAXIMUM L) L))))) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (L) (COUNT L) LESSP (NLISTP MEMBER-MAXIMUM LESSP-DELETE-REWRITE))) IDATE 840117190550. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1DSORT) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (DSORT-SORT2) EVENT (DEFN DSORT (L) (IF (NLISTP L) NIL (CONS (MAXIMUM L) (DSORT (DELETE (MAXIMUM L) L))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DELETE . DSORT) (IMMEDIATE-DEPENDENTS0 MAXIMUM . DSORT) (IMMEDIATE-DEPENDENTS0 MEMBER-MAXIMUM . DSORT) (IMMEDIATE-DEPENDENTS0 LESSP-DELETE-REWRITE . DSORT) (DCELL . 1DSORT))))) 
(PUT1-LST (QUOTE 1ORDERED2) (QUOTE NIL)) 
(PUT1-LST (QUOTE ORDERED2) (QUOTE (TYPE-PRESCRIPTION-LST ((ORDERED2 3. NIL)) LEMMAS ((REWRITE-RULE SORT2-GEN-2 NIL (ORDERED2 (SORT2 X)) NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (L) (IF (LISTP L) (IF (LISTP (CDR L)) (IF (LESSP (CAR L) (CAR (CDR L))) (QUOTE 1FALSE) (ORDERED2 (CDR L))) (QUOTE 1TRUE)) (QUOTE 1TRUE))) LISP-CODE 1ORDERED2 INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP L) (LISTP (CDR L)) (LESSP (CAR L) (CAR (CDR L)))) NIL) (TESTS-AND-CASES ((LISTP L) (LISTP (CDR L)) (NOT (LESSP (CAR L) (CAR (CDR L))))) (((CDR L)))) (TESTS-AND-CASES ((LISTP L) (NOT (LISTP (CDR L)))) NIL) (TESTS-AND-CASES ((NOT (LISTP L))) NIL)) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (L) (COUNT L) LESSP (ZERO CDR-LESSP))) IDATE 840117190548. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1ORDERED2) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (COUNT-LIST-SORT2 SORT2-DELETE-CONS ADDTOLIST2-DELETE SORT2-GEN SORT2-GEN-2) EVENT (DEFN ORDERED2 (L) (IF (LISTP L) (IF (LISTP (CDR L)) (IF (LESSP (CAR L) (CADR L)) F (ORDERED2 (CDR L))) T) T)) LOCAL-UNDO-TUPLES ((DCELL . 1ORDERED2))))) 
(PUT1-LST (QUOTE LESSP-DELETE-REWRITE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117190548. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (DSORT-SORT2 DSORT) EVENT (PROVE-LEMMA LESSP-DELETE-REWRITE (REWRITE) (EQUAL (LESSP (COUNT (DELETE X L)) (COUNT L)) (MEMBER X L))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DELETE-NON-MEMBER . LESSP-DELETE-REWRITE) (IMMEDIATE-DEPENDENTS0 LESSP-COUNT-DELETE . LESSP-DELETE-REWRITE) (IMMEDIATE-DEPENDENTS0 EQUAL-LESSP . LESSP-DELETE-REWRITE) (IMMEDIATE-DEPENDENTS0 DELETE . LESSP-DELETE-REWRITE) (LEMMAS LESSP . LESSP-DELETE-REWRITE))))) 
(PUT1-LST (QUOTE MEMBER-MAXIMUM) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117190547. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (DSORT-SORT2 DSORT) EVENT (PROVE-LEMMA MEMBER-MAXIMUM (REWRITE) (IMPLIES (LISTP X) (MEMBER (MAXIMUM X) X))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 MAXIMUM . MEMBER-MAXIMUM) (LEMMAS MEMBER . MEMBER-MAXIMUM))))) 
(PUT1-LST (QUOTE 1MAXIMUM) (QUOTE NIL)) 
(PUT1-LST (QUOTE MAXIMUM) (QUOTE (TYPE-PRESCRIPTION-LST ((MAXIMUM -1. NIL)) LEMMAS NIL LINEAR-LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (L) (IF (LISTP L) (IF (LESSP (CAR L) (MAXIMUM (CDR L))) (MAXIMUM (CDR L)) (CAR L)) (QUOTE 0.))) LISP-CODE 1MAXIMUM INDUCTION-MACHINE ((TESTS-AND-CASES ((NLISTP L)) NIL) (TESTS-AND-CASES ((NOT (NLISTP L)) (LESSP (CAR L) (MAXIMUM (CDR L)))) (((CDR L)))) (TESTS-AND-CASES ((NOT (NLISTP L)) (NOT (LESSP (CAR L) (MAXIMUM (CDR L))))) (((CDR L))))) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (L) (COUNT L) LESSP (CDR-LESSP NLISTP ZERO CDR-LESSEQP))) IDATE 840117190541. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1MAXIMUM) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (SORT2-DELETE-CONS LESSP-MAXIMUM-ADDTOLIST2 DSORT MEMBER-MAXIMUM) EVENT (DEFN MAXIMUM (L) (IF (NLISTP L) 0. (IF (LESSP (CAR L) (MAXIMUM (CDR L))) (MAXIMUM (CDR L)) (CAR L)))) LOCAL-UNDO-TUPLES ((DCELL . 1MAXIMUM))))) 
(PUT1-LST (QUOTE PRIME-FACTORIZATION-UNIQUENESS) (QUOTE (IDATE 840117190541. EVENT (PROVE-LEMMA PRIME-FACTORIZATION-UNIQUENESS NIL (IMPLIES (AND (PRIME-LIST L1) (PRIME-LIST L2) (EQUAL (TIMES-LIST L1) (TIMES-LIST L2))) (PERM L1 L2))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-EQUAL-1 . PRIME-FACTORIZATION-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 DIVIDES . PRIME-FACTORIZATION-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 PRIME-LIST-TIMES-LIST . PRIME-FACTORIZATION-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 IF-TIMES-THEN-DIVIDES . PRIME-FACTORIZATION-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 TIMES-LIST-DELETE . PRIME-FACTORIZATION-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 DIVIDES-IMPLIES-TIMES . PRIME-FACTORIZATION-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 PRIME-MEMBER . PRIME-FACTORIZATION-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 PRIME-LIST-DELETE . PRIME-FACTORIZATION-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 PRIME . PRIME-FACTORIZATION-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 PERM . PRIME-FACTORIZATION-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 TIMES-LIST . PRIME-FACTORIZATION-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 PRIME-LIST . PRIME-FACTORIZATION-UNIQUENESS))))) 
(PUT1-LST (QUOTE DIVIDES-IMPLIES-TIMES) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117190428. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (HALF-PLUS PRIME-FACTORIZATION-UNIQUENESS) EVENT (PROVE-LEMMA DIVIDES-IMPLIES-TIMES (REWRITE) (IMPLIES (AND (NOT (ZEROP A)) (NUMBERP C) (EQUAL (TIMES A C) B)) (EQUAL (EQUAL C (QUOTIENT B A)) T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 QUOTIENT-TIMES . DIVIDES-IMPLIES-TIMES) (LEMMAS EQUAL . DIVIDES-IMPLIES-TIMES))))) 
(PUT1-LST (QUOTE PRIME-MEMBER) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117190427. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PRIME-FACTORIZATION-UNIQUENESS) EVENT (PROVE-LEMMA PRIME-MEMBER (REWRITE) (IMPLIES (AND (EQUAL (TIMES C (TIMES-LIST L1)) (TIMES-LIST L2)) (PRIME C) (PRIME-LIST L2)) (MEMBER C L2)) ((DISABLE TIMES))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIVIDES . PRIME-MEMBER) (IMMEDIATE-DEPENDENTS0 PRIME-LIST-TIMES-LIST . PRIME-MEMBER) (IMMEDIATE-DEPENDENTS0 IF-TIMES-THEN-DIVIDES . PRIME-MEMBER) (IMMEDIATE-DEPENDENTS0 PRIME-LIST . PRIME-MEMBER) (IMMEDIATE-DEPENDENTS0 PRIME . PRIME-MEMBER) (IMMEDIATE-DEPENDENTS0 TIMES-LIST . PRIME-MEMBER) (LEMMAS MEMBER . PRIME-MEMBER))))) 
(PUT1-LST (QUOTE TIMES-EQUAL-1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117190425. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (INVERSE-IS-UNIQUE PRIME-FACTORIZATION-UNIQUENESS) EVENT (PROVE-LEMMA TIMES-EQUAL-1 (REWRITE) (EQUAL (EQUAL (TIMES A B) 1.) (AND (NOT (EQUAL A 0.)) (NOT (EQUAL B 0.)) (NUMBERP A) (NUMBERP B) (EQUAL (SUB1 A) 0.) (EQUAL (SUB1 B) 0.)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PLUS-RIGHT-ID2 . TIMES-EQUAL-1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . TIMES-EQUAL-1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . TIMES-EQUAL-1) (LEMMAS EQUAL . TIMES-EQUAL-1))))) 
(PUT1-LST (QUOTE IF-TIMES-THEN-DIVIDES) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117190421. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (G0004 PRIME-FACTORIZATION-UNIQUENESS PRIME-MEMBER) EVENT (PROVE-LEMMA IF-TIMES-THEN-DIVIDES (REWRITE) (IMPLIES (AND (NOT (ZEROP C)) (NOT (DIVIDES C X))) (NOT (EQUAL (TIMES C Y) X)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES . IF-TIMES-THEN-DIVIDES) (IMMEDIATE-DEPENDENTS0 DIVIDES . IF-TIMES-THEN-DIVIDES) (LEMMAS EQUAL . IF-TIMES-THEN-DIVIDES))))) 
(PUT1-LST (QUOTE PRIME-LIST-TIMES-LIST) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117190420. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PRIME-FACTORIZATION-UNIQUENESS PRIME-MEMBER) EVENT (PROVE-LEMMA PRIME-LIST-TIMES-LIST (REWRITE) (IMPLIES (AND (PRIME C) (PRIME-LIST L2) (NOT (MEMBER C L2))) (NOT (EQUAL (REMAINDER (TIMES-LIST L2) C) 0.)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PRIME-KEY . PRIME-LIST-TIMES-LIST) (IMMEDIATE-DEPENDENTS0 DIVIDES . PRIME-LIST-TIMES-LIST) (IMMEDIATE-DEPENDENTS0 LITTLE-STEP . PRIME-LIST-TIMES-LIST) (IMMEDIATE-DEPENDENTS0 QUOTIENT-DIVIDES . PRIME-LIST-TIMES-LIST) (IMMEDIATE-DEPENDENTS0 REMAINDER-0-CROCK . PRIME-LIST-TIMES-LIST) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . PRIME-LIST-TIMES-LIST) (IMMEDIATE-DEPENDENTS0 TIMES-LIST . PRIME-LIST-TIMES-LIST) (IMMEDIATE-DEPENDENTS0 PRIME-LIST . PRIME-LIST-TIMES-LIST) (IMMEDIATE-DEPENDENTS0 PRIME . PRIME-LIST-TIMES-LIST) (LEMMAS EQUAL . PRIME-LIST-TIMES-LIST))))) 
(PUT1-LST (QUOTE TIMES-LIST-DELETE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117190141. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PRIME-FACTORIZATION-UNIQUENESS) EVENT (PROVE-LEMMA TIMES-LIST-DELETE (REWRITE) (IMPLIES (AND (NOT (ZEROP C)) (MEMBER C L)) (EQUAL (TIMES-LIST (DELETE C L)) (QUOTIENT (TIMES-LIST L) C)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-DIVIDES . TIMES-LIST-DELETE) (IMMEDIATE-DEPENDENTS0 DIVIDES-TIMES-LIST . TIMES-LIST-DELETE) (IMMEDIATE-DEPENDENTS0 DIVIDES . TIMES-LIST-DELETE) (IMMEDIATE-DEPENDENTS0 QUOTIENT-TIMES . TIMES-LIST-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE . TIMES-LIST-DELETE) (IMMEDIATE-DEPENDENTS0 TIMES-LIST . TIMES-LIST-DELETE) (LEMMAS TIMES-LIST . TIMES-LIST-DELETE))))) 
(PUT1-LST (QUOTE DISTRIBUTIVITY-OF-DIVIDES) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117190135. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PRIME-KEY-REWRITE TIMES-LIST-DELETE) EVENT (PROVE-LEMMA DISTRIBUTIVITY-OF-DIVIDES (REWRITE) (IMPLIES (AND (NOT (ZEROP A)) (DIVIDES A W)) (EQUAL (TIMES C (QUOTIENT W A)) (QUOTIENT (TIMES C W) A)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-TIMES . DISTRIBUTIVITY-OF-DIVIDES) (IMMEDIATE-DEPENDENTS0 QUOTIENT-TIMES . DISTRIBUTIVITY-OF-DIVIDES) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . DISTRIBUTIVITY-OF-DIVIDES) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO2 . DISTRIBUTIVITY-OF-DIVIDES) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . DISTRIBUTIVITY-OF-DIVIDES) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . DISTRIBUTIVITY-OF-DIVIDES) (IMMEDIATE-DEPENDENTS0 DIVIDES . DISTRIBUTIVITY-OF-DIVIDES) (LEMMAS TIMES . DISTRIBUTIVITY-OF-DIVIDES))))) 
(PUT1-LST (QUOTE QUOTIENT-TIMES) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117190127. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LEQ-WINS1-QUOT DIVIDES-IMPLIES-TIMES TIMES-LIST-DELETE DISTRIBUTIVITY-OF-DIVIDES) EVENT (PROVE-LEMMA QUOTIENT-TIMES (REWRITE) (EQUAL (QUOTIENT (TIMES Y X) Y) (IF (ZEROP Y) 0. (FIX X)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIFFERENCE-PLUS1 . QUOTIENT-TIMES) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO2 . QUOTIENT-TIMES) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . QUOTIENT-TIMES) (LEMMAS QUOTIENT . QUOTIENT-TIMES))))) 
(PUT1-LST (QUOTE DIVIDES-TIMES-LIST) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117190122. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (TIMES-LIST-DELETE) EVENT (PROVE-LEMMA DIVIDES-TIMES-LIST (REWRITE) (IMPLIES (AND (NOT (ZEROP C)) (MEMBER C L)) (EQUAL (REMAINDER (TIMES-LIST L) C) 0.))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . DIVIDES-TIMES-LIST) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-TIMES . DIVIDES-TIMES-LIST) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . DIVIDES-TIMES-LIST) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . DIVIDES-TIMES-LIST) (IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES . DIVIDES-TIMES-LIST) (IMMEDIATE-DEPENDENTS0 TIMES-LIST . DIVIDES-TIMES-LIST) (LEMMAS REMAINDER . DIVIDES-TIMES-LIST))))) 
(PUT1-LST (QUOTE PRIME-LIST-DELETE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117185909. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PRIME-FACTORIZATION-UNIQUENESS) EVENT (PROVE-LEMMA PRIME-LIST-DELETE (REWRITE) (IMPLIES (PRIME-LIST L2) (PRIME-LIST (DELETE X L2)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PRIME . PRIME-LIST-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE-NON-MEMBER . PRIME-LIST-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE . PRIME-LIST-DELETE) (IMMEDIATE-DEPENDENTS0 PRIME-LIST . PRIME-LIST-DELETE) (LEMMAS PRIME-LIST . PRIME-LIST-DELETE))))) 
(PUT1-LST (QUOTE REMAINDER-TIMES) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117185848. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (REFLECT-COMMUTES-WITH-TIMES-1 DIFF-MOD-1 COMPLEMENT-IS-UNIQUE INVERSE-IS-UNIQUE PRODUCT-DIVIDES-LEMMA EQUAL-MODS-TRICK-2 REMAINDER-EXP-LEMMA REMAINDER-DIFFERENCE-TIMES REMAINDER-TIMES-1 IF-TIMES-THEN-DIVIDES DIVIDES-TIMES-LIST) EVENT (PROVE-LEMMA REMAINDER-TIMES (REWRITE) (EQUAL (REMAINDER (TIMES Y X) Y) 0.)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . REMAINDER-TIMES) (IMMEDIATE-DEPENDENTS0 DIVIDES-TIMES . REMAINDER-TIMES) (LEMMAS REMAINDER . REMAINDER-TIMES))))) 
(PUT1-LST (QUOTE 1PERM) (QUOTE NIL)) 
(PUT1-LST (QUOTE PERM) (QUOTE (TYPE-PRESCRIPTION-LST ((PERM 3. NIL NIL)) LEMMAS ((REWRITE-RULE PERM-POSITIVES-COMP-LIST ((PRIME P) (NOT (DIVIDES P A)) (NOT (RESIDUE A P))) (PERM (POSITIVES (SUB1 P)) (COMP-LIST (SUB1 P) A P)) NIL) (REWRITE-RULE PERM-POSITIVES-INVERSE-LIST ((PRIME P) (EQUAL I (DIFFERENCE P (QUOTE 2.)))) (PERM (POSITIVES I) (INVERSE-LIST I P)) NIL) (REWRITE-RULE PIGEONHOLE2 ((ALL-DISTINCT L) (ALL-NON-ZEROP L) (ALL-LESSEQP L N) (SUBSETP (POSITIVES N) L)) (PERM (POSITIVES N) L) NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE SELF-REFLEXIVE) SDEFN (LAMBDA (A B) (IF (LISTP A) (IF (MEMBER (CAR A) B) (PERM (CDR A) (DELETE (CAR A) B)) (QUOTE 1FALSE)) (IF (LISTP B) (QUOTE 1FALSE) (QUOTE 1TRUE)))) LISP-CODE 1PERM INDUCTION-MACHINE ((TESTS-AND-CASES ((NLISTP A)) NIL) (TESTS-AND-CASES ((NOT (NLISTP A)) (MEMBER (CAR A) B)) (((CDR A) (DELETE (CAR A) B)))) (TESTS-AND-CASES ((NOT (NLISTP A)) (NOT (MEMBER (CAR A) B))) NIL)) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (A) (COUNT A) LESSP (CDR-LESSP NLISTP ZERO CDR-LESSEQP)) (JUSTIFICATION (B) (COUNT B) LESSP (ZERO LESSP-COUNT-DELETE))) IDATE 840117185846. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1. 2.) SATELLITES (1PERM) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PERM-PLUS-LIST EQUAL-LENGTH-PERM PERM-POSITIVES-COMP-LIST PERM-POSITIVES-INVERSE-LIST PIGEONHOLE2 TIMES-LIST-EQUAL-FACT PERM-TIMES-LIST PIGEON-HOLE-PRINCIPLE PERM-MEMBER PRIME-FACTORIZATION-UNIQUENESS) EVENT (DEFN PERM (A B) (IF (NLISTP A) (NLISTP B) (IF (MEMBER (CAR A) B) (PERM (CDR A) (DELETE (CAR A) B)) F))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DELETE . PERM) (IMMEDIATE-DEPENDENTS0 LESSP-COUNT-DELETE . PERM) (DCELL . 1PERM))))) 
(PUT1-LST (QUOTE LESSP-COUNT-DELETE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117185845. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PIGEON-HOLE-INDUCTION LESSP-DELETE-REWRITE PERM) EVENT (PROVE-LEMMA LESSP-COUNT-DELETE (REWRITE) (IMPLIES (MEMBER N L) (LESSP (COUNT (DELETE N L)) (COUNT L)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LESSP-PLUS-CANCELATION . LESSP-COUNT-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE . LESSP-COUNT-DELETE) (LINEAR-LEMMAS COUNT . LESSP-COUNT-DELETE))))) 
(PUT1-LST (QUOTE LITTLE-STEP) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117185835. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EQUAL-PLUS-QUOT-LIST-WINS EMPTY-INTERSECT-MULTS-1 RESIDUE-QUOT-LIST GAUSS-COROLLARY PRODUCT-DIVIDES PRIME-LIST-TIMES-LIST) EVENT (PROVE-LEMMA LITTLE-STEP (REWRITE) (IMPLIES (AND (PRIME X) (NOT (EQUAL Y 1.)) (NOT (EQUAL X Y))) (NOT (EQUAL (REMAINDER X Y) 0.)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIVIDES . LITTLE-STEP) (IMMEDIATE-DEPENDENTS0 PRIME-BASIC . LITTLE-STEP) (IMMEDIATE-DEPENDENTS0 PRIME . LITTLE-STEP) (LEMMAS EQUAL . LITTLE-STEP))))) 
(PUT1-LST (QUOTE QUOTIENT-DIVIDES) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117185834. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (G0003 PRIME-KEY-REWRITE PRIME-LIST-TIMES-LIST) EVENT (PROVE-LEMMA QUOTIENT-DIVIDES (REWRITE) (IMPLIES (AND (NUMBERP Y) (NOT (EQUAL (TIMES X (QUOTIENT Y X)) Y))) (NOT (EQUAL (REMAINDER Y X) 0.)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-ZERO2 . QUOTIENT-DIVIDES) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . QUOTIENT-DIVIDES) (IMMEDIATE-DEPENDENTS0 REMAINDER-WRT-12 . QUOTIENT-DIVIDES) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . QUOTIENT-DIVIDES) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . QUOTIENT-DIVIDES) (LEMMAS EQUAL . QUOTIENT-DIVIDES))))) 
(PUT1-LST (QUOTE PRIME-KEY) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117185831. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PRIME-KEY-REWRITE PRIME-LIST-TIMES-LIST) EVENT (PROVE-LEMMA PRIME-KEY (REWRITE) (IMPLIES (AND (NUMBERP Z) (PRIME X) (NOT (DIVIDES X Z)) (NOT (DIVIDES X B))) (NOT (EQUAL (TIMES X K) (TIMES B Z))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . PRIME-KEY) (IMMEDIATE-DEPENDENTS0 TIMES-IDENTITY . PRIME-KEY) (IMMEDIATE-DEPENDENTS0 PRIME-GCD . PRIME-KEY) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-GCD . PRIME-KEY) (IMMEDIATE-DEPENDENTS0 GCD-DISTRIBUTES-OVER-AN-OPENED-UP-TIMES . PRIME-KEY) (IMMEDIATE-DEPENDENTS0 HACK1 . PRIME-KEY) (IMMEDIATE-DEPENDENTS0 DIVIDES . PRIME-KEY) (IMMEDIATE-DEPENDENTS0 PRIME . PRIME-KEY) (LEMMAS EQUAL . PRIME-KEY))))) 
(PUT1-LST (QUOTE GCD-DISTRIBUTES-OVER-AN-OPENED-UP-TIMES) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117185823. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PRIME-KEY) EVENT (PROVE-LEMMA GCD-DISTRIBUTES-OVER-AN-OPENED-UP-TIMES (REWRITE) (IMPLIES (AND (NUMBERP X) (NOT (EQUAL X 0.)) (EQUAL FREE (TIMES X Z))) (EQUAL (GCD (TIMES B Z) FREE) (TIMES Z (GCD B X))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-TIMES-OVER-GCD . GCD-DISTRIBUTES-OVER-AN-OPENED-UP-TIMES) (IMMEDIATE-DEPENDENTS0 GCD . GCD-DISTRIBUTES-OVER-AN-OPENED-UP-TIMES) (LEMMAS GCD . GCD-DISTRIBUTES-OVER-AN-OPENED-UP-TIMES))))) 
(PUT1-LST (QUOTE PRIME-GCD) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117185821. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EMPTY-INTERSECT-MULTS-1 PRIME-KEY) EVENT (PROVE-LEMMA PRIME-GCD (REWRITE) (IMPLIES (AND (NOT (DIVIDES X B)) (NOT (ZEROP X)) (NOT (EQUAL (SUB1 X) 0.)) (PRIME1 X (SUB1 X))) (EQUAL (EQUAL (GCD B X) 1.) T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 GCD-DIVIDES-BOTH . PRIME-GCD) (IMMEDIATE-DEPENDENTS0 REMAINDER-GCD-1 . PRIME-GCD) (IMMEDIATE-DEPENDENTS0 PRIME-BASIC . PRIME-GCD) (IMMEDIATE-DEPENDENTS0 GCD . PRIME-GCD) (IMMEDIATE-DEPENDENTS0 PRIME1 . PRIME-GCD) (IMMEDIATE-DEPENDENTS0 DIVIDES . PRIME-GCD) (LEMMAS EQUAL . PRIME-GCD))))) 
(PUT1-LST (QUOTE HACK1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117185819. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EMPTY-INTERSECT-MULTS-1 PRIME-KEY) EVENT (PROVE-LEMMA HACK1 (REWRITE) (IMPLIES (AND (NOT (DIVIDES X A)) (EQUAL A (GCD (TIMES X A) (TIMES B A)))) (NOT (EQUAL (TIMES K X) (TIMES B A))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIVIDES-TIMES1 . HACK1) (IMMEDIATE-DEPENDENTS0 KLUDGE-BRIDGE . HACK1) (IMMEDIATE-DEPENDENTS0 REMAINDER-WRT-1 . HACK1) (IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-TIMES-OVER-PLUS . HACK1) (IMMEDIATE-DEPENDENTS0 REMAINDER-WRT-12 . HACK1) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO2 . HACK1) (IMMEDIATE-DEPENDENTS0 GCD-0 . HACK1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . HACK1) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . HACK1) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . HACK1) (IMMEDIATE-DEPENDENTS0 REMAINDER-0-CROCK . HACK1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-GCD . HACK1) (IMMEDIATE-DEPENDENTS0 TIMES-IDENTITY . HACK1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . HACK1) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . HACK1) (IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-TIMES-OVER-GCD . HACK1) (IMMEDIATE-DEPENDENTS0 GCD . HACK1) (IMMEDIATE-DEPENDENTS0 DIVIDES . HACK1) (LEMMAS EQUAL . HACK1))))) 
(PUT1-LST (QUOTE KLUDGE-BRIDGE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117185746. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (HACK1) EVENT (PROVE-LEMMA KLUDGE-BRIDGE (REWRITE) (IMPLIES (EQUAL Y (TIMES K X)) (EQUAL (GCD Y (TIMES A X)) (TIMES X (GCD A K))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-GCD . KLUDGE-BRIDGE) (IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-TIMES-OVER-GCD . KLUDGE-BRIDGE) (IMMEDIATE-DEPENDENTS0 GCD . KLUDGE-BRIDGE) (LEMMAS GCD . KLUDGE-BRIDGE))))) 
(PUT1-LST (QUOTE TIMES-IDENTITY) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117185743. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EMPTY-INTERSECT-MULTS-1 LEQ-WINS1 LEQ-WINS1-WINS2 LEQ-WINS2 LEQ-QUOT-TIMES-2 LEQ-QUOT-TIMES LEQ-TIMES-QUOT LEQ-N-WINS1 WIN-SOME-LOSE-SOME-2 EVEN3-TIMES REFLECT-COMMUTES-WITH-TIMES-1 DIFF-MOD-1 TIMES-COMP-LIST-2 NON-ZEROP-COMPLEMENT T-I-L-LEMMA T-I-L-LEMMA1 INVERSE-IS-UNIQUE CRYPT-INVERTS-STEP-2 PRODUCT-DIVIDES-LEMMA REMAINDER-EXP-LEMMA CRYPT-CORRECT TIMES-MOD-1 PRIME-KEY HACK1) EVENT (PROVE-LEMMA TIMES-IDENTITY (REWRITE) (EQUAL (EQUAL X (TIMES X Y)) (OR (EQUAL X 0.) (AND (NUMBERP X) (EQUAL Y 1.))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LESSP-TIMES-2 . TIMES-IDENTITY) (IMMEDIATE-DEPENDENTS0 PLUS-RIGHT-ID2 . TIMES-IDENTITY) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . TIMES-IDENTITY) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . TIMES-IDENTITY) (IMMEDIATE-DEPENDENTS0 TIMES-ID-IFF-1 . TIMES-IDENTITY) (LEMMAS EQUAL . TIMES-IDENTITY))))) 
(PUT1-LST (QUOTE TIMES-IDENTITY1) (QUOTE (IDATE 840117185727. EVENT (PROVE-LEMMA TIMES-IDENTITY1 (REWRITE) (IMPLIES (AND (NUMBERP Y) (NOT (EQUAL Y 1.)) (NOT (EQUAL Y 0.)) (NOT (EQUAL X 0.))) (NOT (EQUAL X (TIMES X Y))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LESSP-TIMES-2 . TIMES-IDENTITY1) (LEMMAS EQUAL . TIMES-IDENTITY1))))) 
(PUT1-LST (QUOTE DIVIDES-TIMES1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117185720. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (HACK1) EVENT (PROVE-LEMMA DIVIDES-TIMES1 (REWRITE) (IMPLIES (EQUAL A (TIMES Z Y)) (EQUAL (REMAINDER A Z) 0.))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . DIVIDES-TIMES1) (IMMEDIATE-DEPENDENTS0 DIVIDES-TIMES . DIVIDES-TIMES1) (LEMMAS REMAINDER . DIVIDES-TIMES1))))) 
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(PUT1-LST (QUOTE GREATEREQPR) (QUOTE (TYPE-PRESCRIPTION-LST ((GREATEREQPR 3. NIL NIL)) LEMMAS ((REWRITE-RULE GREATEREQPR-REMAINDER ((NOT (EQUAL Z (ADD1 V))) (DIVIDES Z (ADD1 V))) (GREATEREQPR V Z) NIL) (REWRITE-RULE GREATEREQPR-LESSP NIL (EQUAL (GREATEREQPR X Y) (IF (LESSP X Y) (QUOTE 1FALSE) (QUOTE 1TRUE))) NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE UNCHANGING) SDEFN (LAMBDA (W Z) (IF (EQUAL W (QUOTE 0.)) (IF (EQUAL Z (QUOTE 0.)) (QUOTE 1TRUE) (IF (NUMBERP Z) (QUOTE 1FALSE) (QUOTE 1TRUE))) (IF (NUMBERP W) (IF (EQUAL W Z) (QUOTE 1TRUE) (GREATEREQPR (SUB1 W) Z)) (IF (EQUAL Z (QUOTE 0.)) (QUOTE 1TRUE) (IF (NUMBERP Z) (QUOTE 1FALSE) (QUOTE 1TRUE)))))) LISP-CODE 1GREATEREQPR INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP W)) NIL) (TESTS-AND-CASES ((NOT (ZEROP W)) (EQUAL W Z)) NIL) (TESTS-AND-CASES ((NOT (ZEROP W)) (NOT (EQUAL W Z))) (((SUB1 W) Z)))) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (W) (COUNT W) LESSP (ZERO ZEROP COUNT-NUMBERP))) IDATE 840117185645. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1GREATEREQPR) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (GREATEREQPR-REMAINDER GREATEREQPR-LESSP PRIME1-BASIC) EVENT (DEFN GREATEREQPR (W Z) (IF (ZEROP W) (ZEROP Z) (IF (EQUAL W Z) T (GREATEREQPR (SUB1 W) Z)))) LOCAL-UNDO-TUPLES ((DCELL . 1GREATEREQPR))))) 
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(PUT1-LST (QUOTE 1PRIME-LIST) (QUOTE NIL)) 
(PUT1-LST (QUOTE PRIME-LIST) (QUOTE (TYPE-PRESCRIPTION-LST ((PRIME-LIST 3. NIL)) LEMMAS ((REWRITE-RULE PRIME-LIST-DELETE ((PRIME-LIST L2)) (PRIME-LIST (DELETE X L2)) NIL) (REWRITE-RULE PRIME-LIST-PRIME-FACTORS NIL (PRIME-LIST (PRIME-FACTORS X)) NIL) (REWRITE-RULE PRIME-LIST-APPEND NIL (EQUAL (PRIME-LIST (APPEND X Y)) (IF (PRIME-LIST X) (PRIME-LIST Y) (QUOTE 1FALSE))) NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (L) (IF (LISTP L) (IF (PRIME (CAR L)) (IF (PRIME-LIST (CDR L)) (QUOTE 1TRUE) (QUOTE 1FALSE)) (QUOTE 1FALSE)) (QUOTE 1TRUE))) LISP-CODE 1PRIME-LIST INDUCTION-MACHINE ((TESTS-AND-CASES ((NLISTP L)) NIL) (TESTS-AND-CASES ((NOT (NLISTP L))) (((CDR L))))) LEVEL-NO 4. JUSTIFICATIONS ((JUSTIFICATION (L) (COUNT L) LESSP (CDR-LESSP NLISTP ZERO CDR-LESSEQP))) IDATE 840117185359. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1PRIME-LIST) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PRIME-FACTORIZATION-UNIQUENESS PRIME-MEMBER PRIME-LIST-TIMES-LIST PRIME-LIST-DELETE PRIME-FACTORIZATION-EXISTENCE PRIME-LIST-PRIME-FACTORS PRIME-LIST-APPEND) EVENT (DEFN PRIME-LIST (L) (IF (NLISTP L) T (AND (PRIME (CAR L)) (PRIME-LIST (CDR L))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PRIME . PRIME-LIST) (DCELL . 1PRIME-LIST))))) 
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(PUT1-LST (QUOTE PRIME-FACTORS) (QUOTE (TYPE-PRESCRIPTION-LST ((PRIME-FACTORS 24. NIL)) LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (X) (IF (EQUAL X (QUOTE 0.)) (QUOTE NIL) (IF (NUMBERP X) (IF (EQUAL (SUB1 X) (QUOTE 0.)) (QUOTE NIL) (IF (PRIME1 X (SUB1 X)) (CONS X (QUOTE NIL)) (APPEND (PRIME-FACTORS (GREATEST-FACTOR X (SUB1 X))) (PRIME-FACTORS (QUOTIENT X (GREATEST-FACTOR X (SUB1 X))))))) (QUOTE NIL)))) LISP-CODE 1PRIME-FACTORS INDUCTION-MACHINE ((TESTS-AND-CASES ((OR (ZEROP X) (EQUAL (SUB1 X) (QUOTE 0.)))) NIL) (TESTS-AND-CASES ((NOT (OR (ZEROP X) (EQUAL (SUB1 X) (QUOTE 0.)))) (PRIME1 X (SUB1 X))) NIL) (TESTS-AND-CASES ((NOT (OR (ZEROP X) (EQUAL (SUB1 X) (QUOTE 0.)))) (NOT (PRIME1 X (SUB1 X)))) (((QUOTIENT X (GREATEST-FACTOR X (SUB1 X)))) ((GREATEST-FACTOR X (SUB1 X)))))) LEVEL-NO 4. JUSTIFICATIONS ((JUSTIFICATION (X) (COUNT X) LESSP (GREATEST-FACTOR-LESSP ZERO ZEROP OR COUNT-NUMBERP GREATEST-FACTOR-0 GREATEST-FACTOR-1 LESSP-QUOTIENT1))) IDATE 840117185349. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1PRIME-FACTORS) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PRIME-FACTORIZATION-EXISTENCE ENOUGH-FACTORS PRIME-LIST-PRIME-FACTORS) EVENT (DEFN PRIME-FACTORS (X) (IF (OR (ZEROP X) (EQUAL (SUB1 X) 0.)) NIL (IF (PRIME1 X (SUB1 X)) (CONS X NIL) (APPEND (PRIME-FACTORS (GREATEST-FACTOR X (SUB1 X))) (PRIME-FACTORS (QUOTIENT X (GREATEST-FACTOR X (SUB1 X)))))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 GREATEST-FACTOR . PRIME-FACTORS) (IMMEDIATE-DEPENDENTS0 APPEND . PRIME-FACTORS) (IMMEDIATE-DEPENDENTS0 PRIME1 . PRIME-FACTORS) (IMMEDIATE-DEPENDENTS0 GREATEST-FACTOR-LESSP . PRIME-FACTORS) (IMMEDIATE-DEPENDENTS0 GREATEST-FACTOR-0 . PRIME-FACTORS) (IMMEDIATE-DEPENDENTS0 GREATEST-FACTOR-1 . PRIME-FACTORS) (IMMEDIATE-DEPENDENTS0 LESSP-QUOTIENT1 . PRIME-FACTORS) (DCELL . 1PRIME-FACTORS))))) 
(PUT1-LST (QUOTE NUMBERP-GREATEST-FACTOR) (QUOTE (IDATE 840117185348. EVENT (PROVE-LEMMA NUMBERP-GREATEST-FACTOR (REWRITE) (EQUAL (NUMBERP (GREATEST-FACTOR X Y)) (NOT (AND (OR (ZEROP Y) (EQUAL Y 1.)) (NOT (NUMBERP X)))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIVIDES . NUMBERP-GREATEST-FACTOR) (IMMEDIATE-DEPENDENTS0 GREATEST-FACTOR . NUMBERP-GREATEST-FACTOR) (LEMMAS NUMBERP . NUMBERP-GREATEST-FACTOR))))) 
(PUT1-LST (QUOTE GREATEST-FACTOR-1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117185337. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (ENOUGH-FACTORS PRIME-LIST-PRIME-FACTORS PRIME-FACTORS) EVENT (PROVE-LEMMA GREATEST-FACTOR-1 (REWRITE) (EQUAL (EQUAL (GREATEST-FACTOR X Y) 1.) (EQUAL X 1.))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REMAINDER-0-CROCK . GREATEST-FACTOR-1) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . GREATEST-FACTOR-1) (IMMEDIATE-DEPENDENTS0 DIVIDES . GREATEST-FACTOR-1) (IMMEDIATE-DEPENDENTS0 GREATEST-FACTOR . GREATEST-FACTOR-1) (LEMMAS EQUAL . GREATEST-FACTOR-1))))) 
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(PUT1-LST (QUOTE GREATEST-FACTOR-DIVIDES) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117185314. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (ENOUGH-FACTORS) EVENT (PROVE-LEMMA GREATEST-FACTOR-DIVIDES (REWRITE) (IMPLIES (AND (LESSP Y X) (NOT (PRIME1 X Y)) (NOT (ZEROP X)) (NOT (EQUAL X 1.)) (NOT (ZEROP Y))) (EQUAL (REMAINDER X (GREATEST-FACTOR X Y)) 0.))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIVIDES . GREATEST-FACTOR-DIVIDES) (IMMEDIATE-DEPENDENTS0 GREATEST-FACTOR . GREATEST-FACTOR-DIVIDES) (IMMEDIATE-DEPENDENTS0 PRIME1 . GREATEST-FACTOR-DIVIDES) (LEMMAS REMAINDER . GREATEST-FACTOR-DIVIDES))))) 
(PUT1-LST (QUOTE GREATEST-FACTOR-LESSP) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117185301. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (ENOUGH-FACTORS PRIME-LIST-PRIME-FACTORS PRIME-FACTORS) EVENT (PROVE-LEMMA GREATEST-FACTOR-LESSP (REWRITE) (IMPLIES (AND (LESSP Y X) (NOT (PRIME1 X Y)) (NOT (ZEROP X)) (NOT (EQUAL (SUB1 X) 0.)) (NOT (ZEROP Y))) (LESSP (GREATEST-FACTOR X Y) X))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIVIDES . GREATEST-FACTOR-LESSP) (IMMEDIATE-DEPENDENTS0 GREATEST-FACTOR . GREATEST-FACTOR-LESSP) (IMMEDIATE-DEPENDENTS0 PRIME1 . GREATEST-FACTOR-LESSP) (LINEAR-LEMMAS GREATEST-FACTOR . GREATEST-FACTOR-LESSP))))) 
(PUT1-LST (QUOTE 1GREATEST-FACTOR) (QUOTE NIL)) 
(PUT1-LST (QUOTE GREATEST-FACTOR) (QUOTE (TYPE-PRESCRIPTION-LST ((GREATEST-FACTOR 4. T NIL)) LEMMAS NIL LINEAR-LEMMAS ((LINEAR-LEMMA GREATEST-FACTOR-LESSP ((LESSP Y X) (NOT (PRIME1 X Y)) (NUMBERP X) (NOT (EQUAL X (QUOTE 0.))) (NOT (EQUAL (SUB1 X) (QUOTE 0.))) (NUMBERP Y) (NOT (EQUAL Y (QUOTE 0.)))) (LESSP (GREATEST-FACTOR X Y) X) (GREATEST-FACTOR X Y))) QUICK-BLOCK-INFO (UNCHANGING SELF-REFLEXIVE) SDEFN (LAMBDA (X Y) (IF (EQUAL Y (QUOTE 0.)) X (IF (NUMBERP Y) (IF (EQUAL Y (QUOTE 1.)) X (IF (DIVIDES Y X) Y (GREATEST-FACTOR X (SUB1 Y)))) X))) LISP-CODE 1GREATEST-FACTOR INDUCTION-MACHINE ((TESTS-AND-CASES ((OR (ZEROP Y) (EQUAL Y (QUOTE 1.)))) NIL) (TESTS-AND-CASES ((NOT (OR (ZEROP Y) (EQUAL Y (QUOTE 1.)))) (DIVIDES Y X)) NIL) (TESTS-AND-CASES ((NOT (OR (ZEROP Y) (EQUAL Y (QUOTE 1.)))) (NOT (DIVIDES Y X))) ((X (SUB1 Y))))) LEVEL-NO 3. JUSTIFICATIONS ((JUSTIFICATION (Y) (COUNT Y) LESSP (ZERO ZEROP OR DIVIDES COUNT-NUMBERP))) IDATE 840117185209. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (2.) SATELLITES (1GREATEST-FACTOR) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PRIME-FACTORS NUMBERP-GREATEST-FACTOR GREATEST-FACTOR-1 GREATEST-FACTOR-0 GREATEST-FACTOR-DIVIDES GREATEST-FACTOR-LESSP) EVENT (DEFN GREATEST-FACTOR (X Y) (IF (OR (ZEROP Y) (EQUAL Y 1.)) X (IF (DIVIDES Y X) Y (GREATEST-FACTOR X (SUB1 Y))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIVIDES . GREATEST-FACTOR) (DCELL . 1GREATEST-FACTOR))))) 
(PUT1-LST (QUOTE 1PRIME) (QUOTE NIL)) 
(PUT1-LST (QUOTE PRIME) (QUOTE (TYPE-PRESCRIPTION-LST ((PRIME 3. NIL)) LEMMAS NIL QUICK-BLOCK-INFO NIL SDEFN (LAMBDA (X) (IF (EQUAL X (QUOTE 0.)) (QUOTE 1FALSE) (IF (NUMBERP X) (IF (EQUAL X (QUOTE 1.)) (QUOTE 1FALSE) (PRIME1 X (SUB1 X))) (QUOTE 1FALSE)))) LISP-CODE 1PRIME INDUCTION-MACHINE NIL LEVEL-NO 3. JUSTIFICATIONS NIL IDATE 840117185208. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS NIL SATELLITES (1PRIME) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LAW-OF-QUADRATIC-RECIPROCITY EQUAL-PLUS-QUOT-LIST-WINS EMPTY-INTERSECT-MULTS EMPTY-INTERSECT-MULTS-1 RESIDUE-QUOT-LIST GAUSS-COROLLARY EQUAL-WINS-PLUS-QUOT-LIST EQUAL-QUOT-WINS1 LEQ-QUOT-WINS1 LEQ-QUOT-WINS1-2 RES1-QUOT-LIST PLUS-REFLECT-LIST GAUSS-LEMMA RES1-REM-2 RES1-REM-1 TIMES-REFLECT-LIST ALL-DISTINCT-REFLECT-LIST ALL-DISTINCT-REFLECT-LIST-10 ALL-DISTINCT-REFLECT-LIST-9 ALL-DISTINCT-REFLECT-LIST-8 ALL-DISTINCT-REFLECT-LIST-7 ALL-DISTINCT-REFLECT-LIST-3 ALL-DISTINCT-REFLECT-LIST-1 ALL-NON-ZEROP-REFLECT-LIST EULER-2 EULER-2-2 EULER-2-1 TIMES-COMP-LIST TIMES-COMP-LIST-4 TIMES-COMP-LIST-2 COMP-LIST-FACT PERM-POSITIVES-COMP-LIST ALL-DISTINCT-COMP-LIST ALL-DISTINCT-COMP-LIST-1 COMP-LIST-CLOSED-2 COMP-LIST-CLOSED-1 ALL-NON-ZEROP-COMP-LIST COMPLEMENT-OF-COMPLEMENT NO-SELF-COMPLEMENT COMPLEMENT-IS-UNIQUE NON-ZEROP-COMPLEMENT COMPLEMENT-WORKS EULER-1 EULER-1-7 EULER-1-6 EULER-1-5 EULER-1-4 WILSON-THM W-T-LEMMA INVERSE-LIST-FACT PERM-POSITIVES-INVERSE-LIST TIMES-INVERSE-LIST T-I-L-LEMMA3 ALL-DISTINCT-INVERSE-LIST A-D-I-L-LEMMA3 A-D-I-L-LEMMA2 A-D-I-L-LEMMA1 BOUNDED-INVERSE-LIST ALL-NON-ZEROP-INVERSE-LIST BOUNDED-INVERSE B-I-LEMMA2 NON-ZEROP-INVERSE INVERSE-OF-INVERSE NO-OTHER-INVOLUTIONS N-O-I-LEMMA4 N-O-I-LEMMA2 SUB1-P-IS-INVOLUTION INVERSE-IS-UNIQUE INVERSE-INVERTS INVERSE-INVERTS-LEMMA CRYPT-INVERTS CRYPT-INVERTS-STEP-2 CRYPT-INVERTS-STEP-1B CRYPT-INVERTS-STEP-1A CRYPT-INVERTS-STEP-1 FERMAT-THM ALL-NON-ZEROP-S ALL-DISTINCT-S ALL-DISTINCT-S-LEMMA PRIME-FACT COROLLARY-55 THM-55-SPECIALIZED-TO-PRIMES COROLLARY-53 THM-53-SPECIALIZED-TO-PRIMES PRODUCT-DIVIDES PRIME-KEY-TRICK PRIME-KEY-REWRITE PRIME-FACTORIZATION-UNIQUENESS PRIME-MEMBER PRIME-LIST-TIMES-LIST PRIME-LIST-DELETE LITTLE-STEP PRIME-KEY PRIME-LIST-PRIME-FACTORS PRIME-LIST-APPEND PRIME-LIST) EVENT (DEFN PRIME (X) (AND (NOT (ZEROP X)) (NOT (EQUAL X 1.)) (PRIME1 X (SUB1 X)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PRIME1 . PRIME) (DCELL . 1PRIME))))) 
(PUT1-LST (QUOTE 1PRIME1) (QUOTE NIL)) 
(PUT1-LST (QUOTE PRIME1) (QUOTE (TYPE-PRESCRIPTION-LST ((PRIME1 3. NIL NIL)) LEMMAS ((REWRITE-RULE PRIME-BASIC ((NOT (EQUAL Z (QUOTE 1.))) (NOT (EQUAL Z X)) (NUMBERP X) (NOT (EQUAL X (QUOTE 0.))) (NOT (EQUAL X (QUOTE 1.))) (DIVIDES Z X)) (NOT (PRIME1 X (SUB1 X))) NIL) (REWRITE-RULE PRIME1-BASIC ((NOT (EQUAL Z (QUOTE 1.))) (NOT (EQUAL Z (QUOTE 0.))) (NUMBERP Z) (GREATEREQPR U Z)) (NOT (PRIME1 (TIMES W Z) U)) NIL)) QUICK-BLOCK-INFO (UNCHANGING SELF-REFLEXIVE) SDEFN (LAMBDA (X Y) (IF (EQUAL Y (QUOTE 0.)) (QUOTE 1FALSE) (IF (NUMBERP Y) (IF (EQUAL Y (QUOTE 1.)) (QUOTE 1TRUE) (IF (DIVIDES Y X) (QUOTE 1FALSE) (IF (PRIME1 X (SUB1 Y)) (QUOTE 1TRUE) (QUOTE 1FALSE)))) (QUOTE 1FALSE)))) LISP-CODE 1PRIME1 INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP Y)) NIL) (TESTS-AND-CASES ((NOT (ZEROP Y)) (EQUAL Y (QUOTE 1.))) NIL) (TESTS-AND-CASES ((NOT (ZEROP Y)) (NOT (EQUAL Y (QUOTE 1.)))) ((X (SUB1 Y))))) LEVEL-NO 3. JUSTIFICATIONS ((JUSTIFICATION (Y) (COUNT Y) LESSP (ZERO ZEROP COUNT-NUMBERP))) IDATE 840117185205. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (2.) SATELLITES (1PRIME1) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (WILSON-THM BOUNDED-INVERSE INVERSE-OF-INVERSE INVERSE-IS-UNIQUE PRIME-GCD PRIME-BASIC PRIME1-BASIC PRIME-FACTORS GREATEST-FACTOR-DIVIDES GREATEST-FACTOR-LESSP PRIME) EVENT (DEFN PRIME1 (X Y) (IF (ZEROP Y) F (IF (EQUAL Y 1.) T (AND (NOT (DIVIDES Y X)) (PRIME1 X (SUB1 Y)))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIVIDES . PRIME1) (DCELL . 1PRIME1))))) 
(PUT1-LST (QUOTE CORRECTNESS-OF-SAMEFRINGE) (QUOTE (IDATE 840117185204. EVENT (PROVE-LEMMA CORRECTNESS-OF-SAMEFRINGE (REWRITE) (EQUAL (SAMEFRINGE X Y) (EQUAL (FLATTEN X) (FLATTEN Y)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 GOPHER-RETURNS-CORRECT-STATE . CORRECTNESS-OF-SAMEFRINGE) (IMMEDIATE-DEPENDENTS0 GOPHER-RETURNS-LEFTMOST-ATOM . CORRECTNESS-OF-SAMEFRINGE) (IMMEDIATE-DEPENDENTS0 FLATTEN-SINGLETON . CORRECTNESS-OF-SAMEFRINGE) (IMMEDIATE-DEPENDENTS0 LISTP-GOPHER . CORRECTNESS-OF-SAMEFRINGE) (IMMEDIATE-DEPENDENTS0 GOPHER-PRESERVES-COUNT . CORRECTNESS-OF-SAMEFRINGE) (IMMEDIATE-DEPENDENTS0 FLATTEN . CORRECTNESS-OF-SAMEFRINGE) (IMMEDIATE-DEPENDENTS0 SAMEFRINGE . CORRECTNESS-OF-SAMEFRINGE) (LEMMAS SAMEFRINGE . CORRECTNESS-OF-SAMEFRINGE))))) 
(PUT1-LST (QUOTE GOPHER-RETURNS-CORRECT-STATE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117185152. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-SAMEFRINGE) EVENT (PROVE-LEMMA GOPHER-RETURNS-CORRECT-STATE (REWRITE) (EQUAL (FLATTEN (CDR (GOPHER X))) (IF (LISTP X) (CDR (FLATTEN X)) (CONS 0. NIL)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-APPEND . GOPHER-RETURNS-CORRECT-STATE) (IMMEDIATE-DEPENDENTS0 APPEND . GOPHER-RETURNS-CORRECT-STATE) (IMMEDIATE-DEPENDENTS0 LEFTCOUNT . GOPHER-RETURNS-CORRECT-STATE) (IMMEDIATE-DEPENDENTS0 GOPHER . GOPHER-RETURNS-CORRECT-STATE) (IMMEDIATE-DEPENDENTS0 FLATTEN . GOPHER-RETURNS-CORRECT-STATE) (LEMMAS FLATTEN . GOPHER-RETURNS-CORRECT-STATE))))) 
(PUT1-LST (QUOTE GOPHER-RETURNS-LEFTMOST-ATOM) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117185145. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-SAMEFRINGE) EVENT (PROVE-LEMMA GOPHER-RETURNS-LEFTMOST-ATOM (REWRITE) (EQUAL (CAR (GOPHER X)) (IF (LISTP X) (CAR (FLATTEN X)) 0.))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-APPEND . GOPHER-RETURNS-LEFTMOST-ATOM) (IMMEDIATE-DEPENDENTS0 APPEND . GOPHER-RETURNS-LEFTMOST-ATOM) (IMMEDIATE-DEPENDENTS0 LEFTCOUNT . GOPHER-RETURNS-LEFTMOST-ATOM) (IMMEDIATE-DEPENDENTS0 FLATTEN . GOPHER-RETURNS-LEFTMOST-ATOM) (IMMEDIATE-DEPENDENTS0 GOPHER . GOPHER-RETURNS-LEFTMOST-ATOM) (LEMMAS CAR . GOPHER-RETURNS-LEFTMOST-ATOM))))) 
(PUT1-LST (QUOTE 1SAMEFRINGE) (QUOTE NIL)) 
(PUT1-LST (QUOTE SAMEFRINGE) (QUOTE (TYPE-PRESCRIPTION-LST ((SAMEFRINGE 3. NIL NIL)) LEMMAS ((REWRITE-RULE CORRECTNESS-OF-SAMEFRINGE NIL (EQUAL (SAMEFRINGE X Y) (EQUAL (FLATTEN X) (FLATTEN Y))) NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE SELF-REFLEXIVE) SDEFN (LAMBDA (X Y) (IF (LISTP X) (IF (LISTP Y) (IF (EQUAL (CAR (GOPHER X)) (CAR (GOPHER Y))) (IF (SAMEFRINGE (CDR (GOPHER X)) (CDR (GOPHER Y))) (QUOTE 1TRUE) (QUOTE 1FALSE)) (QUOTE 1FALSE)) (EQUAL X Y)) (EQUAL X Y))) LISP-CODE 1SAMEFRINGE INDUCTION-MACHINE ((TESTS-AND-CASES ((OR (NLISTP X) (NLISTP Y))) NIL) (TESTS-AND-CASES ((NOT (OR (NLISTP X) (NLISTP Y)))) (((CDR (GOPHER X)) (CDR (GOPHER Y)))))) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (X) (COUNT X) LESSP (CDR-LESSP LISTP-GOPHER NLISTP OR ZERO GOPHER-PRESERVES-COUNT CDR-LESSEQP)) (JUSTIFICATION (Y) (COUNT Y) LESSP (CDR-LESSP LISTP-GOPHER NLISTP OR ZERO GOPHER-PRESERVES-COUNT CDR-LESSEQP))) IDATE 840117185135. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1. 2.) SATELLITES (1SAMEFRINGE) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-SAMEFRINGE) EVENT (DEFN SAMEFRINGE (X Y) (IF (OR (NLISTP X) (NLISTP Y)) (EQUAL X Y) (AND (EQUAL (CAR (GOPHER X)) (CAR (GOPHER Y))) (SAMEFRINGE (CDR (GOPHER X)) (CDR (GOPHER Y)))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 GOPHER . SAMEFRINGE) (IMMEDIATE-DEPENDENTS0 LISTP-GOPHER . SAMEFRINGE) (IMMEDIATE-DEPENDENTS0 GOPHER-PRESERVES-COUNT . SAMEFRINGE) (DCELL . 1SAMEFRINGE))))) 
(PUT1-LST (QUOTE LISTP-GOPHER) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117185135. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-SAMEFRINGE SAMEFRINGE) EVENT (PROVE-LEMMA LISTP-GOPHER (REWRITE) (EQUAL (LISTP (GOPHER X)) (LISTP X))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LEFTCOUNT . LISTP-GOPHER) (IMMEDIATE-DEPENDENTS0 GOPHER . LISTP-GOPHER) (LEMMAS LISTP . LISTP-GOPHER))))) 
(PUT1-LST (QUOTE GOPHER-PRESERVES-COUNT) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117185132. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-SAMEFRINGE SAMEFRINGE) EVENT (PROVE-LEMMA GOPHER-PRESERVES-COUNT (REWRITE) (NOT (LESSP (COUNT X) (COUNT (GOPHER X))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . GOPHER-PRESERVES-COUNT) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-PLUS . GOPHER-PRESERVES-COUNT) (IMMEDIATE-DEPENDENTS0 PLUS-ADD1 . GOPHER-PRESERVES-COUNT) (IMMEDIATE-DEPENDENTS0 LEFTCOUNT . GOPHER-PRESERVES-COUNT) (IMMEDIATE-DEPENDENTS0 GOPHER . GOPHER-PRESERVES-COUNT) (LINEAR-LEMMAS COUNT . GOPHER-PRESERVES-COUNT))))) 
(PUT1-LST (QUOTE 1GOPHER) (QUOTE NIL)) 
(PUT1-LST (QUOTE GOPHER) (QUOTE (TYPE-PRESCRIPTION-LST ((GOPHER 16. T)) LEMMAS NIL LINEAR-LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (X) (IF (LISTP X) (IF (LISTP (CAR X)) (GOPHER (CONS (CAR (CAR X)) (CONS (CDR (CAR X)) (CDR X)))) X) X)) LISP-CODE 1GOPHER INDUCTION-MACHINE ((TESTS-AND-CASES ((OR (NLISTP X) (NLISTP (CAR X)))) NIL) (TESTS-AND-CASES ((NOT (OR (NLISTP X) (NLISTP (CAR X))))) (((CONS (CAR (CAR X)) (CONS (CDR (CAR X)) (CDR X))))))) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (X) (LEFTCOUNT X) LESSP (ZERO NLISTP OR CAR-CONS LEFTCOUNT SUB1-ADD1 LESSP))) IDATE 840117185103. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1GOPHER) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (GOPHER-RETURNS-CORRECT-STATE GOPHER-RETURNS-LEFTMOST-ATOM SAMEFRINGE LISTP-GOPHER GOPHER-PRESERVES-COUNT) EVENT (DEFN GOPHER (X) (IF (OR (NLISTP X) (NLISTP (CAR X))) X (GOPHER (CONS (CAAR X) (CONS (CDAR X) (CDR X))))) ((LESSP (LEFTCOUNT X)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LEFTCOUNT . GOPHER) (DCELL . 1GOPHER))))) 
(PUT1-LST (QUOTE 1LEFTCOUNT) (QUOTE NIL)) 
(PUT1-LST (QUOTE LEFTCOUNT) (QUOTE (TYPE-PRESCRIPTION-LST ((LEFTCOUNT 4. NIL)) LEMMAS NIL LINEAR-LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (X) (IF (LISTP X) (ADD1 (LEFTCOUNT (CAR X))) (QUOTE 0.))) LISP-CODE 1LEFTCOUNT INDUCTION-MACHINE ((TESTS-AND-CASES ((NLISTP X)) NIL) (TESTS-AND-CASES ((NOT (NLISTP X))) (((CAR X))))) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (X) (COUNT X) LESSP (CAR-LESSP NLISTP ZERO CAR-LESSEQP))) IDATE 840117185056. CONTROLLER-POCKETS (1.) SATELLITES (1LEFTCOUNT) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (GOPHER-RETURNS-CORRECT-STATE GOPHER-RETURNS-LEFTMOST-ATOM LISTP-GOPHER GOPHER-PRESERVES-COUNT GOPHER) EVENT (DEFN LEFTCOUNT (X) (IF (NLISTP X) 0. (ADD1 (LEFTCOUNT (CAR X))))) LOCAL-UNDO-TUPLES ((DCELL . 1LEFTCOUNT))))) 
(PUT1-LST (QUOTE FLATTEN-SINGLETON) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117185052. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-SAMEFRINGE) EVENT (PROVE-LEMMA FLATTEN-SINGLETON (REWRITE) (EQUAL (EQUAL (FLATTEN X) (CONS Y NIL)) (AND (NLISTP X) (EQUAL X Y)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 APPEND . FLATTEN-SINGLETON) (IMMEDIATE-DEPENDENTS0 FLATTEN . FLATTEN-SINGLETON) (LEMMAS EQUAL . FLATTEN-SINGLETON))))) 
(PUT1-LST (QUOTE TAUTOLOGY-CHECKER-IS-SOUND) (QUOTE (IDATE 840117184832. EVENT (PROVE-LEMMA TAUTOLOGY-CHECKER-IS-SOUND NIL (IMPLIES (TAUTOLOGY-CHECKER X) (VALUE X A))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 NORMALIZE-IS-SOUND . TAUTOLOGY-CHECKER-IS-SOUND) (IMMEDIATE-DEPENDENTS0 APPEND . TAUTOLOGY-CHECKER-IS-SOUND) (IMMEDIATE-DEPENDENTS0 NORMALIZE-NORMALIZES . TAUTOLOGY-CHECKER-IS-SOUND) (IMMEDIATE-DEPENDENTS0 TAUTOLOGY-CHECKER-SOUNDNESS-BRIDGE . TAUTOLOGY-CHECKER-IS-SOUND) (IMMEDIATE-DEPENDENTS0 VALUE . TAUTOLOGY-CHECKER-IS-SOUND) (IMMEDIATE-DEPENDENTS0 TAUTOLOGY-CHECKER . TAUTOLOGY-CHECKER-IS-SOUND))))) 
(PUT1-LST (QUOTE TAUTOLOGY-CHECKER-SOUNDNESS-BRIDGE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117184831. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (TAUTOLOGY-CHECKER-IS-SOUND) EVENT (PROVE-LEMMA TAUTOLOGY-CHECKER-SOUNDNESS-BRIDGE (REWRITE) (IMPLIES (AND (TAUTOLOGYP Y A1) (NORMALIZED-IF-EXPRP Y) (EQUAL (VALUE X A2) (VALUE Y (APPEND A1 A2)))) (VALUE X A2))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TAUTOLOGYP-IS-SOUND . TAUTOLOGY-CHECKER-SOUNDNESS-BRIDGE) (IMMEDIATE-DEPENDENTS0 APPEND . TAUTOLOGY-CHECKER-SOUNDNESS-BRIDGE) (IMMEDIATE-DEPENDENTS0 VALUE . TAUTOLOGY-CHECKER-SOUNDNESS-BRIDGE) (IMMEDIATE-DEPENDENTS0 NORMALIZED-IF-EXPRP . TAUTOLOGY-CHECKER-SOUNDNESS-BRIDGE) (IMMEDIATE-DEPENDENTS0 TAUTOLOGYP . TAUTOLOGY-CHECKER-SOUNDNESS-BRIDGE) (LEMMAS VALUE . TAUTOLOGY-CHECKER-SOUNDNESS-BRIDGE))))) 
(PUT1-LST (QUOTE TAUTOLOGY-CHECKER-IS-COMPLETE) (QUOTE (IDATE 840117184827. EVENT (PROVE-LEMMA TAUTOLOGY-CHECKER-IS-COMPLETE NIL (IMPLIES (NOT (TAUTOLOGY-CHECKER X)) (EQUAL (VALUE X (FALSIFY X)) F))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TAUTOLOGYP-FAILS-MEANS-FALSIFY1-WINS . TAUTOLOGY-CHECKER-IS-COMPLETE) (IMMEDIATE-DEPENDENTS0 NORMALIZE-NORMALIZES . TAUTOLOGY-CHECKER-IS-COMPLETE) (IMMEDIATE-DEPENDENTS0 NORMALIZE-IS-SOUND . TAUTOLOGY-CHECKER-IS-COMPLETE) (IMMEDIATE-DEPENDENTS0 TAUTOLOGY-CHECKER-COMPLETENESS-BRIDGE . TAUTOLOGY-CHECKER-IS-COMPLETE) (IMMEDIATE-DEPENDENTS0 FALSIFY . TAUTOLOGY-CHECKER-IS-COMPLETE) (IMMEDIATE-DEPENDENTS0 VALUE . TAUTOLOGY-CHECKER-IS-COMPLETE) (IMMEDIATE-DEPENDENTS0 TAUTOLOGY-CHECKER . TAUTOLOGY-CHECKER-IS-COMPLETE))))) 
(PUT1-LST (QUOTE TAUTOLOGY-CHECKER-COMPLETENESS-BRIDGE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117184824. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (TAUTOLOGY-CHECKER-IS-COMPLETE) EVENT (PROVE-LEMMA TAUTOLOGY-CHECKER-COMPLETENESS-BRIDGE (REWRITE) (IMPLIES (AND (EQUAL (VALUE Y (FALSIFY1 X A)) (VALUE X (FALSIFY1 X A))) (FALSIFY1 X A) (NORMALIZED-IF-EXPRP X)) (EQUAL (VALUE Y (FALSIFY1 X A)) F))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 FALSIFY1-FALSIFIES . TAUTOLOGY-CHECKER-COMPLETENESS-BRIDGE) (IMMEDIATE-DEPENDENTS0 NORMALIZED-IF-EXPRP . TAUTOLOGY-CHECKER-COMPLETENESS-BRIDGE) (IMMEDIATE-DEPENDENTS0 FALSIFY1 . TAUTOLOGY-CHECKER-COMPLETENESS-BRIDGE) (IMMEDIATE-DEPENDENTS0 VALUE . TAUTOLOGY-CHECKER-COMPLETENESS-BRIDGE) (LEMMAS VALUE . TAUTOLOGY-CHECKER-COMPLETENESS-BRIDGE))))) 
(PUT1-LST (QUOTE NORMALIZE-NORMALIZES) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117184822. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (TAUTOLOGY-CHECKER-IS-SOUND TAUTOLOGY-CHECKER-IS-COMPLETE) EVENT (PROVE-LEMMA NORMALIZE-NORMALIZES (REWRITE) (NORMALIZED-IF-EXPRP (NORMALIZE X))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 IF-COMPLEXITY-GOES-DOWN1 . NORMALIZE-NORMALIZES) (IMMEDIATE-DEPENDENTS0 IF-COMPLEXITY-GOES-DOWN2 . NORMALIZE-NORMALIZES) (IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-TIMES-OVER-PLUS . NORMALIZE-NORMALIZES) (IMMEDIATE-DEPENDENTS0 CONS-IF . NORMALIZE-NORMALIZES) (IMMEDIATE-DEPENDENTS0 IF-COMPLEXITY . NORMALIZE-NORMALIZES) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . NORMALIZE-NORMALIZES) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-TIMES . NORMALIZE-NORMALIZES) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-PLUS . NORMALIZE-NORMALIZES) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-PLUS . NORMALIZE-NORMALIZES) (IMMEDIATE-DEPENDENTS0 IF-DEPTH . NORMALIZE-NORMALIZES) (IMMEDIATE-DEPENDENTS0 LESSP-PLUS-CANCELATION . NORMALIZE-NORMALIZES) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES-CANCELLATION . NORMALIZE-NORMALIZES) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . NORMALIZE-NORMALIZES) (IMMEDIATE-DEPENDENTS0 IF-COMPLEXITY-NOT-0 . NORMALIZE-NORMALIZES) (IMMEDIATE-DEPENDENTS0 NORMALIZE . NORMALIZE-NORMALIZES) (IMMEDIATE-DEPENDENTS0 NORMALIZED-IF-EXPRP . NORMALIZE-NORMALIZES) (LEMMAS NORMALIZED-IF-EXPRP . NORMALIZE-NORMALIZES))))) 
(PUT1-LST (QUOTE NORMALIZE-IS-SOUND) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117184820. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (TAUTOLOGY-CHECKER-IS-SOUND TAUTOLOGY-CHECKER-IS-COMPLETE) EVENT (PROVE-LEMMA NORMALIZE-IS-SOUND (REWRITE) (EQUAL (VALUE (NORMALIZE X) A) (VALUE X A))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 IF-COMPLEXITY-GOES-DOWN1 . NORMALIZE-IS-SOUND) (IMMEDIATE-DEPENDENTS0 IF-COMPLEXITY-GOES-DOWN2 . NORMALIZE-IS-SOUND) (IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-TIMES-OVER-PLUS . NORMALIZE-IS-SOUND) (IMMEDIATE-DEPENDENTS0 CONS-IF . NORMALIZE-IS-SOUND) (IMMEDIATE-DEPENDENTS0 IF-COMPLEXITY . NORMALIZE-IS-SOUND) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . NORMALIZE-IS-SOUND) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-TIMES . NORMALIZE-IS-SOUND) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-PLUS . NORMALIZE-IS-SOUND) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-PLUS . NORMALIZE-IS-SOUND) (IMMEDIATE-DEPENDENTS0 IF-DEPTH . NORMALIZE-IS-SOUND) (IMMEDIATE-DEPENDENTS0 LESSP-PLUS-CANCELATION . NORMALIZE-IS-SOUND) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES-CANCELLATION . NORMALIZE-IS-SOUND) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . NORMALIZE-IS-SOUND) (IMMEDIATE-DEPENDENTS0 IF-COMPLEXITY-NOT-0 . NORMALIZE-IS-SOUND) (IMMEDIATE-DEPENDENTS0 NORMALIZE . NORMALIZE-IS-SOUND) (IMMEDIATE-DEPENDENTS0 VALUE . NORMALIZE-IS-SOUND) (LEMMAS VALUE . NORMALIZE-IS-SOUND))))) 
(PUT1-LST (QUOTE TAUTOLOGYP-FAILS-MEANS-FALSIFY1-WINS) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117184810. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (TAUTOLOGY-CHECKER-IS-COMPLETE) EVENT (PROVE-LEMMA TAUTOLOGYP-FAILS-MEANS-FALSIFY1-WINS (REWRITE) (IMPLIES (AND (NORMALIZED-IF-EXPRP X) (NOT (TAUTOLOGYP X A)) A) (FALSIFY1 X A))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ASSIGNMENT-IMPLIES-ASSIGNED . TAUTOLOGYP-FAILS-MEANS-FALSIFY1-WINS) (IMMEDIATE-DEPENDENTS0 CONS-IF . TAUTOLOGYP-FAILS-MEANS-FALSIFY1-WINS) (IMMEDIATE-DEPENDENTS0 FALSIFY1 . TAUTOLOGYP-FAILS-MEANS-FALSIFY1-WINS) (IMMEDIATE-DEPENDENTS0 TAUTOLOGYP . TAUTOLOGYP-FAILS-MEANS-FALSIFY1-WINS) (IMMEDIATE-DEPENDENTS0 NORMALIZED-IF-EXPRP . TAUTOLOGYP-FAILS-MEANS-FALSIFY1-WINS) (LEMMAS FALSIFY1 . TAUTOLOGYP-FAILS-MEANS-FALSIFY1-WINS))))) 
(PUT1-LST (QUOTE FALSIFY1-FALSIFIES) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117184753. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (TAUTOLOGY-CHECKER-COMPLETENESS-BRIDGE) EVENT (PROVE-LEMMA FALSIFY1-FALSIFIES (REWRITE) (IMPLIES (AND (NORMALIZED-IF-EXPRP X) (FALSIFY1 X A)) (EQUAL (VALUE X (FALSIFY1 X A)) F))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 CONS-IF . FALSIFY1-FALSIFIES) (IMMEDIATE-DEPENDENTS0 ASSUME-TRUE . FALSIFY1-FALSIFIES) (IMMEDIATE-DEPENDENTS0 ASSUME-FALSE . FALSIFY1-FALSIFIES) (IMMEDIATE-DEPENDENTS0 ASSIGNEDP . FALSIFY1-FALSIFIES) (IMMEDIATE-DEPENDENTS0 ASSIGNMENT . FALSIFY1-FALSIFIES) (IMMEDIATE-DEPENDENTS0 FALSIFY1-EXTENDS-MODELS . FALSIFY1-FALSIFIES) (IMMEDIATE-DEPENDENTS0 VALUE-SHORT-CUT . FALSIFY1-FALSIFIES) (IMMEDIATE-DEPENDENTS0 ASSIGNMENT-IMPLIES-ASSIGNED . FALSIFY1-FALSIFIES) (IMMEDIATE-DEPENDENTS0 VALUE . FALSIFY1-FALSIFIES) (IMMEDIATE-DEPENDENTS0 FALSIFY1 . FALSIFY1-FALSIFIES) (IMMEDIATE-DEPENDENTS0 NORMALIZED-IF-EXPRP . FALSIFY1-FALSIFIES) (LEMMAS VALUE . FALSIFY1-FALSIFIES))))) 
(PUT1-LST (QUOTE FALSIFY1-EXTENDS-MODELS) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117183909. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (FALSIFY1-FALSIFIES) EVENT (PROVE-LEMMA FALSIFY1-EXTENDS-MODELS (REWRITE) (IMPLIES (ASSIGNEDP X A) (EQUAL (ASSIGNMENT X (FALSIFY1 Y A)) (IF (FALSIFY1 Y A) (ASSIGNMENT X A) (EQUAL X T))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ASSUME-FALSE . FALSIFY1-EXTENDS-MODELS) (IMMEDIATE-DEPENDENTS0 ASSUME-TRUE . FALSIFY1-EXTENDS-MODELS) (IMMEDIATE-DEPENDENTS0 ASSIGNMENT-IMPLIES-ASSIGNED . FALSIFY1-EXTENDS-MODELS) (IMMEDIATE-DEPENDENTS0 CONS-IF . FALSIFY1-EXTENDS-MODELS) (IMMEDIATE-DEPENDENTS0 FALSIFY1 . FALSIFY1-EXTENDS-MODELS) (IMMEDIATE-DEPENDENTS0 ASSIGNMENT . FALSIFY1-EXTENDS-MODELS) (IMMEDIATE-DEPENDENTS0 ASSIGNEDP . FALSIFY1-EXTENDS-MODELS) (LEMMAS ASSIGNMENT . FALSIFY1-EXTENDS-MODELS))))) 
(PUT1-LST (QUOTE 1FALSIFY) (QUOTE NIL)) 
(PUT1-LST (QUOTE FALSIFY) (QUOTE (TYPE-PRESCRIPTION-LST ((FALSIFY 25. NIL)) SDEFN (LAMBDA (X) (FALSIFY1 (NORMALIZE X) (QUOTE NIL))) LISP-CODE 1FALSIFY INDUCTION-MACHINE NIL LEVEL-NO 2. JUSTIFICATIONS NIL IDATE 840117183814. SATELLITES (1FALSIFY) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (TAUTOLOGY-CHECKER-IS-COMPLETE) EVENT (DEFN FALSIFY (X) (FALSIFY1 (NORMALIZE X) NIL)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 NORMALIZE . FALSIFY) (IMMEDIATE-DEPENDENTS0 FALSIFY1 . FALSIFY) (DCELL . 1FALSIFY))))) 
(PUT1-LST (QUOTE 1FALSIFY1) (QUOTE NIL)) 
(PUT1-LST (QUOTE FALSIFY1) (QUOTE (TYPE-PRESCRIPTION-LST ((FALSIFY1 17. NIL T)) LEMMAS ((REWRITE-RULE TAUTOLOGYP-FAILS-MEANS-FALSIFY1-WINS ((NORMALIZED-IF-EXPRP X) (NOT (TAUTOLOGYP X A)) A) (FALSIFY1 X A) NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE QUESTIONABLE) SDEFN (LAMBDA (X ALIST) (IF (IF-EXPRP X) (IF (ASSIGNEDP (TEST X) ALIST) (IF (ASSIGNMENT (TEST X) ALIST) (FALSIFY1 (LEFT-BRANCH X) ALIST) (FALSIFY1 (RIGHT-BRANCH X) ALIST)) (IF (FALSIFY1 (LEFT-BRANCH X) (ASSUME-TRUE (TEST X) ALIST)) (FALSIFY1 (LEFT-BRANCH X) (ASSUME-TRUE (TEST X) ALIST)) (FALSIFY1 (RIGHT-BRANCH X) (ASSUME-FALSE (TEST X) ALIST)))) (IF (ASSIGNEDP X ALIST) (IF (ASSIGNMENT X ALIST) (QUOTE 1FALSE) ALIST) (CONS (CONS X (QUOTE 1FALSE)) ALIST)))) LISP-CODE 1FALSIFY1 INDUCTION-MACHINE ((TESTS-AND-CASES ((IF-EXPRP X) (ASSIGNEDP (TEST X) ALIST) (ASSIGNMENT (TEST X) ALIST)) (((LEFT-BRANCH X) ALIST))) (TESTS-AND-CASES ((IF-EXPRP X) (ASSIGNEDP (TEST X) ALIST) (NOT (ASSIGNMENT (TEST X) ALIST))) (((RIGHT-BRANCH X) ALIST))) (TESTS-AND-CASES ((IF-EXPRP X) (NOT (ASSIGNEDP (TEST X) ALIST)) (FALSIFY1 (LEFT-BRANCH X) (ASSUME-TRUE (TEST X) ALIST))) (((LEFT-BRANCH X) (ASSUME-TRUE (TEST X) ALIST)))) (TESTS-AND-CASES ((IF-EXPRP X) (NOT (ASSIGNEDP (TEST X) ALIST)) (NOT (FALSIFY1 (LEFT-BRANCH X) (ASSUME-TRUE (TEST X) ALIST)))) (((LEFT-BRANCH X) (ASSUME-TRUE (TEST X) ALIST)) ((RIGHT-BRANCH X) (ASSUME-FALSE (TEST X) ALIST)))) (TESTS-AND-CASES ((NOT (IF-EXPRP X)) (ASSIGNEDP X ALIST) (ASSIGNMENT X ALIST)) NIL) (TESTS-AND-CASES ((NOT (IF-EXPRP X)) (ASSIGNEDP X ALIST) (NOT (ASSIGNMENT X ALIST))) NIL) (TESTS-AND-CASES ((NOT (IF-EXPRP X)) (NOT (ASSIGNEDP X ALIST))) NIL)) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (X) (COUNT X) LESSP (RIGHT-BRANCH-LESSP ZERO LEFT-BRANCH-LESSP))) IDATE 840117183809. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1FALSIFY1) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (TAUTOLOGY-CHECKER-COMPLETENESS-BRIDGE TAUTOLOGYP-FAILS-MEANS-FALSIFY1-WINS FALSIFY1-FALSIFIES FALSIFY1-EXTENDS-MODELS FALSIFY) EVENT (DEFN FALSIFY1 (X ALIST) (IF (IF-EXPRP X) (IF (ASSIGNEDP (TEST X) ALIST) (IF (ASSIGNMENT (TEST X) ALIST) (FALSIFY1 (LEFT-BRANCH X) ALIST) (FALSIFY1 (RIGHT-BRANCH X) ALIST)) (IF (FALSIFY1 (LEFT-BRANCH X) (ASSUME-TRUE (TEST X) ALIST)) (FALSIFY1 (LEFT-BRANCH X) (ASSUME-TRUE (TEST X) ALIST)) (FALSIFY1 (RIGHT-BRANCH X) (ASSUME-FALSE (TEST X) ALIST)))) (IF (ASSIGNEDP X ALIST) (IF (ASSIGNMENT X ALIST) F ALIST) (CONS (CONS X F) ALIST)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ASSUME-FALSE . FALSIFY1) (IMMEDIATE-DEPENDENTS0 ASSUME-TRUE . FALSIFY1) (IMMEDIATE-DEPENDENTS0 CONS-IF . FALSIFY1) (IMMEDIATE-DEPENDENTS0 ASSIGNMENT . FALSIFY1) (IMMEDIATE-DEPENDENTS0 ASSIGNEDP . FALSIFY1) (DCELL . 1FALSIFY1))))) 
(PUT1-LST (QUOTE 1TAUTOLOGY-CHECKER) (QUOTE NIL)) 
(PUT1-LST (QUOTE TAUTOLOGY-CHECKER) (QUOTE (TYPE-PRESCRIPTION-LST ((TAUTOLOGY-CHECKER -1. NIL)) SDEFN (LAMBDA (X) (TAUTOLOGYP (NORMALIZE X) (QUOTE NIL))) LISP-CODE 1TAUTOLOGY-CHECKER INDUCTION-MACHINE NIL LEVEL-NO 2. JUSTIFICATIONS NIL IDATE 840117183809. SATELLITES (1TAUTOLOGY-CHECKER) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (TAUTOLOGY-CHECKER-IS-SOUND TAUTOLOGY-CHECKER-IS-COMPLETE) EVENT (DEFN TAUTOLOGY-CHECKER (X) (TAUTOLOGYP (NORMALIZE X) NIL)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 NORMALIZE . TAUTOLOGY-CHECKER) (IMMEDIATE-DEPENDENTS0 TAUTOLOGYP . TAUTOLOGY-CHECKER) (DCELL . 1TAUTOLOGY-CHECKER))))) 
(PUT1-LST (QUOTE TAUTOLOGYP-IS-SOUND) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117183809. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (TAUTOLOGY-CHECKER-SOUNDNESS-BRIDGE) EVENT (PROVE-LEMMA TAUTOLOGYP-IS-SOUND (REWRITE) (IMPLIES (AND (NORMALIZED-IF-EXPRP X) (TAUTOLOGYP X A1)) (VALUE X (APPEND A1 A2)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ASSIGNMENT-IMPLIES-ASSIGNED . TAUTOLOGYP-IS-SOUND) (IMMEDIATE-DEPENDENTS0 IFF . TAUTOLOGYP-IS-SOUND) (IMMEDIATE-DEPENDENTS0 VALUE-CAN-IGNORE-REDUNDANT-ASSIGNMENTS . TAUTOLOGYP-IS-SOUND) (IMMEDIATE-DEPENDENTS0 ASSUME-FALSE . TAUTOLOGYP-IS-SOUND) (IMMEDIATE-DEPENDENTS0 ASSUME-TRUE . TAUTOLOGYP-IS-SOUND) (IMMEDIATE-DEPENDENTS0 ASSIGNMENT-APPEND . TAUTOLOGYP-IS-SOUND) (IMMEDIATE-DEPENDENTS0 VALUE-SHORT-CUT . TAUTOLOGYP-IS-SOUND) (IMMEDIATE-DEPENDENTS0 CONS-IF . TAUTOLOGYP-IS-SOUND) (IMMEDIATE-DEPENDENTS0 APPEND . TAUTOLOGYP-IS-SOUND) (IMMEDIATE-DEPENDENTS0 VALUE . TAUTOLOGYP-IS-SOUND) (IMMEDIATE-DEPENDENTS0 TAUTOLOGYP . TAUTOLOGYP-IS-SOUND) (IMMEDIATE-DEPENDENTS0 NORMALIZED-IF-EXPRP . TAUTOLOGYP-IS-SOUND) (LEMMAS VALUE . TAUTOLOGYP-IS-SOUND))))) 
(PUT1-LST (QUOTE ASSIGNMENT-IMPLIES-ASSIGNED) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117183708. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (TAUTOLOGYP-FAILS-MEANS-FALSIFY1-WINS FALSIFY1-FALSIFIES FALSIFY1-EXTENDS-MODELS TAUTOLOGYP-IS-SOUND) EVENT (PROVE-LEMMA ASSIGNMENT-IMPLIES-ASSIGNED (REWRITE) (IMPLIES (ASSIGNMENT X A) (ASSIGNEDP X A))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ASSIGNEDP . ASSIGNMENT-IMPLIES-ASSIGNED) (IMMEDIATE-DEPENDENTS0 ASSIGNMENT . ASSIGNMENT-IMPLIES-ASSIGNED) (LEMMAS ASSIGNEDP . ASSIGNMENT-IMPLIES-ASSIGNED))))) 
(PUT1-LST (QUOTE VALUE-SHORT-CUT) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117183704. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (FALSIFY1-FALSIFIES TAUTOLOGYP-IS-SOUND) EVENT (PROVE-LEMMA VALUE-SHORT-CUT (REWRITE) (IMPLIES (AND (IF-EXPRP X) (NORMALIZED-IF-EXPRP X)) (EQUAL (VALUE (TEST X) A) (ASSIGNMENT (TEST X) A)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 CONS-IF . VALUE-SHORT-CUT) (IMMEDIATE-DEPENDENTS0 ASSIGNMENT . VALUE-SHORT-CUT) (IMMEDIATE-DEPENDENTS0 VALUE . VALUE-SHORT-CUT) (IMMEDIATE-DEPENDENTS0 NORMALIZED-IF-EXPRP . VALUE-SHORT-CUT) (LEMMAS VALUE . VALUE-SHORT-CUT))))) 
(PUT1-LST (QUOTE VALUE-CAN-IGNORE-REDUNDANT-ASSIGNMENTS) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117183703. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (TAUTOLOGYP-IS-SOUND) EVENT (PROVE-LEMMA VALUE-CAN-IGNORE-REDUNDANT-ASSIGNMENTS (REWRITE) (AND (IMPLIES (AND (IFF VAL (ASSIGNMENT VAR A)) (VALUE X A)) (VALUE X (CONS (CONS VAR VAL) A))) (IMPLIES (AND (IFF VAL (ASSIGNMENT VAR A)) (NOT (VALUE X A))) (NOT (VALUE X (CONS (CONS VAR VAL) A)))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 CONS-IF . VALUE-CAN-IGNORE-REDUNDANT-ASSIGNMENTS) (IMMEDIATE-DEPENDENTS0 VALUE . VALUE-CAN-IGNORE-REDUNDANT-ASSIGNMENTS) (IMMEDIATE-DEPENDENTS0 ASSIGNMENT . VALUE-CAN-IGNORE-REDUNDANT-ASSIGNMENTS) (IMMEDIATE-DEPENDENTS0 IFF . VALUE-CAN-IGNORE-REDUNDANT-ASSIGNMENTS) (LEMMAS VALUE . VALUE-CAN-IGNORE-REDUNDANT-ASSIGNMENTS) (LEMMAS VALUE . VALUE-CAN-IGNORE-REDUNDANT-ASSIGNMENTS))))) 
(PUT1-LST (QUOTE ASSIGNMENT-APPEND) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117183637. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (TAUTOLOGYP-IS-SOUND) EVENT (PROVE-LEMMA ASSIGNMENT-APPEND (REWRITE) (EQUAL (ASSIGNMENT X (APPEND A B)) (IF (ASSIGNEDP X A) (ASSIGNMENT X A) (ASSIGNMENT X B)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ASSIGNEDP . ASSIGNMENT-APPEND) (IMMEDIATE-DEPENDENTS0 APPEND . ASSIGNMENT-APPEND) (IMMEDIATE-DEPENDENTS0 ASSIGNMENT . ASSIGNMENT-APPEND) (LEMMAS ASSIGNMENT . ASSIGNMENT-APPEND))))) 
(PUT1-LST (QUOTE 1TAUTOLOGYP) (QUOTE NIL)) 
(PUT1-LST (QUOTE TAUTOLOGYP) (QUOTE (TYPE-PRESCRIPTION-LST ((TAUTOLOGYP -1. NIL NIL)) LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE QUESTIONABLE) SDEFN (LAMBDA (X ALIST) (IF (IF-EXPRP X) (IF (ASSIGNEDP (TEST X) ALIST) (IF (ASSIGNMENT (TEST X) ALIST) (TAUTOLOGYP (LEFT-BRANCH X) ALIST) (TAUTOLOGYP (RIGHT-BRANCH X) ALIST)) (IF (TAUTOLOGYP (LEFT-BRANCH X) (ASSUME-TRUE (TEST X) ALIST)) (IF (TAUTOLOGYP (RIGHT-BRANCH X) (ASSUME-FALSE (TEST X) ALIST)) (QUOTE 1TRUE) (QUOTE 1FALSE)) (QUOTE 1FALSE))) (ASSIGNMENT X ALIST))) LISP-CODE 1TAUTOLOGYP INDUCTION-MACHINE ((TESTS-AND-CASES ((IF-EXPRP X) (ASSIGNEDP (TEST X) ALIST) (ASSIGNMENT (TEST X) ALIST)) (((LEFT-BRANCH X) ALIST))) (TESTS-AND-CASES ((IF-EXPRP X) (ASSIGNEDP (TEST X) ALIST) (NOT (ASSIGNMENT (TEST X) ALIST))) (((RIGHT-BRANCH X) ALIST))) (TESTS-AND-CASES ((IF-EXPRP X) (NOT (ASSIGNEDP (TEST X) ALIST))) (((RIGHT-BRANCH X) (ASSUME-FALSE (TEST X) ALIST)) ((LEFT-BRANCH X) (ASSUME-TRUE (TEST X) ALIST)))) (TESTS-AND-CASES ((NOT (IF-EXPRP X))) NIL)) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (X) (COUNT X) LESSP (RIGHT-BRANCH-LESSP ZERO LEFT-BRANCH-LESSP))) IDATE 840117183633. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1TAUTOLOGYP) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (TAUTOLOGY-CHECKER-SOUNDNESS-BRIDGE TAUTOLOGYP-FAILS-MEANS-FALSIFY1-WINS TAUTOLOGY-CHECKER TAUTOLOGYP-IS-SOUND) EVENT (DEFN TAUTOLOGYP (X ALIST) (IF (IF-EXPRP X) (IF (ASSIGNEDP (TEST X) ALIST) (IF (ASSIGNMENT (TEST X) ALIST) (TAUTOLOGYP (LEFT-BRANCH X) ALIST) (TAUTOLOGYP (RIGHT-BRANCH X) ALIST)) (AND (TAUTOLOGYP (LEFT-BRANCH X) (ASSUME-TRUE (TEST X) ALIST)) (TAUTOLOGYP (RIGHT-BRANCH X) (ASSUME-FALSE (TEST X) ALIST)))) (ASSIGNMENT X ALIST))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ASSUME-FALSE . TAUTOLOGYP) (IMMEDIATE-DEPENDENTS0 ASSUME-TRUE . TAUTOLOGYP) (IMMEDIATE-DEPENDENTS0 CONS-IF . TAUTOLOGYP) (IMMEDIATE-DEPENDENTS0 ASSIGNMENT . TAUTOLOGYP) (IMMEDIATE-DEPENDENTS0 ASSIGNEDP . TAUTOLOGYP) (DCELL . 1TAUTOLOGYP))))) 
(PUT1-LST (QUOTE 1ASSUME-FALSE) (QUOTE NIL)) 
(PUT1-LST (QUOTE ASSUME-FALSE) (QUOTE (TYPE-PRESCRIPTION-LST ((ASSUME-FALSE 16. NIL NIL)) LEMMAS NIL SDEFN (LAMBDA (VAR ALIST) (CONS (CONS VAR (QUOTE 1FALSE)) ALIST)) LISP-CODE 1ASSUME-FALSE INDUCTION-MACHINE NIL LEVEL-NO 0. JUSTIFICATIONS NIL IDATE 840117183632. CONTROLLER-POCKETS NIL SATELLITES (1ASSUME-FALSE) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (FALSIFY1-FALSIFIES FALSIFY1-EXTENDS-MODELS FALSIFY1 TAUTOLOGYP-IS-SOUND TAUTOLOGYP) EVENT (DEFN ASSUME-FALSE (VAR ALIST) (CONS (CONS VAR F) ALIST)) LOCAL-UNDO-TUPLES ((DCELL . 1ASSUME-FALSE))))) 
(PUT1-LST (QUOTE 1ASSUME-TRUE) (QUOTE NIL)) 
(PUT1-LST (QUOTE ASSUME-TRUE) (QUOTE (TYPE-PRESCRIPTION-LST ((ASSUME-TRUE 16. NIL NIL)) LEMMAS NIL SDEFN (LAMBDA (VAR ALIST) (CONS (CONS VAR (QUOTE 1TRUE)) ALIST)) LISP-CODE 1ASSUME-TRUE INDUCTION-MACHINE NIL LEVEL-NO 0. JUSTIFICATIONS NIL IDATE 840117183631. CONTROLLER-POCKETS NIL SATELLITES (1ASSUME-TRUE) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (FALSIFY1-FALSIFIES FALSIFY1-EXTENDS-MODELS FALSIFY1 TAUTOLOGYP-IS-SOUND TAUTOLOGYP) EVENT (DEFN ASSUME-TRUE (VAR ALIST) (CONS (CONS VAR T) ALIST)) LOCAL-UNDO-TUPLES ((DCELL . 1ASSUME-TRUE))))) 
(PUT1-LST (QUOTE 1ASSIGNEDP) (QUOTE NIL)) 
(PUT1-LST (QUOTE ASSIGNEDP) (QUOTE (TYPE-PRESCRIPTION-LST ((ASSIGNEDP 3. NIL NIL)) LEMMAS ((REWRITE-RULE ASSIGNMENT-IMPLIES-ASSIGNED ((ASSIGNMENT X A)) (ASSIGNEDP X A) NIL)) QUICK-BLOCK-INFO (UNCHANGING SELF-REFLEXIVE) SDEFN (LAMBDA (VAR ALIST) (IF (EQUAL VAR (QUOTE 1TRUE)) (QUOTE 1TRUE) (IF (EQUAL VAR (QUOTE 1FALSE)) (QUOTE 1TRUE) (IF (LISTP ALIST) (IF (EQUAL VAR (CAR (CAR ALIST))) (QUOTE 1TRUE) (ASSIGNEDP VAR (CDR ALIST))) (QUOTE 1FALSE))))) LISP-CODE 1ASSIGNEDP INDUCTION-MACHINE ((TESTS-AND-CASES ((EQUAL VAR (QUOTE 1TRUE))) NIL) (TESTS-AND-CASES ((NOT (EQUAL VAR (QUOTE 1TRUE))) (EQUAL VAR (QUOTE 1FALSE))) NIL) (TESTS-AND-CASES ((NOT (EQUAL VAR (QUOTE 1TRUE))) (NOT (EQUAL VAR (QUOTE 1FALSE))) (NLISTP ALIST)) NIL) (TESTS-AND-CASES ((NOT (EQUAL VAR (QUOTE 1TRUE))) (NOT (EQUAL VAR (QUOTE 1FALSE))) (NOT (NLISTP ALIST)) (EQUAL VAR (CAR (CAR ALIST)))) NIL) (TESTS-AND-CASES ((NOT (EQUAL VAR (QUOTE 1TRUE))) (NOT (EQUAL VAR (QUOTE 1FALSE))) (NOT (NLISTP ALIST)) (NOT (EQUAL VAR (CAR (CAR ALIST))))) ((VAR (CDR ALIST))))) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (ALIST) (COUNT ALIST) LESSP (CDR-LESSP NLISTP ZERO CDR-LESSEQP))) IDATE 840117183630. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (2.) SATELLITES (1ASSIGNEDP) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (FALSIFY1-FALSIFIES FALSIFY1-EXTENDS-MODELS FALSIFY1 ASSIGNMENT-IMPLIES-ASSIGNED ASSIGNMENT-APPEND TAUTOLOGYP) EVENT (DEFN ASSIGNEDP (VAR ALIST) (IF (EQUAL VAR T) T (IF (EQUAL VAR F) T (IF (NLISTP ALIST) F (IF (EQUAL VAR (CAAR ALIST)) T (ASSIGNEDP VAR (CDR ALIST))))))) LOCAL-UNDO-TUPLES ((DCELL . 1ASSIGNEDP))))) 
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(PUT1-LST (QUOTE NORMALIZED-IF-EXPRP) (QUOTE (TYPE-PRESCRIPTION-LST ((NORMALIZED-IF-EXPRP 3. NIL)) LEMMAS ((REWRITE-RULE NORMALIZE-NORMALIZES NIL (NORMALIZED-IF-EXPRP (NORMALIZE X)) NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (X) (IF (IF-EXPRP X) (IF (IF-EXPRP (TEST X)) (QUOTE 1FALSE) (IF (NORMALIZED-IF-EXPRP (LEFT-BRANCH X)) (IF (NORMALIZED-IF-EXPRP (RIGHT-BRANCH X)) (QUOTE 1TRUE) (QUOTE 1FALSE)) (QUOTE 1FALSE))) (QUOTE 1TRUE))) LISP-CODE 1NORMALIZED-IF-EXPRP INDUCTION-MACHINE ((TESTS-AND-CASES ((IF-EXPRP X)) (((RIGHT-BRANCH X)) ((LEFT-BRANCH X)))) (TESTS-AND-CASES ((NOT (IF-EXPRP X))) NIL)) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (X) (COUNT X) LESSP (LEFT-BRANCH-LESSP ZERO RIGHT-BRANCH-LESSP))) IDATE 840117183629. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1NORMALIZED-IF-EXPRP) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (TAUTOLOGY-CHECKER-SOUNDNESS-BRIDGE TAUTOLOGY-CHECKER-COMPLETENESS-BRIDGE NORMALIZE-NORMALIZES TAUTOLOGYP-FAILS-MEANS-FALSIFY1-WINS FALSIFY1-FALSIFIES TAUTOLOGYP-IS-SOUND VALUE-SHORT-CUT) EVENT (DEFN NORMALIZED-IF-EXPRP (X) (IF (IF-EXPRP X) (AND (NOT (IF-EXPRP (TEST X))) (NORMALIZED-IF-EXPRP (LEFT-BRANCH X)) (NORMALIZED-IF-EXPRP (RIGHT-BRANCH X))) T)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 CONS-IF . NORMALIZED-IF-EXPRP) (DCELL . 1NORMALIZED-IF-EXPRP))))) 
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(PUT1-LST (QUOTE NORMALIZE) (QUOTE (TYPE-PRESCRIPTION-LST ((NORMALIZE 128. T)) LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (X) (IF (IF-EXPRP X) (IF (IF-EXPRP (TEST X)) (NORMALIZE (CONS-IF (TEST (TEST X)) (CONS-IF (LEFT-BRANCH (TEST X)) (LEFT-BRANCH X) (RIGHT-BRANCH X)) (CONS-IF (RIGHT-BRANCH (TEST X)) (LEFT-BRANCH X) (RIGHT-BRANCH X)))) (CONS-IF (TEST X) (NORMALIZE (LEFT-BRANCH X)) (NORMALIZE (RIGHT-BRANCH X)))) X)) LISP-CODE 1NORMALIZE INDUCTION-MACHINE ((TESTS-AND-CASES ((IF-EXPRP X) (IF-EXPRP (TEST X))) (((CONS-IF (TEST (TEST X)) (CONS-IF (LEFT-BRANCH (TEST X)) (LEFT-BRANCH X) (RIGHT-BRANCH X)) (CONS-IF (RIGHT-BRANCH (TEST X)) (LEFT-BRANCH X) (RIGHT-BRANCH X)))))) (TESTS-AND-CASES ((IF-EXPRP X) (NOT (IF-EXPRP (TEST X)))) (((RIGHT-BRANCH X)) ((LEFT-BRANCH X)))) (TESTS-AND-CASES ((NOT (IF-EXPRP X))) NIL)) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (X) (CONS (IF-COMPLEXITY X) (CONS (IF-DEPTH X) (QUOTE NIL))) LEX2 (IF-COMPLEXITY-GOES-DOWN1 IF-COMPLEXITY-GOES-DOWN2 ADD1 CONS CAR ZERO DISTRIBUTIVITY-OF-TIMES-OVER-PLUS RIGHT-BRANCH-CONS-IF LEFT-BRANCH-CONS-IF TEST-CONS-IF IF-COMPLEXITY COMMUTATIVITY-OF-TIMES COMMUTATIVITY2-OF-TIMES COMMUTATIVITY2-OF-PLUS ASSOCIATIVITY-OF-PLUS IF-DEPTH LESSP SUB1-ADD1 CDR-CONS LESSP-PLUS-CANCELATION LESSP-TIMES-CANCELLATION EQUAL-TIMES-0 IF-COMPLEXITY-NOT-0 CAR-CONS LEX2))) IDATE 840117183611. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1NORMALIZE) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (NORMALIZE-NORMALIZES NORMALIZE-IS-SOUND FALSIFY TAUTOLOGY-CHECKER) EVENT (DEFN NORMALIZE (X) (IF (IF-EXPRP X) (IF (IF-EXPRP (TEST X)) (NORMALIZE (CONS-IF (TEST (TEST X)) (CONS-IF (LEFT-BRANCH (TEST X)) (LEFT-BRANCH X) (RIGHT-BRANCH X)) (CONS-IF (RIGHT-BRANCH (TEST X)) (LEFT-BRANCH X) (RIGHT-BRANCH X)))) (CONS-IF (TEST X) (NORMALIZE (LEFT-BRANCH X)) (NORMALIZE (RIGHT-BRANCH X)))) X) ((LEX2 (LIST (IF-COMPLEXITY X) (IF-DEPTH X))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 CONS-IF . NORMALIZE) (IMMEDIATE-DEPENDENTS0 IF-COMPLEXITY-GOES-DOWN1 . NORMALIZE) (IMMEDIATE-DEPENDENTS0 IF-COMPLEXITY-GOES-DOWN2 . NORMALIZE) (IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-TIMES-OVER-PLUS . NORMALIZE) (IMMEDIATE-DEPENDENTS0 IF-COMPLEXITY . NORMALIZE) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . NORMALIZE) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-TIMES . NORMALIZE) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-PLUS . NORMALIZE) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-PLUS . NORMALIZE) (IMMEDIATE-DEPENDENTS0 IF-DEPTH . NORMALIZE) (IMMEDIATE-DEPENDENTS0 LESSP-PLUS-CANCELATION . NORMALIZE) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES-CANCELLATION . NORMALIZE) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . NORMALIZE) (IMMEDIATE-DEPENDENTS0 IF-COMPLEXITY-NOT-0 . NORMALIZE) (DCELL . 1NORMALIZE))))) 
(PUT1-LST (QUOTE IF-COMPLEXITY-GOES-DOWN2) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117183611. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (NORMALIZE-NORMALIZES NORMALIZE-IS-SOUND NORMALIZE) EVENT (PROVE-LEMMA IF-COMPLEXITY-GOES-DOWN2 (REWRITE) (IMPLIES (IF-EXPRP X) (LESSP (IF-COMPLEXITY (RIGHT-BRANCH X)) (IF-COMPLEXITY X)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LESSP-TIMES-1 . IF-COMPLEXITY-GOES-DOWN2) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES-2 . IF-COMPLEXITY-GOES-DOWN2) (IMMEDIATE-DEPENDENTS0 IF-COMPLEXITY-NOT-0 . IF-COMPLEXITY-GOES-DOWN2) (IMMEDIATE-DEPENDENTS0 CONS-IF . IF-COMPLEXITY-GOES-DOWN2) (IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-TIMES-OVER-PLUS . IF-COMPLEXITY-GOES-DOWN2) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . IF-COMPLEXITY-GOES-DOWN2) (IMMEDIATE-DEPENDENTS0 IF-COMPLEXITY . IF-COMPLEXITY-GOES-DOWN2) (LINEAR-LEMMAS IF-COMPLEXITY . IF-COMPLEXITY-GOES-DOWN2))))) 
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(PUT1-LST (QUOTE IF-COMPLEXITY) (QUOTE (TYPE-PRESCRIPTION-LST ((IF-COMPLEXITY 4. NIL)) LEMMAS NIL LINEAR-LEMMAS ((LINEAR-LEMMA IF-COMPLEXITY-GOES-DOWN2 ((IF-EXPRP X)) (LESSP (IF-COMPLEXITY (RIGHT-BRANCH X)) (IF-COMPLEXITY X)) (IF-COMPLEXITY (RIGHT-BRANCH X))) (LINEAR-LEMMA IF-COMPLEXITY-GOES-DOWN1 ((IF-EXPRP X)) (LESSP (IF-COMPLEXITY (LEFT-BRANCH X)) (IF-COMPLEXITY X)) (IF-COMPLEXITY (LEFT-BRANCH X)))) QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (X) (IF (IF-EXPRP X) (TIMES (IF-COMPLEXITY (TEST X)) (PLUS (IF-COMPLEXITY (LEFT-BRANCH X)) (IF-COMPLEXITY (RIGHT-BRANCH X)))) (QUOTE 1.))) LISP-CODE 1IF-COMPLEXITY INDUCTION-MACHINE ((TESTS-AND-CASES ((IF-EXPRP X)) (((RIGHT-BRANCH X)) ((LEFT-BRANCH X)) ((TEST X)))) (TESTS-AND-CASES ((NOT (IF-EXPRP X))) NIL)) LEVEL-NO 3. JUSTIFICATIONS ((JUSTIFICATION (X) (COUNT X) LESSP (TEST-LESSP LEFT-BRANCH-LESSP ZERO RIGHT-BRANCH-LESSP))) IDATE 840117183451. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1IF-COMPLEXITY) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (NORMALIZE-NORMALIZES NORMALIZE-IS-SOUND NORMALIZE IF-COMPLEXITY-GOES-DOWN2 IF-COMPLEXITY-GOES-DOWN1 IF-COMPLEXITY-NOT-0) EVENT (DEFN IF-COMPLEXITY (X) (IF (IF-EXPRP X) (TIMES (IF-COMPLEXITY (TEST X)) (PLUS (IF-COMPLEXITY (LEFT-BRANCH X)) (IF-COMPLEXITY (RIGHT-BRANCH X)))) 1.)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 CONS-IF . IF-COMPLEXITY) (DCELL . 1IF-COMPLEXITY))))) 
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(PUT1-LST (QUOTE IF-DEPTH) (QUOTE (TYPE-PRESCRIPTION-LST ((IF-DEPTH 4. NIL)) LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (X) (IF (IF-EXPRP X) (ADD1 (IF-DEPTH (TEST X))) (QUOTE 0.))) LISP-CODE 1IF-DEPTH INDUCTION-MACHINE ((TESTS-AND-CASES ((IF-EXPRP X)) (((TEST X)))) (TESTS-AND-CASES ((NOT (IF-EXPRP X))) NIL)) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (X) (COUNT X) LESSP (ZERO TEST-LESSP))) IDATE 840117183449. CONTROLLER-POCKETS (1.) SATELLITES (1IF-DEPTH) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (NORMALIZE-NORMALIZES NORMALIZE-IS-SOUND NORMALIZE) EVENT (DEFN IF-DEPTH (X) (IF (IF-EXPRP X) (ADD1 (IF-DEPTH (TEST X))) 0.)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 CONS-IF . IF-DEPTH) (DCELL . 1IF-DEPTH))))) 
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(PUT1-LST (QUOTE VALUE) (QUOTE (TYPE-PRESCRIPTION-LST ((VALUE -1. NIL NIL)) LEMMAS ((REWRITE-RULE TAUTOLOGY-CHECKER-SOUNDNESS-BRIDGE ((TAUTOLOGYP Y A1) (NORMALIZED-IF-EXPRP Y) (EQUAL (VALUE X A2) (VALUE Y (APPEND A1 A2)))) (VALUE X A2) NIL) (REWRITE-RULE TAUTOLOGY-CHECKER-COMPLETENESS-BRIDGE ((EQUAL (VALUE Y (FALSIFY1 X A)) (VALUE X (FALSIFY1 X A))) (FALSIFY1 X A) (NORMALIZED-IF-EXPRP X)) (EQUAL (VALUE Y (FALSIFY1 X A)) (QUOTE 1FALSE)) NIL) (REWRITE-RULE NORMALIZE-IS-SOUND NIL (EQUAL (VALUE (NORMALIZE X) A) (VALUE X A)) NIL) (REWRITE-RULE FALSIFY1-FALSIFIES ((NORMALIZED-IF-EXPRP X) (FALSIFY1 X A)) (EQUAL (VALUE X (FALSIFY1 X A)) (QUOTE 1FALSE)) NIL) (REWRITE-RULE TAUTOLOGYP-IS-SOUND ((NORMALIZED-IF-EXPRP X) (TAUTOLOGYP X A1)) (VALUE X (APPEND A1 A2)) NIL) (REWRITE-RULE VALUE-SHORT-CUT ((IF-EXPRP X) (NORMALIZED-IF-EXPRP X)) (EQUAL (VALUE (TEST X) A) (ASSIGNMENT (TEST X) A)) NIL) (REWRITE-RULE VALUE-CAN-IGNORE-REDUNDANT-ASSIGNMENTS ((IFF VAL (ASSIGNMENT VAR A)) (NOT (VALUE X A))) (NOT (VALUE X (CONS (CONS VAR VAL) A))) NIL) (REWRITE-RULE VALUE-CAN-IGNORE-REDUNDANT-ASSIGNMENTS ((IFF VAL (ASSIGNMENT VAR A)) (VALUE X A)) (VALUE X (CONS (CONS VAR VAL) A)) NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE UNCHANGING) SDEFN (LAMBDA (X ALIST) (IF (IF-EXPRP X) (IF (VALUE (TEST X) ALIST) (VALUE (LEFT-BRANCH X) ALIST) (VALUE (RIGHT-BRANCH X) ALIST)) (ASSIGNMENT X ALIST))) LISP-CODE 1VALUE INDUCTION-MACHINE ((TESTS-AND-CASES ((IF-EXPRP X) (VALUE (TEST X) ALIST)) (((TEST X) ALIST) ((LEFT-BRANCH X) ALIST))) (TESTS-AND-CASES ((IF-EXPRP X) (NOT (VALUE (TEST X) ALIST))) (((TEST X) ALIST) ((RIGHT-BRANCH X) ALIST))) (TESTS-AND-CASES ((NOT (IF-EXPRP X))) NIL)) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (X) (COUNT X) LESSP (RIGHT-BRANCH-LESSP LEFT-BRANCH-LESSP ZERO TEST-LESSP))) IDATE 840117183448. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1VALUE) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (TAUTOLOGY-CHECKER-IS-SOUND TAUTOLOGY-CHECKER-SOUNDNESS-BRIDGE TAUTOLOGY-CHECKER-IS-COMPLETE TAUTOLOGY-CHECKER-COMPLETENESS-BRIDGE NORMALIZE-IS-SOUND FALSIFY1-FALSIFIES TAUTOLOGYP-IS-SOUND VALUE-SHORT-CUT VALUE-CAN-IGNORE-REDUNDANT-ASSIGNMENTS) EVENT (DEFN VALUE (X ALIST) (IF (IF-EXPRP X) (IF (VALUE (TEST X) ALIST) (VALUE (LEFT-BRANCH X) ALIST) (VALUE (RIGHT-BRANCH X) ALIST)) (ASSIGNMENT X ALIST))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ASSIGNMENT . VALUE) (IMMEDIATE-DEPENDENTS0 CONS-IF . VALUE) (DCELL . 1VALUE))))) 
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(PUT1-LST (QUOTE LEFT-BRANCH) (QUOTE (TYPE-PRESCRIPTION-LST ((CONS-IF -1. NIL)) LEMMAS ((REWRITE-RULE LEFT-BRANCH-NIF-EXPRP ((NOT (IF-EXPRP X))) (EQUAL (LEFT-BRANCH X) (QUOTE 0.)) NIL) (REWRITE-RULE LEFT-BRANCH-CONS-IF NIL (EQUAL (LEFT-BRANCH (CONS-IF TEST LEFT-BRANCH RIGHT-BRANCH)) LEFT-BRANCH) NIL)) QUICK-BLOCK-INFO NIL SDEFN NIL LISP-CODE 1LEFT-BRANCH INDUCTION-MACHINE NIL LEVEL-NO NIL JUSTIFICATIONS NIL ELIMINATE-DESTRUCTORS-SEQ (REWRITE-RULE TEST-LEFT-BRANCH-RIGHT-BRANCH-ELIM ((IF-EXPRP X)) (EQUAL (CONS-IF (TEST X) (LEFT-BRANCH X) (RIGHT-BRANCH X)) X) NIL) ELIMINATE-DESTRUCTORS-DESTS ((LEFT-BRANCH X) (RIGHT-BRANCH X) (TEST X)) MAIN-EVENT CONS-IF EVENT NIL))) 
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(PUT1-LST (QUOTE TEST) (QUOTE (TYPE-PRESCRIPTION-LST ((CONS-IF -1. NIL)) LEMMAS ((REWRITE-RULE TEST-NIF-EXPRP ((NOT (IF-EXPRP X))) (EQUAL (TEST X) (QUOTE 0.)) NIL) (REWRITE-RULE TEST-CONS-IF NIL (EQUAL (TEST (CONS-IF TEST LEFT-BRANCH RIGHT-BRANCH)) TEST) NIL)) SDEFN NIL LISP-CODE 1TEST INDUCTION-MACHINE NIL LEVEL-NO NIL ELIMINATE-DESTRUCTORS-SEQ (REWRITE-RULE TEST-LEFT-BRANCH-RIGHT-BRANCH-ELIM ((IF-EXPRP X)) (EQUAL (CONS-IF (TEST X) (LEFT-BRANCH X) (RIGHT-BRANCH X)) X) NIL) ELIMINATE-DESTRUCTORS-DESTS ((TEST X) (RIGHT-BRANCH X) (LEFT-BRANCH X)) MAIN-EVENT CONS-IF EVENT NIL))) 
(PUT1-LST (QUOTE 1IF-EXPRP) (QUOTE NIL)) 
(PUT1-LST (QUOTE IF-EXPRP) (QUOTE (TYPE-PRESCRIPTION-LST ((CONS-IF 3. NIL)) LEMMAS NIL QUICK-BLOCK-INFO NIL SDEFN NIL LISP-CODE 1IF-EXPRP INDUCTION-MACHINE NIL LEVEL-NO NIL JUSTIFICATIONS NIL ELIMINATE-DESTRUCTORS-SEQ NIL MAIN-EVENT CONS-IF EVENT NIL))) 
(PUT1-LST (QUOTE 1CONS-IF) (QUOTE NIL)) 
(PUT1-LST (QUOTE CONS-IF) (QUOTE (TYPE-PRESCRIPTION-LST ((CONS-IF 128. NIL NIL NIL)) LEMMAS ((REWRITE-RULE CONS-IF-TEST-LEFT-BRANCH-RIGHT-BRANCH NIL (EQUAL (CONS-IF (TEST X) (LEFT-BRANCH X) (RIGHT-BRANCH X)) (IF (IF-EXPRP X) X (QUOTE (1QUOTE CONS-IF 0. 0. 0.)))) NIL)) SDEFN NIL LISP-CODE 1CONS-IF TYPE-RESTRICTIONS ((TYPE-RESTRICTION (QUOTE 1TRUE) -1. (QUOTE 0.)) (TYPE-RESTRICTION (QUOTE 1TRUE) -1. (QUOTE 0.)) (TYPE-RESTRICTION (QUOTE 1TRUE) -1. (QUOTE 0.))) INDUCTION-MACHINE NIL LEVEL-NO NIL IDATE 840117183446. ELIMINATE-DESTRUCTORS-SEQ NIL SATELLITES (COUNT-CONS-IF TEST-LEFT-BRANCH-RIGHT-BRANCH-ELIM CONS-IF-TEST-LEFT-BRANCH-RIGHT-BRANCH CONS-IF-EQUAL RIGHT-BRANCH-LESSEQP RIGHT-BRANCH-LESSP RIGHT-BRANCH-NIF-EXPRP RIGHT-BRANCH-CONS-IF LEFT-BRANCH-LESSEQP LEFT-BRANCH-LESSP LEFT-BRANCH-NIF-EXPRP LEFT-BRANCH-CONS-IF TEST-LESSEQP TEST-LESSP TEST-NIF-EXPRP TEST-CONS-IF 1RIGHT-BRANCH RIGHT-BRANCH 1LEFT-BRANCH LEFT-BRANCH 1TEST TEST 1IF-EXPRP IF-EXPRP 1CONS-IF) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (NORMALIZE-NORMALIZES NORMALIZE-IS-SOUND TAUTOLOGYP-FAILS-MEANS-FALSIFY1-WINS FALSIFY1-FALSIFIES FALSIFY1-EXTENDS-MODELS FALSIFY1 TAUTOLOGYP-IS-SOUND VALUE-SHORT-CUT VALUE-CAN-IGNORE-REDUNDANT-ASSIGNMENTS TAUTOLOGYP NORMALIZED-IF-EXPRP NORMALIZE IF-COMPLEXITY-GOES-DOWN2 IF-COMPLEXITY-GOES-DOWN1 IF-COMPLEXITY-NOT-0 IF-COMPLEXITY IF-DEPTH VALUE) EVENT (ADD-SHELL CONS-IF NIL IF-EXPRP ((TEST (NONE-OF) ZERO) (LEFT-BRANCH (NONE-OF) ZERO) (RIGHT-BRANCH (NONE-OF) ZERO))) LOCAL-UNDO-TUPLES ((LEMMAS COUNT . COUNT-CONS-IF) (LEMMAS EQUAL . CONS-IF-EQUAL) (LINEAR-LEMMAS COUNT . RIGHT-BRANCH-LESSEQP) (LINEAR-LEMMAS COUNT . RIGHT-BRANCH-LESSP) (LINEAR-LEMMAS COUNT . LEFT-BRANCH-LESSEQP) (LINEAR-LEMMAS COUNT . LEFT-BRANCH-LESSP) (LINEAR-LEMMAS COUNT . TEST-LESSEQP) (LINEAR-LEMMAS COUNT . TEST-LESSP) (RECOGNIZER-ALIST NIL IF-EXPRP . 128.) (SHELL-POCKETS NIL CONS-IF TEST LEFT-BRANCH RIGHT-BRANCH) (SHELL-ALIST NIL CONS-IF . 7.) (DCELL . 1RIGHT-BRANCH) (DCELL . 1LEFT-BRANCH) (DCELL . 1TEST) (DCELL . 1IF-EXPRP) (DCELL . 1CONS-IF))))) 
(PUT1-LST (QUOTE GCD-IS-THE-GREATEST) (QUOTE (IDATE 840117183446. EVENT (PROVE-LEMMA GCD-IS-THE-GREATEST NIL (IMPLIES (AND (NOT (ZEROP X)) (NOT (ZEROP Y)) (DIVIDES Z X) (DIVIDES Z Y)) (LEQ Z (GCD X Y)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LESSP-TIMES-2 . GCD-IS-THE-GREATEST) (IMMEDIATE-DEPENDENTS0 GCD-EQUAL-0 . GCD-IS-THE-GREATEST) (IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-TIMES-OVER-GCD . GCD-IS-THE-GREATEST) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . GCD-IS-THE-GREATEST) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . GCD-IS-THE-GREATEST) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-GCD . GCD-IS-THE-GREATEST) (IMMEDIATE-DEPENDENTS0 REMAINDER-WRT-12 . GCD-IS-THE-GREATEST) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . GCD-IS-THE-GREATEST) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . GCD-IS-THE-GREATEST) (IMMEDIATE-DEPENDENTS0 GCD . GCD-IS-THE-GREATEST) (IMMEDIATE-DEPENDENTS0 DIVIDES . GCD-IS-THE-GREATEST))))) 
(PUT1-LST (QUOTE GCD-DIVIDES-BOTH) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117183434. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PRIME-GCD REMAINDER-GCD) EVENT (PROVE-LEMMA GCD-DIVIDES-BOTH (REWRITE) (AND (EQUAL (REMAINDER X (GCD X Y)) 0.) (EQUAL (REMAINDER Y (GCD X Y)) 0.))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EUCLID . GCD-DIVIDES-BOTH) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-GCD . GCD-DIVIDES-BOTH) (IMMEDIATE-DEPENDENTS0 REMAINDER-X-X . GCD-DIVIDES-BOTH) (IMMEDIATE-DEPENDENTS0 GCD-0 . GCD-DIVIDES-BOTH) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-CANCELLATION-0 . GCD-DIVIDES-BOTH) (IMMEDIATE-DEPENDENTS0 GCD . GCD-DIVIDES-BOTH) (LEMMAS REMAINDER . GCD-DIVIDES-BOTH) (LEMMAS REMAINDER . GCD-DIVIDES-BOTH))))) 
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(PUT1-LST (QUOTE LESSP-PLUS-CANCELLATION3) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117183250. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EVEN3-REM REM-DIFF-TIMES EXECUTE1 IF-COMPLEXITY-GOES-DOWN1 DISTRIBUTIVITY-OF-TIMES-OVER-GCD) EVENT (PROVE-LEMMA LESSP-PLUS-CANCELLATION3 (REWRITE) (EQUAL (LESSP Y (PLUS X Y)) (NOT (ZEROP X)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQUAL-LESSP . LESSP-PLUS-CANCELLATION3) (LEMMAS LESSP . LESSP-PLUS-CANCELLATION3))))) 
(PUT1-LST (QUOTE LESSP-TIMES-CANCELLATION) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117183246. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LEQ-WINS1 LEQ-QUOT-TIMES-2 LEQ-QUOT-TIMES REFLECT-COMMUTES-WITH-TIMES-1 TIMES-DISTRIBUTES-OVER-PDIFFERENCE NORMALIZE-NORMALIZES NORMALIZE-IS-SOUND NORMALIZE DISTRIBUTIVITY-OF-TIMES-OVER-GCD) EVENT (PROVE-LEMMA LESSP-TIMES-CANCELLATION (REWRITE) (EQUAL (LESSP (TIMES X Z) (TIMES Y Z)) (AND (NOT (ZEROP Z)) (LESSP X Y)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-ZERO2 . LESSP-TIMES-CANCELLATION) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . LESSP-TIMES-CANCELLATION) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . LESSP-TIMES-CANCELLATION) (IMMEDIATE-DEPENDENTS0 EQUAL-LESSP . LESSP-TIMES-CANCELLATION) (LEMMAS LESSP . LESSP-TIMES-CANCELLATION))))) 
(PUT1-LST (QUOTE EUCLID) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117183236. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (G0002 REMAINDER-DIFFERENCE-TIMES GCD-DIVIDES-BOTH) EVENT (PROVE-LEMMA EUCLID (REWRITE) (IMPLIES (EQUAL (REMAINDER X Z) 0.) (EQUAL (EQUAL (REMAINDER (DIFFERENCE Y X) Z) 0.) (IF (LESSP X Y) (EQUAL (REMAINDER Y Z) 0.) T)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . EUCLID) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-PLUS . EUCLID) (IMMEDIATE-DEPENDENTS0 DIVIDES-PLUS-REWRITE1 . EUCLID) (IMMEDIATE-DEPENDENTS0 DIVIDES-TIMES . EUCLID) (IMMEDIATE-DEPENDENTS0 DIVIDES-PLUS-REWRITE-COMMUTED . EUCLID) (IMMEDIATE-DEPENDENTS0 REMAINDER-WRT-12 . EUCLID) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . EUCLID) (IMMEDIATE-DEPENDENTS0 PLUS-RIGHT-ID2 . EUCLID) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-ELIM . EUCLID) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . EUCLID) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . EUCLID) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . EUCLID) (LEMMAS EQUAL . EUCLID))))) 
(PUT1-LST (QUOTE DIVIDES-PLUS-REWRITE-COMMUTED) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117183212. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EUCLID) EVENT (PROVE-LEMMA DIVIDES-PLUS-REWRITE-COMMUTED (REWRITE) (IMPLIES (EQUAL (REMAINDER X Z) 0.) (EQUAL (EQUAL (REMAINDER (PLUS Y X) Z) 0.) (EQUAL (REMAINDER Y Z) 0.)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . DIVIDES-PLUS-REWRITE-COMMUTED) (IMMEDIATE-DEPENDENTS0 DIVIDES-PLUS-REWRITE . DIVIDES-PLUS-REWRITE-COMMUTED) (LEMMAS EQUAL . DIVIDES-PLUS-REWRITE-COMMUTED))))) 
(PUT1-LST (QUOTE LESSP-PLUS-CANCELATION) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117183209. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LEQ-QUOT-TIMES DIFF-MOD-1 EQUAL-MODS-TRICK-2 LESSP-COUNT-DELETE NORMALIZE-NORMALIZES NORMALIZE-IS-SOUND NORMALIZE) EVENT (PROVE-LEMMA LESSP-PLUS-CANCELATION (REWRITE) (EQUAL (LESSP (PLUS X Y) (PLUS X Z)) (LESSP Y Z))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQUAL-LESSP . LESSP-PLUS-CANCELATION) (LEMMAS LESSP . LESSP-PLUS-CANCELATION))))) 
(PUT1-LST (QUOTE DIVIDES-PLUS-REWRITE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117183206. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (DIVIDES-PLUS-REWRITE-COMMUTED) EVENT (PROVE-LEMMA DIVIDES-PLUS-REWRITE (REWRITE) (IMPLIES (EQUAL (REMAINDER X Z) 0.) (EQUAL (EQUAL (REMAINDER (PLUS X Y) Z) 0.) (EQUAL (REMAINDER Y Z) 0.)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIVIDES-PLUS-REWRITE1 . DIVIDES-PLUS-REWRITE) (IMMEDIATE-DEPENDENTS0 DIVIDES-PLUS-REWRITE2 . DIVIDES-PLUS-REWRITE) (LEMMAS EQUAL . DIVIDES-PLUS-REWRITE))))) 
(PUT1-LST (QUOTE DIVIDES-PLUS-REWRITE2) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117183200. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (DIVIDES-PLUS-REWRITE) EVENT (PROVE-LEMMA DIVIDES-PLUS-REWRITE2 (REWRITE) (IMPLIES (AND (EQUAL (REMAINDER X Z) 0.) (NOT (EQUAL (REMAINDER Y Z) 0.))) (NOT (EQUAL (REMAINDER (PLUS X Y) Z) 0.)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-PLUS . DIVIDES-PLUS-REWRITE2) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-PLUS3 . DIVIDES-PLUS-REWRITE2) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-ELIM . DIVIDES-PLUS-REWRITE2) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-PLUS . DIVIDES-PLUS-REWRITE2) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . DIVIDES-PLUS-REWRITE2) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . DIVIDES-PLUS-REWRITE2) (IMMEDIATE-DEPENDENTS0 REMAINDER-WRT-12 . DIVIDES-PLUS-REWRITE2) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . DIVIDES-PLUS-REWRITE2) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . DIVIDES-PLUS-REWRITE2) (LEMMAS EQUAL . DIVIDES-PLUS-REWRITE2))))) 
(PUT1-LST (QUOTE DIVIDES-PLUS-REWRITE1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117183111. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (INVERSE-IS-UNIQUE EUCLID DIVIDES-PLUS-REWRITE) EVENT (PROVE-LEMMA DIVIDES-PLUS-REWRITE1 (REWRITE) (IMPLIES (AND (EQUAL (REMAINDER X Z) 0.) (EQUAL (REMAINDER Y Z) 0.)) (EQUAL (REMAINDER (PLUS X Y) Z) 0.))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-PLUS . DIVIDES-PLUS-REWRITE1) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-PLUS . DIVIDES-PLUS-REWRITE1) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-PLUS3 . DIVIDES-PLUS-REWRITE1) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-ELIM . DIVIDES-PLUS-REWRITE1) (IMMEDIATE-DEPENDENTS0 DIVIDES-TIMES . DIVIDES-PLUS-REWRITE1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . DIVIDES-PLUS-REWRITE1) (IMMEDIATE-DEPENDENTS0 REMAINDER-WRT-12 . DIVIDES-PLUS-REWRITE1) (IMMEDIATE-DEPENDENTS0 PLUS-RIGHT-ID2 . DIVIDES-PLUS-REWRITE1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . DIVIDES-PLUS-REWRITE1) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . DIVIDES-PLUS-REWRITE1) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . DIVIDES-PLUS-REWRITE1) (LEMMAS REMAINDER . DIVIDES-PLUS-REWRITE1))))) 
(PUT1-LST (QUOTE REMAINDER-ADD1) (QUOTE (IDATE 840117183022. EVENT (PROVE-LEMMA REMAINDER-ADD1 (REWRITE) (IMPLIES (AND (NOT (ZEROP Y)) (NOT (EQUAL Y 1.))) (NOT (EQUAL (REMAINDER (ADD1 (TIMES X Y)) Y) 0.)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . REMAINDER-ADD1) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-ADD1-CANCELLATION . REMAINDER-ADD1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . REMAINDER-ADD1) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . REMAINDER-ADD1) (LEMMAS EQUAL . REMAINDER-ADD1))))) 
(PUT1-LST (QUOTE DIFFERENCE-ADD1-CANCELLATION) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182929. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (REMAINDER-ADD1) EVENT (PROVE-LEMMA DIFFERENCE-ADD1-CANCELLATION (REWRITE) (EQUAL (DIFFERENCE (ADD1 (PLUS Y Z)) Z) (ADD1 Y))) LOCAL-UNDO-TUPLES ((LEMMAS DIFFERENCE . DIFFERENCE-ADD1-CANCELLATION))))) 
(PUT1-LST (QUOTE DIFFERENCE-PLUS3) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182929. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (DIVIDES-PLUS-REWRITE2 DIVIDES-PLUS-REWRITE1) EVENT (PROVE-LEMMA DIFFERENCE-PLUS3 (REWRITE) (EQUAL (DIFFERENCE (PLUS B (PLUS A C)) A) (PLUS B C))) LOCAL-UNDO-TUPLES ((LEMMAS DIFFERENCE . DIFFERENCE-PLUS3))))) 
(PUT1-LST (QUOTE DIVIDES-TIMES) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182929. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (REFLECT-COMMUTES-WITH-TIMES-1 PRODUCT-DIVIDES-LEMMA REMAINDER-DIFFERENCE-TIMES REMAINDER-PLUS-TIMES-1 REMAINDER-TIMES DIVIDES-TIMES1 PRIME-BASIC PRIME1-BASIC EUCLID DIVIDES-PLUS-REWRITE1) EVENT (PROVE-LEMMA DIVIDES-TIMES (REWRITE) (EQUAL (REMAINDER (TIMES X Z) Z) 0.)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . DIVIDES-TIMES) (IMMEDIATE-DEPENDENTS0 REMAINDER-WRT-12 . DIVIDES-TIMES) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . DIVIDES-TIMES) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-PLUS1 . DIVIDES-TIMES) (LEMMAS REMAINDER . DIVIDES-TIMES))))) 
(PUT1-LST (QUOTE 1DIVIDES) (QUOTE NIL)) 
(PUT1-LST (QUOTE DIVIDES) (QUOTE (TYPE-PRESCRIPTION-LST ((DIVIDES 3. NIL NIL)) LEMMAS NIL QUICK-BLOCK-INFO NIL SDEFN (LAMBDA (X Y) (EQUAL (REMAINDER Y X) (QUOTE 0.))) LISP-CODE 1DIVIDES INDUCTION-MACHINE NIL LEVEL-NO 2. JUSTIFICATIONS NIL IDATE 840117182923. CONTROLLER-POCKETS NIL SATELLITES (1DIVIDES) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LAW-OF-QUADRATIC-RECIPROCITY EQUAL-PLUS-QUOT-LIST-WINS EMPTY-INTERSECT-MULTS-1 RESIDUE-QUOT-LIST GAUSS-COROLLARY EQUAL-WINS-PLUS-QUOT-LIST EQUAL-QUOT-WINS1 LEQ-QUOT-WINS1 LEQ-QUOT-WINS1-2 LEQ-QUOT-WINS1-1 RES1-QUOT-LIST PLUS-REFLECT-LIST EVEN3-EVEN GAUSS-LEMMA TWO-EVEN RES1-REM-2 RES1-REM-1 RES1-REM-1-1 TIMES-REFLECT-LIST ALL-DISTINCT-REFLECT-LIST ALL-DISTINCT-REFLECT-LIST-10 ALL-DISTINCT-REFLECT-LIST-9 ALL-DISTINCT-REFLECT-LIST-8 ALL-DISTINCT-REFLECT-LIST-7 ALL-DISTINCT-REFLECT-LIST-3 ALL-DISTINCT-REFLECT-LIST-1 ALL-NON-ZEROP-REFLECT-LIST EULER-2 EULER-2-4 EULER-2-3 EULER-2-2 EULER-2-1 TIMES-COMP-LIST-4 TIMES-COMP-LIST-2 COMP-LIST-FACT PERM-POSITIVES-COMP-LIST ALL-DISTINCT-COMP-LIST ALL-DISTINCT-COMP-LIST-1 COMP-LIST-CLOSED-2 COMP-LIST-CLOSED-1 ALL-NON-ZEROP-COMP-LIST COMPLEMENT-OF-COMPLEMENT NO-SELF-COMPLEMENT COMPLEMENT-IS-UNIQUE NON-ZEROP-COMPLEMENT COMPLEMENT-WORKS EULER-1 EULER-1-7 EULER-1-6 EULER-1-5 EULER-1-4 EULER-1-2 EULER-1-1 RESIDUE WILSON-THM PRIME-KEY-REWRITE PRIME-FACTORIZATION-UNIQUENESS PRIME-MEMBER IF-TIMES-THEN-DIVIDES PRIME-LIST-TIMES-LIST TIMES-LIST-DELETE DISTRIBUTIVITY-OF-DIVIDES LITTLE-STEP PRIME-KEY PRIME-GCD HACK1 PRIME-BASIC GREATEREQPR-REMAINDER PRIME1-BASIC ENOUGH-FACTORS QUOTIENT-TIMES1 NUMBERP-GREATEST-FACTOR GREATEST-FACTOR-1 GREATEST-FACTOR-0 GREATEST-FACTOR-DIVIDES GREATEST-FACTOR-LESSP GREATEST-FACTOR PRIME1 GCD-IS-THE-GREATEST) EVENT (DEFN DIVIDES (X Y) (ZEROP (REMAINDER Y X))) LOCAL-UNDO-TUPLES ((DCELL . 1DIVIDES))))) 
(PUT1-LST (QUOTE TIMES-DIFFERENCE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182923. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LEQ-TIMES-QUOT REFLECT-COMMUTES-WITH-TIMES-1 TIMES-DISTRIBUTES-OVER-PDIFFERENCE REMAINDER-DIFFERENCE-TIMES DISTRIBUTIVITY-OF-TIMES-OVER-GCD) EVENT (PROVE-LEMMA TIMES-DIFFERENCE (REWRITE) (EQUAL (TIMES X (DIFFERENCE C W)) (DIFFERENCE (TIMES C X) (TIMES W X)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIFFERENCE-PLUS-CANCELATION . TIMES-DIFFERENCE) (IMMEDIATE-DEPENDENTS0 PLUS-EQUAL-0 . TIMES-DIFFERENCE) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . TIMES-DIFFERENCE) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . TIMES-DIFFERENCE) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . TIMES-DIFFERENCE) (IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE-0 . TIMES-DIFFERENCE) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-ELIM . TIMES-DIFFERENCE) (LEMMAS TIMES . TIMES-DIFFERENCE))))) 
(PUT1-LST (QUOTE DIFFERENCE-PLUS-CANCELATION) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182902. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EQUAL-MODS-TRICK-2 TIMES-DIFFERENCE) EVENT (PROVE-LEMMA DIFFERENCE-PLUS-CANCELATION (REWRITE) (EQUAL (DIFFERENCE (PLUS X Y) (PLUS X Z)) (DIFFERENCE Y Z))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . DIFFERENCE-PLUS-CANCELATION) (LEMMAS DIFFERENCE . DIFFERENCE-PLUS-CANCELATION))(βy 
(PUT1-LST (QUOTE DIFFERENCE-PLUS2) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182901. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EXECUTE1 DISTRIBUTIVITY-OF-TIMES-OVER-GCD) EVENT (PROVE-LEMMA DIFFERENCE-PLUS2 (REWRITE) (EQUAL (DIFFERENCE (PLUS Y X) X) (FIX Y))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . DIFFERENCE-PLUS2) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-PLUS1 . DIFFERENCE-PLUS2) (LEMMAS DIFFERENCE . DIFFERENCE-PLUS2))))) 
(PUT1-LST (QUOTE DIFFERENCE-PLUS1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182901. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (REM-DIFF-TIMES DIFF-MOD-1 QUOTIENT-PLUS-1 REMAINDER-PLUS-TIMES-1 QUOTIENT-TIMES DIVIDES-TIMES DIFFERENCE-PLUS2) EVENT (PROVE-LEMMA DIFFERENCE-PLUS1 (REWRITE) (EQUAL (DIFFERENCE (PLUS X Y) X) (FIX Y))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIFFERENCE-PLUS . DIFFERENCE-PLUS1) (LEMMAS DIFFERENCE . DIFFERENCE-PLUS1))))) 
(PUT1-LST (QUOTE NTH-APPEND) (QUOTE (IDATE 840117182900. EVENT (PROVE-LEMMA NTH-APPEND (REWRITE) (EQUAL (NTH (APPEND A B) I) (APPEND (NTH A I) (NTH B (DIFFERENCE I (LENGTH A)))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 NTH-0 . NTH-APPEND) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . NTH-APPEND) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-ELIM . NTH-APPEND) (IMMEDIATE-DEPENDENTS0 APPEND . NTH-APPEND) (IMMEDIATE-DEPENDENTS0 NTH . NTH-APPEND) (LEMMAS NTH . NTH-APPEND))))) 
(PUT1-LST (QUOTE COMMUTATIVITY-OF-GCD) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182850. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EMPTY-INTERSECT-MULTS-1 PRIME-KEY HACK1 KLUDGE-BRIDGE GCD-IS-THE-GREATEST GCD-DIVIDES-BOTH DISTRIBUTIVITY-OF-TIMES-OVER-GCD) EVENT (PROVE-LEMMA COMMUTATIVITY-OF-GCD (REWRITE) (EQUAL (GCD X Y) (GCD Y X))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 GCD-0 . COMMUTATIVITY-OF-GCD) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-CANCELLATION-0 . COMMUTATIVITY-OF-GCD) (IMMEDIATE-DEPENDENTS0 GCD . COMMUTATIVITY-OF-GCD) (LEMMAS GCD . COMMUTATIVITY-OF-GCD))))) 
(PUT1-LST (QUOTE GCD-0) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182845. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (HACK1 GCD-DIVIDES-BOTH DISTRIBUTIVITY-OF-TIMES-OVER-GCD COMMUTATIVITY-OF-GCD) EVENT (PROVE-LEMMA GCD-0 (REWRITE) (EQUAL (GCD 0. Y) (FIX Y))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 GCD . GCD-0) (LEMMAS GCD . GCD-0))))) 
(PUT1-LST (QUOTE GCD-EQUAL-0) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182845. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (GCD-IS-THE-GREATEST) EVENT (PROVE-LEMMA GCD-EQUAL-0 (REWRITE) (EQUAL (EQUAL (GCD X Y) 0.) (AND (ZEROP X) (ZEROP Y)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE-0 . GCD-EQUAL-0) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-CANCELLATION-0 . GCD-EQUAL-0) (IMMEDIATE-DEPENDENTS0 GCD . GCD-EQUAL-0) (LEMMAS EQUAL . GCD-EQUAL-0))))) 
(PUT1-LST (QUOTE NUMBERP-GCD) (QUOTE (IDATE 840117182838. EVENT (PROVE-LEMMA NUMBERP-GCD (REWRITE) (NUMBERP (GCD X Y))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 GCD . NUMBERP-GCD) (LEMMAS NUMBERP . NUMBERP-GCD))))) 
(PUT1-LST (QUOTE 1GCD) (QUOTE NIL)) 
(PUT1-LST (QUOTE GCD) (QUOTE (TYPE-PRESCRIPTION-LST ((GCD 4. NIL NIL)) LEMMAS ((REWRITE-RULE GCD-DISTRIBUTES-OVER-AN-OPENED-UP-TIMES ((NUMBERP X) (NOT (EQUAL X (QUOTE 0.))) (EQUAL FREE (TIMES X Z))) (EQUAL (GCD (TIMES B Z) FREE) (TIMES Z (GCD B X))) NIL) (REWRITE-RULE KLUDGE-BRIDGE ((EQUAL Y (TIMES K X))) (EQUAL (GCD Y (TIMES A X)) (TIMES X (GCD A K))) NIL) (REWRITE-RULE DISTRIBUTIVITY-OF-TIMES-OVER-GCD NIL (EQUAL (GCD (TIMES X Z) (TIMES Y Z)) (TIMES Z (GCD X Y))) NIL) (REWRITE-RULE COMMUTATIVITY-OF-GCD NIL (EQUAL (GCD X Y) (GCD Y X)) ((X . Y))) (REWRITE-RULE GCD-0 NIL (EQUAL (GCD (QUOTE 0.) Y) (IF (NUMBERP Y) Y (QUOTE 0.))) NIL)) LINEAR-LEMMAS NIL QUICK-BLOCK-INFO (QUESTIONABLE QUESTIONABLE) SDEFN (LAMBDA (X Y) (IF (EQUAL X (QUOTE 0.)) (IF (NUMBERP Y) Y (QUOTE 0.)) (IF (NUMBERP X) (IF (EQUAL Y (QUOTE 0.)) X (IF (NUMBERP Y) (IF (LESSP X Y) (GCD X (DIFFERENCE Y X)) (GCD (DIFFERENCE X Y) Y)) X)) (IF (NUMBERP Y) Y (QUOTE 0.))))) LISP-CODE 1GCD INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP X)) NIL) (TESTS-AND-CASES ((NOT (ZEROP X)) (ZEROP Y)) NIL) (TESTS-AND-CASES ((NOT (ZEROP X)) (NOT (ZEROP Y)) (LESSP X Y)) ((X (DIFFERENCE Y X)))) (TESTS-AND-CASES ((NOT (ZEROP X)) (NOT (ZEROP Y)) (NOT (LESSP X Y))) (((DIFFERENCE X Y) Y)))) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (Y X) (CONS (COUNT X) (CONS (COUNT Y) (QUOTE NIL))) LEX2 (DIFFERENCE-CANCELLATION-0 ZERO ZEROP COUNT-NUMBERP CDR-CONS CAR-CONS LEX2))) IDATE 840117182835. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (3.) SATELLITES (1GCD) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (GCD-DISTRIBUTES-OVER-AN-OPENED-UP-TIMES PRIME-GCD HACK1 KLUDGE-BRIDGE REMAINDER-GCD-1 REMAINDER-GCD GCD-IS-THE-GREATEST GCD-DIVIDES-BOTH DISTRIBUTIVITY-OF-TIMES-OVER-GCD COMMUTATIVITY-OF-GCD GCD-0 GCD-EQUAL-0 NUMBERP-GCD) EVENT (DEFN GCD (X Y) (IF (ZEROP X) (FIX Y) (IF (ZEROP Y) X (IF (LESSP X Y) (GCD X (DIFFERENCE Y X)) (GCD (DIFFERENCE X Y) Y)))) ((LEX2 (LIST (COUNT X) (COUNT Y))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIFFERENCE-CANCELLATION-0 . GCD) (DCELL . 1GCD))))) 
(PUT1-LST (QUOTE CORRECTNESS-OF-BIG-PLUS) (QUOTE (IDATE 840117182834. EVENT (PROVE-LEMMA CORRECTNESS-OF-BIG-PLUS (REWRITE) (EQUAL (POWER-EVAL (BIG-PLUS (POWER-REP I BASE) (POWER-REP J BASE) 0. BASE) BASE) (PLUS I J))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . CORRECTNESS-OF-BIG-PLUS) (IMMEDIATE-DEPENDENTS0 PLUS-RIGHT-ID2 . CORRECTNESS-OF-BIG-PLUS) (IMMEDIATE-DEPENDENTS0 POWER-EVAL-POWER-REP . CORRECTNESS-OF-BIG-PLUS) (IMMEDIATE-DEPENDENTS0 POWER-EVAL-BIG-PLUS . CORRECTNESS-OF-BIG-PLUS) (IMMEDIATE-DEPENDENTS0 POWER-REP . CORRECTNESS-OF-BIG-PLUS) (IMMEDIATE-DEPENDENTS0 BIG-PLUS . CORRECTNESS-OF-BIG-PLUS) (IMMEDIATE-DEPENDENTS0 POWER-EVAL . CORRECTNESS-OF-BIG-PLUS) (LEMMAS POWER-EVAL . CORRECTNESS-OF-BIG-PLUS))))) 
(PUT1-LST (QUOTE POWER-EVAL-POWER-REP) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182831. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-BIG-PLUS) EVENT (PROVE-LEMMA POWER-EVAL-POWER-REP (REWRITE) (EQUAL (POWER-EVAL (POWER-REP I BASE) BASE) (FIX I))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT . POWER-EVAL-POWER-REP) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . POWER-EVAL-POWER-REP) (IMMEDIATE-DEPENDENTS0 LESSP-QUOTIENT1 . POWER-EVAL-POWER-REP) (IMMEDIATE-DEPENDENTS0 POWER-REP . POWER-EVAL-POWER-REP) (IMMEDIATE-DEPENDENTS0 POWER-EVAL . POWER-EVAL-POWER-REP) (LEMMAS POWER-EVAL . POWER-EVAL-POWER-REP))))) 
(PUT1-LST (QUOTE 1POWER-REP) (QUOTE NIL)) 
(PUT1-LST (QUOTE POWER-REP) (QUOTE (TYPE-PRESCRIPTION-LST ((POWER-REP 24. NIL NIL)) LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE UNCHANGING) SDEFN (LAMBDA (I BASE) (IF (EQUAL I (QUOTE 0.)) (QUOTE NIL) (IF (NUMBERP I) (IF (EQUAL BASE (QUOTE 0.)) (CONS I (QUOTE NIL)) (IF (NUMBERP BASE) (IF (EQUAL BASE (QUOTE 1.)) (CONS I (QUOTE NIL)) (CONS (REMAINDER I BASE) (POWER-REP (QUOTIENT I BASE) BASE))) (CONS I (QUOTE NIL)))) (QUOTE NIL)))) LISP-CODE 1POWER-REP INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP I)) NIL) (TESTS-AND-CASES ((NOT (ZEROP I)) (ZEROP BASE)) NIL) (TESTS-AND-CASES ((NOT (ZEROP I)) (NOT (ZEROP BASE)) (EQUAL BASE (QUOTE 1.))) NIL) (TESTS-AND-CASES ((NOT (ZEROP I)) (NOT (ZEROP BASE)) (NOT (EQUAL BASE (QUOTE 1.)))) (((QUOTIENT I BASE) BASE)))) LEVEL-NO 3. JUSTIFICATIONS ((JUSTIFICATION (I) (COUNT I) LESSP (ZEROP COUNT-NUMBERP LESSP-QUOTIENT1))) IDATE 840117182821. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1POWER-REP) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-BIG-PLUS POWER-EVAL-POWER-REP) EVENT (DEFN POWER-REP (I BASE) (IF (ZEROP I) NIL (IF (ZEROP BASE) (CONS I NIL) (IF (EQUAL BASE 1.) (CONS I NIL) (CONS (REMAINDER I BASE) (POWER-REP (QUOTIENT I BASE) BASE)))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LESSP-QUOTIENT1 . POWER-REP) (DCELL . 1POWER-REP))))) 
(PUT1-LST (QUOTE LESSP-REMAINDER1) (QUOTE (IDATE 840117182821. EVENT (PROVE-LEMMA LESSP-REMAINDER1 (REWRITE) (EQUAL (LESSP (REMAINDER X Y) X) (AND (NOT (ZEROP Y)) (NOT (ZEROP X)) (NOT (LESSP X Y))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REMAINDER-WRT-12 . LESSP-REMAINDER1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . LESSP-REMAINDER1) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . LESSP-REMAINDER1) (IMMEDIATE-DEPENDENTS0 PLUS-EQUAL-0 . LESSP-REMAINDER1) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . LESSP-REMAINDER1) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . LESSP-REMAINDER1) (IMMEDIATE-DEPENDENTS0 EQUAL-LESSP . LESSP-REMAINDER1) (LEMMAS LESSP . LESSP-REMAINDER1))))) 
(PUT1-LST (QUOTE LESSP-QUOTIENT1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182812. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LAW-OF-QUADRATIC-RECIPROCITY EMPTY-INTERSECT-MULTS PLUS-REFLECT-LIST RES1-REM-2 RES1-REM-1 TIMES-REFLECT-LIST CRYPT-CORRECT CRYPT ENOUGH-FACTORS PRIME-LIST-PRIME-FACTORS PRIME-FACTORS POWER-EVAL-POWER-REP POWER-REP) EVENT (PROVE-LEMMA LESSP-QUOTIENT1 (REWRITE) (EQUAL (LESSP (QUOTIENT I J) I) (AND (NOT (ZEROP I)) (OR (ZEROP J) (NOT (EQUAL J 1.)))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . LESSP-QUOTIENT1) (IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE-0 . LESSP-QUOTIENT1) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES-1 . LESSP-QUOTIENT1) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . LESSP-QUOTIENT1) (IMMEDIATE-DEPENDENTS0 PLUS-EQUAL-0 . LESSP-QUOTIENT1) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER2 . LESSP-QUOTIENT1) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . LESSP-QUOTIENT1) (IMMEDIATE-DEPENDENTS0 EQUAL-LESSP . LESSP-QUOTIENT1) (LEMMAS LESSP . LESSP-QUOTIENT1))))) 
(PUT1-LST (QUOTE LESSP-TIMES-2) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182750. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LEQ-TIMES-QUOT N-O-I-LEMMA4 CRYPT-INVERTS-STEP-2 TIMES-IDENTITY TIMES-IDENTITY1 IF-COMPLEXITY-GOES-DOWN2 IF-COMPLEXITY-GOES-DOWN1 GCD-IS-THE-GREATEST) EVENT (PROVE-LEMMA LESSP-TIMES-2 (REWRITE) (IMPLIES (NOT (ZEROP I)) (NOT (LESSP (TIMES J I) J)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LESSP-TIMES-1 . LESSP-TIMES-2) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . LESSP-TIMES-2) (LINEAR-LEMMAS TIMES . LESSP-TIMES-2))))) 
(PUT1-LST (QUOTE LESSP-TIMES-1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182749. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LEQ-TIMES-QUOT CRYPT-INVERTS IF-COMPLEXITY-GOES-DOWN2 IF-COMPLEXITY-GOES-DOWN1 LESSP-QUOTIENT1 LESSP-TIMES-2) EVENT (PROVE-LEMMA LESSP-TIMES-1 (REWRITE) (IMPLIES (NOT (ZEROP I)) (NOT (LESSP (TIMES I J) J)))) LOCAL-UNDO-TUPLES ((LINEAR-LEMMAS TIMES . LESSP-TIMES-1))))) 
(PUT1-LST (QUOTE REMAINDER-QUOTIENT-ELIM) (QUOTE (IDATE 840117182747. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EQUAL-PLUS-QUOT-LIST-WINS LEQ-QUOT-WINS1 LEQ-QUOT-WINS1-1 LEQ-QUOT-TIMES LEQ-TIMES-QUOT EVEN3-EVEN EVEN3-REM RES1-REM-2 ALL-DISTINCT-REFLECT-LIST-9 ALL-DISTINCT-REFLECT-LIST-6 ALL-DISTINCT-REFLECT-LIST-3 ALL-LESSEQP-REFLECT-LIST ALL-LESSEQP-REFLECT-LIST-1 DIFF-MOD-1 COMPLEMENT-IS-UNIQUE EULER-1-2 EULER-1-1 N-O-I-LEMMA3 INVERSE-IS-UNIQUE CRYPT-INVERTS-STEP-2 ALL-NON-ZEROP-S ALL-DISTINCT-S PRODUCT-DIVIDES PRODUCT-DIVIDES-LEMMA EQUAL-MODS-TRICK-2 EQUAL-MODS-TRICK-1 REMAINDER-EXP REMAINDER-EXP-LEMMA CRYPT-CORRECT TIMES-MOD-1 PRIME-KEY-REWRITE REMAINDER-PLUS-TIMES-1 HALF-PLUS DISTRIBUTIVITY-OF-DIVIDES DIVIDES-TIMES-LIST QUOTIENT-DIVIDES HACK1 PRIME-BASIC QUOTIENT-LESSP QUOTIENT-TIMES1 GCD-IS-THE-GREATEST EUCLID DIVIDES-PLUS-REWRITE2 DIVIDES-PLUS-REWRITE1 LESSP-REMAINDER1 LESSP-QUOTIENT1) EVENT (PROVE-LEMMA REMAINDER-QUOTIENT-ELIM (ELIM) (IMPLIES (AND (NOT (ZEROP Y)) (NUMBERP X)) (EQUAL (PLUS (REMAINDER X Y) (TIMES Y (QUOTIENT X Y))) X))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT . REMAINDER-QUOTIENT-ELIM) (ELIMINATE-DESTRUCTORS-DESTS . REMAINDER) (ELIMINATE-DESTRUCTORS-SEQ . REMAINDER) (ELIMINATE-DESTRUCTORS-DESTS . QUOTIENT) (ELIMINATE-DESTRUCTORS-SEQ . QUOTIENT))))) 
(PUT1-LST (QUOTE REMAINDER-X-X) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182745. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (REFLECT-COMMUTES-WITH-TIMES-1 N-O-I-LEMMA3 PRODUCT-DIVIDES-LEMMA GCD-DIVIDES-BOTH) EVENT (PROVE-LEMMA REMAINDER-X-X (REWRITE) (EQUAL (REMAINDER X X) 0.)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . REMAINDER-X-X) (LEMMAS REMAINDER . REMAINDER-X-X))))) 
(PUT1-LST (QUOTE LESSP-REMAINDER2) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182745. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EQUAL-PLUS-QUOT-LIST-WINS LEQ-QUOT-WINS1 LEQ-QUOT-WINS1-1 LEQ-QUOT-TIMES LEQ-TIMES-QUOT EVEN3-EVEN EVEN3-REM RES1-REM-2 ALL-DISTINCT-REFLECT-LIST-9 ALL-DISTINCT-REFLECT-LIST-6 ALL-DISTINCT-REFLECT-LIST-5 ALL-DISTINCT-REFLECT-LIST-3 ALL-NON-ZEROP-REFLECT-LIST ALL-LESSEQP-REFLECT-LIST ALL-LESSEQP-REFLECT-LIST-1 REM-REFLECT-LIST-4 REFLECT-COMMUTES-WITH-TIMES-1 DIFF-MOD-1 TIMES-COMP-LIST-4 COMPLEMENT-IS-UNIQUE BOUNDED-COMPLEMENT EULER-1-2 EULER-1-1 N-O-I-LEMMA3 INVERSE-IS-UNIQUE CRYPT-INVERTS-STEP-2 ALL-NON-ZEROP-S ALL-DISTINCT-S PRODUCT-DIVIDES PRODUCT-DIVIDES-LEMMA EQUAL-MODS-TRICK-2 EQUAL-MODS-TRICK-1 REMAINDER-EXP REMAINDER-EXP-LEMMA CRYPT-CORRECT TIMES-MOD-1 LESSP-REMAINDER-DIVISOR PRIME-KEY-REWRITE REMAINDER-PLUS-TIMES-1 HALF-PLUS DISTRIBUTIVITY-OF-DIVIDES DIVIDES-TIMES-LIST QUOTIENT-DIVIDES HACK1 PRIME-BASIC QUOTIENT-LESSP QUOTIENT-TIMES1 GCD-IS-THE-GREATEST EUCLID DIVIDES-PLUS-REWRITE2 DIVIDES-PLUS-REWRITE1 LESSP-REMAINDER1 LESSP-QUOTIENT1) EVENT (PROVE-LEMMA LESSP-REMAINDER2 (REWRITE GENERALIZE) (EQUAL (LESSP (REMAINDER X Y) Y) (NOT (ZEROP Y)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REMAINDER-WRT-12 . LESSP-REMAINDER2) (IMMEDIATE-DEPENDENTS0 EQUAL-LESSP . LESSP-REMAINDER2) (GENERALIZE-LEMMAS NIL . LESSP-REMAINDER2) (LEMMAS LESSP . LESSP-REMAINDER2))))) 
(PUT1-LST (QUOTE REMAINDER-WRT-12) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182741. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LEQ-QUOT-WINS1-1 PLUS-REFLECT-LIST DOUBLE-REFLECT REFLECT-COMMUTES-WITH-TIMES-1 DIFF-MOD-1 COMP-LIST-CLOSED-1 ALL-NON-ZEROP-COMP-LIST COMPLEMENT-IS-UNIQUE TIMES-INVERSE-LIST A-D-I-L-LEMMA1 N-O-I-LEMMA3 PRODUCT-DIVIDES-LEMMA EQUAL-MODS-TRICK-2 EQUAL-MODS-TRICK-1 REMAINDER-EXP-LEMMA CRYPT-CORRECT TIMES-MOD-1 REMAINDER-PLUS-TIMES-1 QUOTIENT-DIVIDES HACK1 PRIME-BASIC GCD-IS-THE-GREATEST EUCLID DIVIDES-PLUS-REWRITE2 DIVIDES-PLUS-REWRITE1 DIVIDES-TIMES LESSP-REMAINDER1 LESSP-REMAINDER2) EVENT (PROVE-LEMMA REMAINDER-WRT-12 (REWRITE) (IMPLIES (NOT (NUMBERP X)) (EQUAL (REMAINDER Y X) (FIX Y)))) LOCAL-UNDO-TUPLES ((LEMMAS REMAINDER . REMAINDER-WRT-12))))) 
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(PUT1-LST (QUOTE 1BIG-PLUS) (QUOTE NIL)) 
(PUT1-LST (QUOTE BIG-PLUS) (QUOTE (TYPE-PRESCRIPTION-LST ((BIG-PLUS 16. NIL NIL NIL NIL)) LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE SELF-REFLEXIVE SELF-REFLEXIVE UNCHANGING) SDEFN (LAMBDA (X Y I BASE) (IF (LISTP X) (IF (LISTP Y) (CONS (REMAINDER (PLUS I (PLUS (CAR X) (CAR Y))) BASE) (BIG-PLUS (CDR X) (CDR Y) (QUOTIENT (PLUS I (PLUS (CAR X) (CAR Y))) BASE) BASE)) (BIG-PLUS1 X I BASE)) (BIG-PLUS1 Y I BASE))) LISP-CODE 1BIG-PLUS INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP X) (LISTP Y)) (((CDR X) (CDR Y) (QUOTIENT (PLUS I (PLUS (CAR X) (CAR Y))) BASE) BASE))) (TESTS-AND-CASES ((LISTP X) (NOT (LISTP Y))) NIL) (TESTS-AND-CASES ((NOT (LISTP X))) NIL)) LEVEL-NO 4. JUSTIFICATIONS ((JUSTIFICATION (X) (COUNT X) LESSP (ZERO CDR-LESSP)) (JUSTIFICATION (Y) (COUNT Y) LESSP (ZERO CDR-LESSP))) IDATE 840117182510. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1. 2.) SATELLITES (1BIG-PLUS) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-BIG-PLUS POWER-EVAL-BIG-PLUS) EVENT (DEFN BIG-PLUS (X Y I BASE) (IF (LISTP X) (IF (LISTP Y) (CONS (REMAINDER (PLUS I (PLUS (CAR X) (CAR Y))) BASE) (BIG-PLUS (CDR X) (CDR Y) (QUOTIENT (PLUS I (PLUS (CAR X) (CAR Y))) BASE) BASE)) (BIG-PLUS1 X I BASE)) (BIG-PLUS1 Y I BASE))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 BIG-PLUS1 . BIG-PLUS) (DCELL . 1BIG-PLUS))))) 
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(PUT1-LST (QUOTE REMAINDER-QUOTIENT) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182457. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (REM-QUOT-LIST PLUS-MOD-1 DIFF-MOD-1 EULER-2-4 PRIME-KEY-REWRITE POWER-EVAL-POWER-REP REMAINDER-QUOTIENT-ELIM POWER-EVAL-BIG-PLUS POWER-EVAL-BIG-PLUS1) EVENT (PROVE-LEMMA REMAINDER-QUOTIENT (REWRITE) (EQUAL (PLUS (REMAINDER X Y) (TIMES Y (QUOTIENT X Y))) (FIX X))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-ADD1 . REMAINDER-QUOTIENT) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-PLUS . REMAINDER-QUOTIENT) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . REMAINDER-QUOTIENT) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO2 . REMAINDER-QUOTIENT) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . REMAINDER-QUOTIENT) (LEMMAS PLUS . REMAINDER-QUOTIENT))))) 
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(PUT1-LST (QUOTE BIG-PLUS1) (QUOTE (TYPE-PRESCRIPTION-LST ((BIG-PLUS1 16. NIL NIL NIL)) LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE SELF-REFLEXIVE UNCHANGING) SDEFN (LAMBDA (L I BASE) (IF (LISTP L) (IF (EQUAL I (QUOTE 0.)) L (IF (NUMBERP I) (CONS (REMAINDER (PLUS (CAR L) I) BASE) (BIG-PLUS1 (CDR L) (QUOTIENT (PLUS (CAR L) I) BASE) BASE)) L)) (CONS I (QUOTE NIL)))) LISP-CODE 1BIG-PLUS1 INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP L) (ZEROP I)) NIL) (TESTS-AND-CASES ((LISTP L) (NOT (ZEROP I))) (((CDR L) (QUOTIENT (PLUS (CAR L) I) BASE) BASE))) (TESTS-AND-CASES ((NOT (LISTP L))) NIL)) LEVEL-NO 3. JUSTIFICATIONS ((JUSTIFICATION (L) (COUNT L) LESSP (ZERO CDR-LESSP))) IDATE 840117182443. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1BIG-PLUS1) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (BIG-PLUS POWER-EVAL-BIG-PLUS1) EVENT (DEFN BIG-PLUS1 (L I BASE) (IF (LISTP L) (IF (ZEROP I) L (CONS (REMAINDER (PLUS (CAR L) I) BASE) (BIG-PLUS1 (CDR L) (QUOTIENT (PLUS (CAR L) I) BASE) BASE))) (CONS I NIL))) LOCAL-UNDO-TUPLES ((DCELL . 1BIG-PLUS1))))) 
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(PUT1-LST (QUOTE POWER-EVAL) (QUOTE (TYPE-PRESCRIPTION-LST ((POWER-EVAL 4. NIL NIL)) LEMMAS ((REWRITE-RULE CORRECTNESS-OF-BIG-PLUS NIL (EQUAL (POWER-EVAL (BIG-PLUS (POWER-REP I BASE) (POWER-REP J BASE) (QUOTE 0.) BASE) BASE) (PLUS I J)) NIL) (REWRITE-RULE POWER-EVAL-POWER-REP NIL (EQUAL (POWER-EVAL (POWER-REP I BASE) BASE) (IF (NUMBERP I) I (QUOTE 0.))) NIL) (REWRITE-RULE POWER-EVAL-BIG-PLUS NIL (EQUAL (POWER-EVAL (BIG-PLUS X Y I BASE) BASE) (PLUS I (PLUS (POWER-EVAL X BASE) (POWER-EVAL Y BASE)))) NIL) (REWRITE-RULE POWER-EVAL-BIG-PLUS1 NIL (EQUAL (POWER-EVAL (BIG-PLUS1 L I BASE) BASE) (PLUS (POWER-EVAL L BASE) I)) NIL)) LINEAR-LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE UNCHANGING) SDEFN (LAMBDA (L BASE) (IF (LISTP L) (PLUS (CAR L) (TIMES BASE (POWER-EVAL (CDR L) BASE))) (QUOTE 0.))) LISP-CODE 1POWER-EVAL INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP L)) (((CDR L) BASE))) (TESTS-AND-CASES ((NOT (LISTP L))) NIL)) LEVEL-NO 3. JUSTIFICATIONS ((JUSTIFICATION (L) (COUNT L) LESSP (ZERO CDR-LESSP))) IDATE 840117182442. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1POWER-EVAL) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-BIG-PLUS POWER-EVAL-POWER-REP POWER-EVAL-BIG-PLUS POWER-EVAL-BIG-PLUS1) EVENT (DEFN POWER-EVAL (L BASE) (IF (LISTP L) (PLUS (CAR L) (TIMES BASE (POWER-EVAL (CDR L) BASE))) 0.)) LOCAL-UNDO-TUPLES ((DCELL . 1POWER-EVAL))))) 
(PUT1-LST (QUOTE DIFFERENCE-ELIM) (QUOTE (IDATE 840117182442. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EVEN3-REM EVEN3-DIFF RES1-REM-1-1 REM-DIFF-TIMES DIFF-MOD-1 N-O-I-LEMMA3 EQUAL-MODS-TRICK-1 DISTRIBUTIVITY-OF-TIMES-OVER-GCD EUCLID DIVIDES-PLUS-REWRITE2 DIVIDES-PLUS-REWRITE1 TIMES-DIFFERENCE NTH-APPEND) EVENT (PROVE-LEMMA DIFFERENCE-ELIM (ELIM) (IMPLIES (AND (NUMBERP Y) (NOT (LESSP Y X))) (EQUAL (PLUS X (DIFFERENCE Y X)) Y))) LOCAL-UNDO-TUPLES ((ELIMINATE-DESTRUCTORS-DESTS . DIFFERENCE) (ELIMINATE-DESTRUCTORS-SEQ . DIFFERENCE))))) 
(PUT1-LST (QUOTE EQUAL-LESSP) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182442. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LEQ-WINS1 LEQ-QUOT-TIMES-2 REFLECT-COMMUTES-WITH-TIMES-1 CRYPT-INVERTS-STEP-2 MEMBER-POSITIVES LESSP-DELETE-REWRITE LESSP-PLUS-CANCELLATION3 LESSP-TIMES-CANCELLATION LESSP-PLUS-CANCELATION LESSP-REMAINDER1 LESSP-QUOTIENT1 LESSP-REMAINDER2) EVENT (PROVE-LEMMA EQUAL-LESSP (REWRITE) (EQUAL (EQUAL (LESSP X Y) Z) (IF (LESSP X Y) (EQUAL T Z) (EQUAL F Z)))) LOCAL-UNDO-TUPLES ((LEMMAS EQUAL . EQUAL-LESSP))))) 
(PUT1-LST (QUOTE APPEND-CANCELLATION) (QUOTE (IDATE 840117182441. EVENT (PROVE-LEMMA APPEND-CANCELLATION (REWRITE) (EQUAL (EQUAL (APPEND A B) (APPEND A C)) (EQUAL B C))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 APPEND . APPEND-CANCELLATION) (LEMMAS EQUAL . APPEND-CANCELLATION))))) 
(PUT1-LST (QUOTE COUNT-SORT-LP) (QUOTE (IDATE 840117182440. EVENT (PROVE-LEMMA COUNT-SORT-LP (REWRITE) (EQUAL (COUNT-LIST Z (SORT-LP X Y)) (PLUS (COUNT-LIST Z X) (COUNT-LIST Z Y)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ADDTOLIST . COUNT-SORT-LP) (IMMEDIATE-DEPENDENTS0 PLUS-ADD1 . COUNT-SORT-LP) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL . COUNT-SORT-LP) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . COUNT-SORT-LP) (IMMEDIATE-DEPENDENTS0 SORT-LP . COUNT-SORT-LP) (IMMEDIATE-DEPENDENTS0 COUNT-LIST . COUNT-SORT-LP) (LEMMAS COUNT-LIST . COUNT-SORT-LP))))) 
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(PUT1-LST (QUOTE 1SORT-LP) (QUOTE NIL)) 
(PUT1-LST (QUOTE SORT-LP) (QUOTE (TYPE-PRESCRIPTION-LST ((SORT-LP 16. NIL T)) LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE SELF-REFLEXIVE) SDEFN (LAMBDA (X Y) (IF (LISTP X) (SORT-LP (CDR X) (ADDTOLIST (CAR X) Y)) Y)) LISP-CODE 1SORT-LP INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP X)) (((CDR X) (ADDTOLIST (CAR X) Y)))) (TESTS-AND-CASES ((NOT (LISTP X))) NIL)) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (X) (COUNT X) LESSP (ZERO CDR-LESSP))) IDATE 840117182328. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1SORT-LP) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (COUNT-SORT-LP ORDERED-SORT-LP) EVENT (DEFN SORT-LP (X Y) (IF (LISTP X) (SORT-LP (CDR X) (ADDTOLIST (CAR X) Y)) Y)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ADDTOLIST . SORT-LP) (DCELL . 1SORT-LP))))) 
(PUT1-LST (QUOTE REVERSE-REVERSE-) (QUOTE (IDATE 840117182328. EVENT (PROVE-LEMMA REVERSE-REVERSE- NIL (IMPLIES (PLISTP X) (EQUAL (REVERSE- (REVERSE- X)) X))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REVERSE-REVERSE . REVERSE-REVERSE-) (IMMEDIATE-DEPENDENTS0 REVERSE-LOOP-REVERSE . REVERSE-REVERSE-) (IMMEDIATE-DEPENDENTS0 REVERSE- . REVERSE-REVERSE-) (IMMEDIATE-DEPENDENTS0 PLISTP . REVERSE-REVERSE-))))) 
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(PUT1-LST (QUOTE REVERSE-LOOP-REVERSE) (QUOTE (IDATE 840117182327. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (REVERSE-REVERSE- REVERSE-APPEND) EVENT (PROVE-LEMMA REVERSE-LOOP-REVERSE (REWRITE) (EQUAL (REVERSE-LOOP X NIL) (REVERSE X))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PLISTP-REVERSE . REVERSE-LOOP-REVERSE) (IMMEDIATE-DEPENDENTS0 APPEND-RIGHT-ID . REVERSE-LOOP-REVERSE) (IMMEDIATE-DEPENDENTS0 REVERSE-LOOP-APPEND-REVERSE . REVERSE-LOOP-REVERSE) (IMMEDIATE-DEPENDENTS0 REVERSE . REVERSE-LOOP-REVERSE) (IMMEDIATE-DEPENDENTS0 REVERSE-LOOP . REVERSE-LOOP-REVERSE) (LEMMAS REVERSE-LOOP . REVERSE-LOOP-REVERSE))))) 
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(PUT1-LST (QUOTE 1REVERSE-) (QUOTE NIL)) 
(PUT1-LST (QUOTE REVERSE-) (QUOTE (TYPE-PRESCRIPTION-LST ((REVERSE- 24. NIL)) SDEFN (LAMBDA (X) (REVERSE-LOOP X (QUOTE NIL))) LISP-CODE 1REVERSE- INDUCTION-MACHINE NIL LEVEL-NO 1. JUSTIFICATIONS NIL IDATE 840117182325. SATELLITES (1REVERSE-) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (REVERSE-REVERSE- REVERSE-APPEND) EVENT (DEFN REVERSE- (X) (REVERSE-LOOP X NIL)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REVERSE-LOOP . REVERSE-) (DCELL . 1REVERSE-))))) 
(PUT1-LST (QUOTE 1REVERSE-LOOP) (QUOTE NIL)) 
(PUT1-LST (QUOTE REVERSE-LOOP) (QUOTE (TYPE-PRESCRIPTION-LST ((REVERSE-LOOP 16. NIL T)) LEMMAS ((REWRITE-RULE REVERSE-LOOP-REVERSE NIL (EQUAL (REVERSE-LOOP X (QUOTE NIL)) (REVERSE X)) NIL) (REWRITE-RULE REVERSE-LOOP-APPEND-REVERSE NIL (EQUAL (REVERSE-LOOP X Y) (APPEND (REVERSE X) Y)) NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE SELF-REFLEXIVE) SDEFN (LAMBDA (X ANS) (IF (LISTP X) (REVERSE-LOOP (CDR X) (CONS (CAR X) ANS)) ANS)) LISP-CODE 1REVERSE-LOOP INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP X)) (((CDR X) (CONS (CAR X) ANS)))) (TESTS-AND-CASES ((NOT (LISTP X))) NIL)) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (X) (COUNT X) LESSP (ZERO CDR-LESSP))) IDATE 840117182325. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1REVERSE-LOOP) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (REVERSE-LOOP-REVERSE REVERSE-LOOP-APPEND-REVERSE REVERSE-) EVENT (DEFN REVERSE-LOOP (X ANS) (IF (LISTP X) (REVERSE-LOOP (CDR X) (CONS (CAR X) ANS)) ANS)) LOCAL-UNDO-TUPLES ((DCELL . 1REVERSE-LOOP))))) 
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(PUT1-LST (QUOTE FACT-) (QUOTE (TYPE-PRESCRIPTION-LST ((FACT- 4. NIL)) SDEFN (LAMBDA (I) (FACT-LOOP I (QUOTE 1.))) LISP-CODE 1FACT- INDUCTION-MACHINE NIL LEVEL-NO 3. JUSTIFICATIONS NIL IDATE 840117182321. SATELLITES (1FACT-) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (FACT-FACT) EVENT (DEFN FACT- (I) (FACT-LOOP I 1.)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 FACT-LOOP . FACT-) (DCELL . 1FACT-))))) 
(PUT1-LST (QUOTE 1FACT-LOOP) (QUOTE NIL)) 
(PUT1-LST (QUOTE FACT-LOOP) (QUOTE (TYPE-PRESCRIPTION-LST ((FACT-LOOP 4. NIL T)) LEMMAS ((REWRITE-RULE FACT-LOOP-FACT ((NUMBERP I)) (EQUAL (FACT-LOOP J I) (TIMES I (FACT J))) NIL)) LINEAR-LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE SELF-REFLEXIVE) SDEFN (LAMBDA (I ANS) (IF (EQUAL I (QUOTE 0.)) ANS (IF (NUMBERP I) (FACT-LOOP (SUB1 I) (TIMES I ANS)) ANS))) LISP-CODE 1FACT-LOOP INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP I)) NIL) (TESTS-AND-CASES ((NOT (ZEROP I))) (((SUB1 I) (TIMES I ANS))))) LEVEL-NO 3. JUSTIFICATIONS ((JUSTIFICATION (I) (COUNT I) LESSP (ZERO ZEROP COUNT-NUMBERP))) IDATE 840117182320. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1FACT-LOOP) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (FACT-LOOP-FACT FACT-) EVENT (DEFN FACT-LOOP (I ANS) (IF (ZEROP I) ANS (FACT-LOOP (SUB1 I) (TIMES I ANS)))) LOCAL-UNDO-TUPLES ((DCELL . 1FACT-LOOP))))) 
(PUT1-LST (QUOTE 1FACT) (QUOTE NIL)) 
(PUT1-LST (QUOTE FACT) (QUOTE (TYPE-PRESCRIPTION-LST ((FACT 4. NIL)) LEMMAS NIL LINEAR-LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (I) (IF (EQUAL I (QUOTE 0.)) (QUOTE 1.) (IF (NUMBERP I) (TIMES I (FACT (SUB1 I))) (QUOTE 1.)))) LISP-CODE 1FACT INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP I)) NIL) (TESTS-AND-CASES ((NOT (ZEROP I))) (((SUB1 I))))) LEVEL-NO 3. JUSTIFICATIONS ((JUSTIFICATION (I) (COUNT I) LESSP (ZERO ZEROP COUNT-NUMBERP))) IDATE 840117182320. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1FACT) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (TIMES-REFLECT-LIST REM-REFLECT-LIST REM-REFLECT-LIST-BASE-CASE REM-REFLECT-LIST-4 REM-REFLECT-LIST-3 REM-REFLECT-LIST-2 REM-REFLECT-LIST-1 TIMES-EXP-FACT COMP-LIST-FACT WILSON-THM W-T-LEMMA INVERSE-LIST-FACT REMAINDER-TIMES-LIST-S PRIME-FACT TIMES-LIST-EQUAL-FACT TIMES-LIST-POSITIVES FACT-FACT FACT-LOOP-FACT) EVENT (DEFN FACT (I) (IF (ZEROP I) 1. (TIMES I (FACT (SUB1 I))))) LOCAL-UNDO-TUPLES ((DCELL . 1FACT))))) 
(PUT1-LST (QUOTE COUNTPS-COUNTPS) (QUOTE (IDATE 840117182320. EVENT (PROVE-LEMMA COUNTPS-COUNTPS (REWRITE) (IMPLIES (NUMBERP N) (EQUAL (COUNTPS-LOOP L PRED N) (PLUS N (COUNTPS L PRED))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . COUNTPS-COUNTPS) (IMMEDIATE-DEPENDENTS0 PLUS-ADD1 . COUNTPS-COUNTPS) (IMMEDIATE-DEPENDENTS0 COUNTPS . COUNTPS-COUNTPS) (IMMEDIATE-DEPENDENTS0 COUNTPS-LOOP . COUNTPS-COUNTPS) (LEMMAS COUNTPS-LOOP . COUNTPS-COUNTPS))))) 
(PUT1-LST (QUOTE COUNTPS) (QUOTE (TYPE-PRESCRIPTION-LST ((COUNTPS 4. NIL NIL)) LEMMAS NIL LINEAR-LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE UNCHANGING) SDEFN (LAMBDA (L PRED) (IF (LISTP L) (IF (CALL PRED (CAR L) (QUOTE NIL)) (ADD1 (COUNTPS (CDR L) PRED)) (COUNTPS (CDR L) PRED)) (QUOTE 0.))) INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP L) (CALL PRED (CAR L) (QUOTE NIL))) (((CDR L) PRED))) (TESTS-AND-CASES ((LISTP L) (QUOTE 1FALSE)) (((CDR L) PRED))) (TESTS-AND-CASES ((NOT (LISTP L))) NIL)) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (L) (COUNT L) LESSP (ZERO CDR-LESSP))) IDATE 840117182317. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (COUNTPS-COUNTPS) EVENT (DEFN COUNTPS (L PRED) (IF (LISTP L) (IF (CALL PRED (CAR L) NIL) (ADD1 (COUNTPS (CDR L) PRED)) (COUNTPS (CDR L) PRED)) 0.)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 CALL . COUNTPS))))) 
(PUT1-LST (QUOTE COUNTPS-) (QUOTE (TYPE-PRESCRIPTION-LST ((COUNTPS- 4. NIL NIL)) SDEFN (LAMBDA (L PRED) (COUNTPS-LOOP L PRED (QUOTE 0.))) LEVEL-NO 1. JUSTIFICATIONS NIL IDATE 840117182317. EVENT (DEFN COUNTPS- (L PRED) (COUNTPS-LOOP L PRED 0.)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COUNTPS-LOOP . COUNTPS-))))) 
(PUT1-LST (QUOTE COUNTPS-LOOP) (QUOTE (TYPE-PRESCRIPTION-LST ((COUNTPS-LOOP 4. NIL NIL T)) LEMMAS ((REWRITE-RULE COUNTPS-COUNTPS ((NUMBERP N)) (EQUAL (COUNTPS-LOOP L PRED N) (PLUS N (COUNTPS L PRED))) NIL)) LINEAR-LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE UNCHANGING QUESTIONABLE) SDEFN (LAMBDA (L PRED ANS) (IF (LISTP L) (IF (CALL PRED (CAR L) (QUOTE NIL)) (COUNTPS-LOOP (CDR L) PRED (ADD1 ANS)) (COUNTPS-LOOP (CDR L) PRED ANS)) ANS)) LISP-CODE NIL INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP L) (CALL PRED (CAR L) (QUOTE NIL))) (((CDR L) PRED (ADD1 ANS)))) (TESTS-AND-CASES ((LISTP L) (QUOTE 1FALSE)) (((CDR L) PRED ANS))) (TESTS-AND-CASES ((NOT (LISTP L))) NIL)) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (L) (COUNT L) LESSP (ZERO CDR-LESSP))) IDATE 840117182316. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (COUNTPS-COUNTPS COUNTPS-) EVENT (DEFN COUNTPS-LOOP (L PRED ANS) (IF (LISTP L) (IF (CALL PRED (CAR L) NIL) (COUNTPS-LOOP (CDR L) PRED (ADD1 ANS)) (COUNTPS-LOOP (CDR L) PRED ANS)) ANS)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 CALL . COUNTPS-LOOP))))) 
(PUT1-LST (QUOTE OCCUR-SUBST) (QUOTE (IDATE 840117182316. EVENT (PROVE-LEMMA OCCUR-SUBST NIL (IMPLIES (NOT (OCCUR A B)) (EQUAL (SUBST C A B) B))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SUBST . OCCUR-SUBST) (IMMEDIATE-DEPENDENTS0 OCCUR . OCCUR-SUBST))))) 
(PUT1-LST (QUOTE 1OCCUR) (QUOTE NIL)) 
(PUT1-LST (QUOTE OCCUR) (QUOTE (TYPE-PRESCRIPTION-LST ((OCCUR 3. NIL NIL)) LEMMAS NIL QUICK-BLOCK-INFO (UNCHANGING SELF-REFLEXIVE) SDEFN (LAMBDA (X Y) (IF (EQUAL X Y) (QUOTE 1TRUE) (IF (LISTP Y) (IF (OCCUR X (CAR Y)) (QUOTE 1TRUE) (OCCUR X (CDR Y))) (QUOTE 1FALSE)))) LISP-CODE 1OCCUR INDUCTION-MACHINE ((TESTS-AND-CASES ((EQUAL X Y)) NIL) (TESTS-AND-CASES ((NOT (EQUAL X Y)) (LISTP Y) (OCCUR X (CAR Y))) ((X (CAR Y)))) (TESTS-AND-CASES ((NOT (EQUAL X Y)) (LISTP Y) (NOT (OCCUR X (CAR Y)))) ((X (CAR Y)) (X (CDR Y)))) (TESTS-AND-CASES ((NOT (EQUAL X Y)) (NOT (LISTP Y))) NIL)) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (Y) (COUNT Y) LESSP (CDR-LESSP ZERO CAR-LESSP))) IDATE 840117182314. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (2.) SATELLITES (1OCCUR) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (OCCUR-SUBST) EVENT (DEFN OCCUR (X Y) (IF (EQUAL X Y) T (IF (LISTP Y) (IF (OCCUR X (CAR Y)) T (OCCUR X (CDR Y))) F))) LOCAL-UNDO-TUPLES ((DCELL . 1OCCUR))))) 
(PUT1-LST (QUOTE SUBST-A-A) (QUOTE (IDATE 840117182314. EVENT (PROVE-LEMMA SUBST-A-A NIL (EQUAL (SUBST A A B) B)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SUBST . SUBST-A-A))))) 
(PUT1-LST (QUOTE 1SUBST) (QUOTE NIL)) 
(PUT1-LST (QUOTE SUBST) (QUOTE (TYPE-PRESCRIPTION-LST ((SUBST 16. T NIL T)) LEMMAS NIL QUICK-BLOCK-INFO (UNCHANGING UNCHANGING SELF-REFLEXIVE) SDEFN (LAMBDA (X Y Z) (IF (EQUAL Y Z) X (IF (LISTP Z) (CONS (SUBST X Y (CAR Z)) (SUBST X Y (CDR Z))) Z))) LISP-CODE 1SUBST INDUCTION-MACHINE ((TESTS-AND-CASES ((EQUAL Y Z)) NIL) (TESTS-AND-CASES ((NOT (EQUAL Y Z)) (LISTP Z)) ((X Y (CDR Z)) (X Y (CAR Z)))) (TESTS-AND-CASES ((NOT (EQUAL Y Z)) (NOT (LISTP Z))) NIL)) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (Z) (COUNT Z) LESSP (CAR-LESSP ZERO CDR-LESSP))) IDATE 840117182313. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (4.) SATELLITES (1SUBST) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (OCCUR-SUBST SUBST-A-A) EVENT (DEFN SUBST (X Y Z) (IF (EQUAL Y Z) X (IF (LISTP Z) (CONS (SUBST X Y (CAR Z)) (SUBST X Y (CDR Z))) Z))) LOCAL-UNDO-TUPLES ((DCELL . 1SUBST))))) 
(PUT1-LST (QUOTE SORT-ORDERED) (QUOTE (IDATE 840117182313. EVENT (PROVE-LEMMA SORT-ORDERED (REWRITE) (IMPLIES (NUMBER-LISTP L) (EQUAL (EQUAL (SORT L) L) (ORDERED L)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 CROCK-DUE-TO-LACK-OF-BOUNCE . SORT-ORDERED) (IMMEDIATE-DEPENDENTS0 SORT-OF-ORDERED-NUMBER-LIST . SORT-ORDERED) (IMMEDIATE-DEPENDENTS0 ORDERED . SORT-ORDERED) (IMMEDIATE-DEPENDENTS0 SORT . SORT-ORDERED) (IMMEDIATE-DEPENDENTS0 NUMBER-LISTP . SORT-ORDERED) (LEMMAS EQUAL . SORT-ORDERED))))) 
(PUT1-LST (QUOTE CROCK-DUE-TO-LACK-OF-BOUNCE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182311. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (SORT-ORDERED) EVENT (PROVE-LEMMA CROCK-DUE-TO-LACK-OF-BOUNCE (REWRITE) (IMPLIES (EQUAL X (SORT L)) (ORDERED X))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ORDERED-SORT . CROCK-DUE-TO-LACK-OF-BOUNCE) (IMMEDIATE-DEPENDENTS0 ORDERED . CROCK-DUE-TO-LACK-OF-BOUNCE) (IMMEDIATE-DEPENDENTS0 SORT . CROCK-DUE-TO-LACK-OF-BOUNCE) (LEMMAS ORDERED . CROCK-DUE-TO-LACK-OF-BOUNCE))))) 
(PUT1-LST (QUOTE 1XOR) (QUOTE NIL)) 
(PUT1-LST (QUOTE XOR) (QUOTE (TYPE-PRESCRIPTION-LST ((XOR 3. NIL NIL)) SDEFN (LAMBDA (P Q) (IF Q (IF P (QUOTE 1FALSE) (QUOTE 1TRUE)) (EQUAL P (QUOTE 1TRUE)))) LISP-CODE 1XOR LEVEL-NO 0. JUSTIFICATIONS NIL IDATE 840117182310. SATELLITES (1XOR) EVENT (DEFN XOR (P Q) (IF Q (IF P F T) (EQUAL P T))) LOCAL-UNDO-TUPLES ((DCELL . 1XOR))))) 
(PUT1-LST (QUOTE SORT-OF-ORDERED-NUMBER-LIST) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182310. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (SORT-ORDERED) EVENT (PROVE-LEMMA SORT-OF-ORDERED-NUMBER-LIST (REWRITE) (IMPLIES (AND (ORDERED X) (NUMBER-LISTP X)) (EQUAL (SORT X) X))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ADDTOLIST . SORT-OF-ORDERED-NUMBER-LIST) (IMMEDIATE-DEPENDENTS0 ADDTOLIST-OF-ORDERED-NUMBER-LIST . SORT-OF-ORDERED-NUMBER-LIST) (IMMEDIATE-DEPENDENTS0 SORT . SORT-OF-ORDERED-NUMBER-LIST) (IMMEDIATE-DEPENDENTS0 NUMBER-LISTP . SORT-OF-ORDERED-NUMBER-LIST) (IMMEDIATE-DEPENDENTS0 ORDERED . SORT-OF-ORDERED-NUMBER-LIST) (LEMMAS SORT . SORT-OF-ORDERED-NUMBER-LIST))))) 
(PUT1-LST (QUOTE ADDTOLIST-OF-ORDERED-NUMBER-LIST) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182303. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (SORT-OF-ORDERED-NUMBER-LIST) EVENT (PROVE-LEMMA ADDTOLIST-OF-ORDERED-NUMBER-LIST (REWRITE) (IMPLIES (AND (ORDERED X) (NUMBER-LISTP X) (NUMBERP I) (NOT (LESSP (CAR X) I))) (EQUAL (ADDTOLIST I X) (CONS I X)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ADDTOLIST . ADDTOLIST-OF-ORDERED-NUMBER-LIST) (IMMEDIATE-DEPENDENTS0 NUMBER-LISTP . ADDTOLIST-OF-ORDERED-NUMBER-LIST) (IMMEDIATE-DEPENDENTS0 ORDERED . ADDTOLIST-OF-ORDERED-NUMBER-LIST) (LEMMAS ADDTOLIST . ADDTOLIST-OF-ORDERED-NUMBER-LIST))))) 
(PUT1-LST (QUOTE ORDERED-SORT) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182250. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CROCK-DUE-TO-LACK-OF-BOUNCE) EVENT (PROVE-LEMMA ORDERED-SORT (REWRITE) (ORDERED (SORT X))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ADDTOLIST . ORDERED-SORT) (IMMEDIATE-DEPENDENTS0 SORT . ORDERED-SORT) (IMMEDIATE-DEPENDENTS0 ORDERED . ORDERED-SORT) (LEMMAS ORDERED . ORDERED-SORT))))) 
(PUT1-LST (QUOTE 1NUMBER-LISTP) (QUOTE NIL)) 
(PUT1-LST (QUOTE NUMBER-LISTP) (QUOTE (TYPE-PRESCRIPTION-LST ((NUMBER-LISTP 3. NIL)) LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (L) (IF (LISTP L) (IF (NUMBERP (CAR L)) (NUMBER-LISTP (CDR L)) (QUOTE 1FALSE)) (EQUAL L (QUOTE NIL)))) LISP-CODE 1NUMBER-LISTP INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP L) (NUMBERP (CAR L))) (((CDR L)))) (TESTS-AND-CASES ((LISTP L) (NOT (NUMBERP (CAR L)))) NIL) (TESTS-AND-CASES ((NOT (LISTP L))) NIL)) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (L) (COUNT L) LESSP (ZERO CDR-LESSP))) IDATE 840117182231. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1NUMBER-LISTP) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (SORT-ORDERED SORT-OF-ORDERED-NUMBER-LIST ADDTOLIST-OF-ORDERED-NUMBER-LIST) EVENT (DEFN NUMBER-LISTP (L) (IF (LISTP L) (IF (NUMBERP (CAR L)) (NUMBER-LISTP (CDR L)) F) (EQUAL L NIL))) LOCAL-UNDO-TUPLES ((DCELL . 1NUMBER-LISTP))))) 
(PUT1-LST (QUOTE LEQ-HALF) (QUOTE (IDATE 840117182230. EVENT (PROVE-LEMMA LEQ-HALF NIL (LEQ (HALF I) I)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 HALF . LEQ-HALF))))) 
(PUT1-LST (QUOTE ORDERED-APPEND) (QUOTE (IDATE 840117182228. EVENT (PROVE-LEMMA ORDERED-APPEND NIL (IMPLIES (ORDERED (APPEND A B)) (ORDERED A))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 APPEND . ORDERED-APPEND) (IMMEDIATE-DEPENDENTS0 ORDERED . ORDERED-APPEND))))) 
(PUT1-LST (QUOTE COUNT-LIST-SORT) (QUOTE (IDATE 840117182222. EVENT (PROVE-LEMMA COUNT-LIST-SORT NIL (EQUAL (COUNT-LIST A (SORT L)) (COUNT-LIST A L))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ADDTOLIST . COUNT-LIST-SORT) (IMMEDIATE-DEPENDENTS0 SORT . COUNT-LIST-SORT) (IMMEDIATE-DEPENDENTS0 COUNT-LIST . COUNT-LIST-SORT))))) 
(PUT1-LST (QUOTE 1COUNT-LIST) (QUOTE NIL)) 
(PUT1-LST (QUOTE COUNT-LIST) (QUOTE (TYPE-PRESCRIPTION-LST ((COUNT-LIST 4. NIL NIL)) LEMMAS ((REWRITE-RULE COUNT-SORT-LP NIL (EQUAL (COUNT-LIST Z (SORT-LP X Y)) (PLUS (COUNT-LIST Z X) (COUNT-LIST Z Y))) NIL)) LINEAR-LEMMAS NIL QUICK-BLOCK-INFO (UNCHANGING SELF-REFLEXIVE) SDEFN (LAMBDA (A L) (IF (LISTP L) (IF (EQUAL A (CAR L)) (ADD1 (COUNT-LIST A (CDR L))) (COUNT-LIST A (CDR L))) (QUOTE 0.))) LISP-CODE 1COUNT-LIST INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP L) (EQUAL A (CAR L))) ((A (CDR L)))) (TESTS-AND-CASES ((LISTP L) (NOT (EQUAL A (CAR L)))) ((A (CDR L)))) (TESTS-AND-CASES ((NOT (LISTP L))) NIL)) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (L) (COUNT L) LESSP (ZERO CDR-LESSP))) IDATE 840117182207. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (2.) SATELLITES (1COUNT-LIST) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (COUNT-LIST-SORT2 COUNT-SORT-LP COUNT-LIST-SORT) EVENT (DEFN COUNT-LIST (A L) (IF (LISTP L) (IF (EQUAL A (CAR L)) (ADD1 (COUNT-LIST A (CDR L))) (COUNT-LIST A (CDR L))) 0.)) LOCAL-UNDO-TUPLES ((DCELL . 1COUNT-LIST))))) 
(PUT1-LST (QUOTE LENGTH-SORT) (QUOTE (IDATE 840117182207. EVENT (PROVE-LEMMA LENGTH-SORT NIL (EQUAL (LENGTH (SORT A)) (LENGTH A))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ADDTOLIST . LENGTH-SORT) (IMMEDIATE-DEPENDENTS0 SORT . LENGTH-SORT))))) 
(PUT1-LST (QUOTE MEMBER-SORT) (QUOTE (IDATE 840117182200. EVENT (PROVE-LEMMA MEMBER-SORT NIL (EQUAL (MEMBER A (SORT B)) (MEMBER A B))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ADDTOLIST . MEMBER-SORT) (IMMEDIATE-DEPENDENTS0 SORT . MEMBER-SORT))))) 
(PUT1-LST (QUOTE LEQ-NTH) (QUOTE (IDATE 840117182143. EVENT (PROVE-LEMMA LEQ-NTH NIL (LEQ (LENGTH (NTH L I)) (LENGTH L))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 NTH-0 . LEQ-NTH) (IMMEDIATE-DEPENDENTS0 NTH . LEQ-NTH))))) 
(PUT1-LST (QUOTE EVEN1-EVEN2) (QUOTE (IDATE 840117182138. EVENT (PROVE-LEMMA EVEN1-EVEN2 NIL (EQUAL (EVEN1 X) (EVEN2 X))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ODD . EVEN1-EVEN2) (IMMEDIATE-DEPENDENTS0 EVEN2 . EVEN1-EVEN2) (IMMEDIATE-DEPENDENTS0 EVEN1 . EVEN1-EVEN2))))) 
(PUT1-LST (QUOTE EXP-PLUS) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182135. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EULER-1-2 INVERSE-OF-INVERSE CRYPT-INVERTS-STEP-2 CRYPT-CORRECT EXP-EXP) EVENT (PROVE-LEMMA EXP-PLUS (REWRITE) (EQUAL (EXP I (PLUS J K)) (TIMES (EXP I J) (EXP I K)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . EXP-PLUS) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-TIMES . EXP-PLUS) (IMMEDIATE-DEPENDENTS0 EXP . EXP-PLUS) (LEMMAS EXP . EXP-PLUS))))) 
(PUT1-LST (QUOTE 1EXP) (QUOTE NIL)) 
(PUT1-LST (QUOTE EXP) (QUOTE (TYPE-PRESCRIPTION-LST ((EXP 4. NIL NIL)) LEMMAS ((REWRITE-RULE EXP-EXP NIL (EQUAL (EXP (EXP I J) K) (EXP I (TIMES J K))) NIL) (REWRITE-RULE EXP-TIMES NIL (EQUAL (EXP (TIMES I J) K) (TIMES (EXP I K) (EXP J K))) NIL) (REWRITE-RULE EXP-BY-0 NIL (EQUAL (EXP X (QUOTE 0.)) (QUOTE 1.)) NIL) (REWRITE-RULE EXP-OF-1 NIL (EQUAL (EXP (QUOTE 1.) K) (QUOTE 1.)) NIL) (REWRITE-RULE EXP-OF-0 NIL (EQUAL (EXP (QUOTE 0.) K) (IF (EQUAL K (QUOTE 0.)) (QUOTE 1.) (IF (NUMBERP K) (QUOTE 0.) (QUOTE 1.)))) NIL) (REWRITE-RULE EXP-PLUS NIL (EQUAL (EXP I (PLUS J K)) (TIMES (EXP I J) (EXP I K))) NIL)) LINEAR-LEMMAS NIL QUICK-BLOCK-INFO (UNCHANGING SELF-REFLEXIVE) SDEFN (LAMBDA (I J) (IF (EQUAL J (QUOTE 0.)) (QUOTE 1.) (IF (NUMBERP J) (TIMES I (EXP I (SUB1 J))) (QUOTE 1.)))) LISP-CODE 1EXP INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP J)) NIL) (TESTS-AND-CASES ((NOT (ZEROP J))) ((I (SUB1 J))))) LEVEL-NO 3. JUSTIFICATIONS ((JUSTIFICATION (J) (COUNT J) LESSP (ZERO ZEROP COUNT-NUMBERP))) IDATE 840117182126. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (2.) SATELLITES (1EXP) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (RES1-REM-2 RES1-REM-1 REM-REFLECT-LIST REM-REFLECT-LIST-BASE-CASE REM-REFLECT-LIST-4 REM-REFLECT-LIST-3 REM-REFLECT-LIST-2 REM-REFLECT-LIST-1 TIMES-EXP-FACT EULER-2 EULER-2-1 TIMES-COMP-LIST TIMES-COMP-LIST-5 TIMES-COMP-LIST-4 EULER-1 EULER-1-7 EULER-1-6 EULER-1-4 EULER-1-3 EULER-1-2 N-Z-I-LEMMA INVERSE-OF-INVERSE INVERSE-INVERTS-LEMMA INVERSE CRYPT-INVERTS-STEP-2 CRYPT-INVERTS-STEP-1B CRYPT-INVERTS-STEP-1A CRYPT-INVERTS-STEP-1 FERMAT-THM REMAINDER-TIMES-LIST-S EXP-MOD-IS-1 REMAINDER-EXP CRYPT-CORRECT EXP-EXP EXP-TIMES EXP-BY-0 EXP-OF-1 EXP-OF-0 EXP-PLUS) EVENT (DEFN EXP (I J) (IF (ZEROP J) 1. (TIMES I (EXP I (SUB1 J))))) LOCAL-UNDO-TUPLES ((DCELL . 1EXP))))) 
(PUT1-LST (QUOTE LAST-REVERSE) (QUOTE (IDATE 840117182126. EVENT (PROVE-LEMMA LAST-REVERSE NIL (IMPLIES (LISTP A) (EQUAL (LAST (REVERSE A)) (CONS (CAR A) NIL)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LAST-APPEND . LAST-REVERSE) (IMMEDIATE-DEPENDENTS0 REVERSE . LAST-REVERSE))))) 
(PUT1-LST (QUOTE LAST-APPEND) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182124. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LAST-REVERSE) EVENT (PROVE-LEMMA LAST-APPEND (REWRITE) (EQUAL (LAST (APPEND A B)) (IF (LISTP B) (LAST B) (IF (LISTP A) (CONS (CAR (LAST A)) B) B)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 APPEND . LAST-APPEND) (LEMMAS LAST . LAST-APPEND))))) 
(PUT1-LST (QUOTE SUBSETP-CONS) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182119. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (SUBSETP-POSITIVES-COMP-LIST SUBSETP-POSITIVES) EVENT (PROVE-LEMMA SUBSETP-CONS (REWRITE) (IMPLIES (SUBSETP X Y) (SUBSETP X (CONS Z Y)))) LOCAL-UNDO-TUPLES ((LEMMAS SUBSETP . SUBSETP-CONS))))) 
(PUT1-LST (QUOTE DOUBLE-TIMES-2) (QUOTE (IDATE 840117182117. EVENT (PROVE-LEMMA DOUBLE-TIMES-2 NIL (EQUAL (DOUBLE I) (TIMES 2. I))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-ADD1 . DOUBLE-TIMES-2) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO2 . DOUBLE-TIMES-2) (IMMEDIATE-DEPENDENTS0 DOUBLE . DOUBLE-TIMES-2))))) 
(PUT1-LST (QUOTE DOUBLE-HALF) (QUOTE (IDATE 840117182113. EVENT (PROVE-LEMMA DOUBLE-HALF (REWRITE) (IMPLIES (AND (NUMBERP I) (EVEN1 I)) (EQUAL (DOUBLE (HALF I)) I))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ODD . DOUBLE-HALF) (IMMEDIATE-DEPENDENTS0 HALF . DOUBLE-HALF) (IMMEDIATE-DEPENDENTS0 DOUBLE . DOUBLE-HALF) (IMMEDIATE-DEPENDENTS0 EVEN1 . DOUBLE-HALF) (LEMMAS DOUBLE . DOUBLE-HALF))))) 
(PUT1-LST (QUOTE HALF-DOUBLE) (QUOTE (IDATE 840117182106. EVENT (PROVE-LEMMA HALF-DOUBLE (REWRITE) (IMPLIES (NUMBERP I) (EQUAL (HALF (DOUBLE I)) I))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DOUBLE . HALF-DOUBLE) (IMMEDIATE-DEPENDENTS0 HALF . HALF-DOUBLE) (LEMMAS HALF . HALF-DOUBLE))))) 
(PUT1-LST (QUOTE 1HALF) (QUOTE NIL)) 
(PUT1-LST (QUOTE HALF) (QUOTE (TYPE-PRESCRIPTION-LST ((HALF 4. NIL)) LEMMAS ((REWRITE-RULE HALF-DOUBLE ((NUMBERP I)) (EQUAL (HALF (DOUBLE I)) I) NIL)) LINEAR-LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (I) (IF (EQUAL I (QUOTE 0.)) (QUOTE 0.) (IF (NUMBERP I) (IF (EQUAL (SUB1 I) (QUOTE 0.)) (QUOTE 0.) (ADD1 (HALF (SUB1 (SUB1 I))))) (QUOTE 0.)))) LISP-CODE 1HALF INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP I)) NIL) (TESTS-AND-CASES ((NOT (ZEROP I)) (ZEROP (SUB1 I))) NIL) (TESTS-AND-CASES ((NOT (ZEROP I)) (NOT (ZEROP (SUB1 I)))) (((SUB1 (SUB1 I)))))) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (I) (COUNT I) LESSP (ZERO ZEROP COUNT-NUMBERP))) IDATE 840117182105. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1HALF) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LEQ-HALF DOUBLE-HALF HALF-DOUBLE) EVENT (DEFN HALF (I) (IF (ZEROP I) 0. (IF (ZEROP (SUB1 I)) 0. (ADD1 (HALF (SUB1 (SUB1 I))))))) LOCAL-UNDO-TUPLES ((DCELL . 1HALF))))) 
(PUT1-LST (QUOTE EVEN1-DOUBLE) (QUOTE (IDATE 840117182104. EVENT (PROVE-LEMMA EVEN1-DOUBLE (REWRITE) (EVEN1 (DOUBLE I))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ODD . EVEN1-DOUBLE) (IMMEDIATE-DEPENDENTS0 DOUBLE . EVEN1-DOUBLE) (IMMEDIATE-DEPENDENTS0 EVEN1 . EVEN1-DOUBLE) (LEMMAS EVEN1 . EVEN1-DOUBLE))))) 
(PUT1-LST (QUOTE 1DOUBLE) (QUOTE NIL)) 
(PUT1-LST (QUOTE DOUBLE) (QUOTE (TYPE-PRESCRIPTION-LST ((DOUBLE 4. NIL)) LEMMAS ((REWRITE-RULE DOUBLE-HALF ((NUMBERP I) (EVEN1 I)) (EQUAL (DOUBLE (HALF I)) I) NIL)) LINEAR-LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (I) (IF (EQUAL I (QUOTE 0.)) (QUOTE 0.) (IF (NUMBERP I) (ADD1 (ADD1 (DOUBLE (SUB1 I)))) (QUOTE 0.)))) LISP-CODE 1DOUBLE INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP I)) NIL) (TESTS-AND-CASES ((NOT (ZEROP I))) (((SUB1 I))))) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (I) (COUNT I) LESSP (ZERO ZEROP COUNT-NUMBERP))) IDATE 840117182100. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1DOUBLE) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (DOUBLE-TIMES-2 DOUBLE-HALF HALF-DOUBLE EVEN1-DOUBLE) EVENT (DEFN DOUBLE (I) (IF (ZEROP I) 0. (ADD1 (ADD1 (DOUBLE (SUB1 I)))))) LOCAL-UNDO-TUPLES ((DCELL . 1DOUBLE))))) 
(PUT1-LST (QUOTE 1EVEN2) (QUOTE NIL)) 
(PUT1-LST (QUOTE EVEN2) (QUOTE (TYPE-PRESCRIPTION-LST ((EVEN2 3. NIL)) LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (X) (IF (EQUAL X (QUOTE 0.)) (QUOTE 1TRUE) (IF (NUMBERP X) (IF (EQUAL (SUB1 X) (QUOTE 0.)) (QUOTE 1FALSE) (EVEN2 (SUB1 (SUB1 X)))) (QUOTE 1TRUE)))) LISP-CODE 1EVEN2 INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP X)) NIL) (TESTS-AND-CASES ((NOT (ZEROP X)) (ZEROP (SUB1 X))) NIL) (TESTS-AND-CASES ((NOT (ZEROP X)) (NOT (ZEROP (SUB1 X)))) (((SUB1 (SUB1 X)))))) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (X) (COUNT X) LESSP (ZERO ZEROP COUNT-NUMBERP))) IDATE 840117182059. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1EVEN2) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EVEN1-EVEN2) EVENT (DEFN EVEN2 (X) (IF (ZEROP X) T (IF (ZEROP (SUB1 X)) F (EVEN2 (SUB1 (SUB1 X)))))) LOCAL-UNDO-TUPLES ((DCELL . 1EVEN2))))) 
(PUT1-LST (QUOTE 1EVEN1) (QUOTE NIL)) 
(PUT1-LST (QUOTE EVEN1) (QUOTE (TYPE-PRESCRIPTION-LST ((EVEN1 3. NIL)) LEMMAS ((REWRITE-RULE EVEN1-DOUBLE NIL (EVEN1 (DOUBLE I)) NIL)) QUICK-BLOCK-INFO NIL SDEFN (LAMBDA (X) (IF (EQUAL X (QUOTE 0.)) (QUOTE 1TRUE) (IF (NUMBERP X) (ODD (SUB1 X)) (QUOTE 1TRUE)))) LISP-CODE 1EVEN1 INDUCTION-MACHINE NIL LEVEL-NO 1. JUSTIFICATIONS NIL IDATE 840117182059. CONTROLLER-POCKETS NIL SATELLITES (1EVEN1) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EVEN1-EVEN2 DOUBLE-HALF EVEN1-DOUBLE) EVENT (DEFN EVEN1 (X) (IF (ZEROP X) T (ODD (SUB1 X)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ODD . EVEN1) (DCELL . 1EVEN1))))) 
(PUT1-LST (QUOTE 1ODD) (QUOTE NIL)) 
(PUT1-LST (QUOTE ODD) (QUOTE (TYPE-PRESCRIPTION-LST ((ODD 3. NIL)) LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (X) (IF (EQUAL X (QUOTE 0.)) (QUOTE 1FALSE) (IF (NUMBERP X) (IF (EQUAL (SUB1 X) (QUOTE 0.)) (QUOTE 1TRUE) (ODD (SUB1 (SUB1 X)))) (QUOTE 1FALSE)))) LISP-CODE 1ODD INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP X)) NIL) (TESTS-AND-CASES ((NOT (ZEROP X)) (ZEROP (SUB1 X))) NIL) (TESTS-AND-CASES ((NOT (ZEROP X)) (NOT (ZEROP (SUB1 X)))) (((SUB1 (SUB1 X)))))) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (X) (COUNT X) LESSP (ZERO ZEROP COUNT-NUMBERP))) IDATE 840117182058. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1ODD) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (TWO-EVEN EULER-2-3 EVEN1-EVEN2 DOUBLE-HALF EVEN1-DOUBLE EVEN1) EVENT (DEFN ODD (X) (IF (ZEROP X) F (IF (ZEROP (SUB1 X)) T (ODD (SUB1 (SUB1 X)))))) LOCAL-UNDO-TUPLES ((DCELL . 1ODD))))) 
(PUT1-LST (QUOTE ASSOCIATIVITY-OF-EQUAL) (QUOTE (IDATE 840117182058. EVENT (PROVE-LEMMA ASSOCIATIVITY-OF-EQUAL NIL (IMPLIES (AND (BOOLEAN A) (AND (BOOLEAN B) (BOOLEAN C))) (EQUAL (EQUAL (EQUAL A B) C) (EQUAL A (EQUAL B C))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 BOOLEAN . ASSOCIATIVITY-OF-EQUAL))))) 
(PUT1-LST (QUOTE NTH-APPEND1) (QUOTE (IDATE 840117182057. EVENT (PROVE-LEMMA NTH-APPEND1 (REWRITE) (EQUAL (NTH A (PLUS I J)) (NTH (NTH A I) J))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 NTH . NTH-APPEND1) (LEMMAS NTH . NTH-APPEND1))))) 
(PUT1-LST (QUOTE NTH-NIL) (QUOTE (IDATE 840117182054. EVENT (PROVE-LEMMA NTH-NIL (REWRITE) (EQUAL (NTH NIL I) (IF (ZEROP I) NIL 0.))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 NTH-0 . NTH-NIL) (IMMEDIATE-DEPENDENTS0 NTH . NTH-NIL) (LEMMAS NTH . NTH-NIL))))) 
(PUT1-LST (QUOTE NTH-0) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182053. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (NTH-APPEND LEQ-NTH NTH-NIL) EVENT (PROVE-LEMMA NTH-0 (REWRITE) (EQUAL (NTH 0. I) 0.)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 NTH . NTH-0) (LEMMAS NTH . NTH-0))))) 
(PUT1-LST (QUOTE IFF-EQUAL-EQUAL) (QUOTE (IDATE 840117182051. EVENT (PROVE-LEMMA IFF-EQUAL-EQUAL NIL (IMPLIES (AND (BOOLEAN P) (BOOLEAN Q)) (EQUAL (IFF P Q) (EQUAL P Q)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 IFF . IFF-EQUAL-EQUAL) (IMMEDIATE-DEPENDENTS0 BOOLEAN . IFF-EQUAL-EQUAL))))) 
(PUT1-LST (QUOTE 1IFF) (QUOTE NIL)) 
(PUT1-LST (QUOTE IFF) (QUOTE (TYPE-PRESCRIPTION-LST ((IFF 3. NIL NIL)) LEMMAS NIL QUICK-BLOCK-INFO NIL SDEFN (LAMBDA (X Y) (IF X (IF Y (QUOTE 1TRUE) (QUOTE 1FALSE)) (IF Y (QUOTE 1FALSE) (QUOTE 1TRUE)))) LISP-CODE 1IFF INDUCTION-MACHINE NIL LEVEL-NO 0. JUSTIFICATIONS NIL IDATE 840117182049. CONTROLLER-POCKETS NIL SATELLITES (1IFF) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (RES1-QUOT-LIST EVEN3-REM-REFLECT TAUTOLOGYP-IS-SOUND VALUE-CAN-IGNORE-REDUNDANT-ASSIGNMENTS IFF-EQUAL-EQUAL) EVENT (DEFN IFF (X Y) (AND (IMPLIES X Y) (IMPLIES Y X))) LOCAL-UNDO-TUPLES ((DCELL . 1IFF))))) 
(PUT1-LST (QUOTE 1BOOLEAN) (QUOTE NIL)) 
(PUT1-LST (QUOTE BOOLEAN) (QUOTE (TYPE-PRESCRIPTION-LST ((BOOLEAN 3. NIL)) LEMMAS NIL SDEFN (LAMBDA (X) (IF (EQUAL X (QUOTE 1TRUE)) (QUOTE 1TRUE) (EQUAL X (QUOTE 1FALSE)))) LISP-CODE 1BOOLEAN INDUCTION-MACHINE NIL LEVEL-NO 0. JUSTIFICATIONS NIL IDATE 840117182048. CONTROLLER-POCKETS NIL SATELLITES (1BOOLEAN) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (ASSOCIATIVITY-OF-EQUAL IFF-EQUAL-EQUAL) EVENT (DEFN BOOLEAN (X) (OR (EQUAL X T) (EQUAL X F))) LOCAL-UNDO-TUPLES ((DCELL . 1BOOLEAN))))) 
(PUT1-LST (QUOTE 1ASSOC) (QUOTE NIL)) 
(PUT1-LST (QUOTE ASSOC) (QUOTE (TYPE-PRESCRIPTION-LST ((ASSOC -1. NIL NIL)) LEMMAS NIL QUICK-BLOCK-INFO (UNCHANGING SELF-REFLEXIVE) SDEFN (LAMBDA (X Y) (IF (LISTP Y) (IF (EQUAL X (CAR (CAR Y))) (CAR Y) (ASSOC X (CDR Y))) (QUOTE NIL))) LISP-CODE 1ASSOC INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP Y) (EQUAL X (CAR (CAR Y)))) NIL) (TESTS-AND-CASES ((LISTP Y) (NOT (EQUAL X (CAR (CAR Y))))) ((X (CDR Y)))) (TESTS-AND-CASES ((NOT (LISTP Y))) NIL)) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (Y) (COUNT Y) LESSP (ZERO CDR-LESSP))) IDATE 840117182048. CONTROLLER-POCKETS (2.) SATELLITES (1ASSOC) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (SUBST2-OK EVAL2) EVENT (DEFN ASSOC (X Y) (IF (LISTP Y) (IF (EQUAL X (CAAR Y)) (CAR Y) (ASSOC X (CDR Y))) NIL)) LOCAL-UNDO-TUPLES ((DCELL . 1ASSOC))))) 
(PUT1-LST (QUOTE 1SORT) (QUOTE NIL)) 
(PUT1-LST (QUOTE SORT) (QUOTE (TYPE-PRESCRIPTION-LST ((SORT 24. NIL)) LEMMAS ((REWRITE-RULE SORT-OF-ORDERED-NUMBER-LIST ((ORDERED X) (NUMBER-LISTP X)) (EQUAL (SORT X) X) NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (L) (IF (LISTP L) (ADDTOLIST (CAR L) (SORT (CDR L))) (QUOTE NIL))) LISP-CODE 1SORT INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP L)) (((CDR L)))) (TESTS-AND-CASES ((NOT (LISTP L))) NIL)) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (L) (COUNT L) LESSP (ZERO CDR-LESSP))) IDATE 840117182047. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1SORT) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (SORT-ORDERED CROCK-DUE-TO-LACK-OF-BOUNCE SORT-OF-ORDERED-NUMBER-LIST ORDERED-SORT COUNT-LIST-SORT LENGTH-SORT MEMBER-SORT) EVENT (DEFN SORT (L) (IF (LISTP L) (ADDTOLIST (CAR L) (SORT (CDR L))) NIL)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ADDTOLIST . SORT) (DCELL . 1SORT))))) 
(PUT1-LST (QUOTE 1ADDTOLIST) (QUOTE NIL)) 
(PUT1-LST (QUOTE ADDTOLIST) (QUOTE (TYPE-PRESCRIPTION-LST ((ADDTOLIST 16. NIL NIL)) LEMMAS ((REWRITE-RULE ADDTOLIST-OF-ORDERED-NUMBER-LIST ((ORDERED X) (NUMBER-LISTP X) (NUMBERP I) (NOT (LESSP (CAR X) I))) (EQUAL (ADDTOLIST I X) (CONS I X)) NIL)) QUICK-BLOCK-INFO (UNCHANGING SELF-REFLEXIVE) SDEFN (LAMBDA (X L) (IF (LISTP L) (IF (LESSP X (CAR L)) (CONS X L) (CONS (CAR L) (ADDTOLIST X (CDR L)))) (CONS X (QUOTE NIL)))) LISP-CODE 1ADDTOLIST INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP L) (LESSP X (CAR L))) NIL) (TESTS-AND-CASES ((LISTP L) (NOT (LESSP X (CAR L)))) ((X (CDR L)))) (TESTS-AND-CASES ((NOT (LISTP L))) NIL)) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (L) (COUNT L) LESSP (ZERO CDR-LESSP))) IDATE 840117182047. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (2.) SATELLITES (1ADDTOLIST) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (COUNT-SORT-LP ORDERED-ADDTOLIST SORT-LP SORT-OF-ORDERED-NUMBER-LIST ADDTOLIST-OF-ORDERED-NUMBER-LIST ORDERED-SORT COUNT-LIST-SORT LENGTH-SORT MEMBER-SORT SORT) EVENT (DEFN ADDTOLIST (X L) (IF (LISTP L) (IF (LESSP X (CAR L)) (CONS X L) (CONS (CAR L) (ADDTOLIST X (CDR L)))) (CONS X NIL))) LOCAL-UNDO-TUPLES ((DCELL . 1ADDTOLIST))))) 
(PUT1-LST (QUOTE 1ORDERED) (QUOTE NIL)) 
(PUT1-LST (QUOTE ORDERED) (QUOTE (TYPE-PRESCRIPTION-LST ((ORDERED 3. NIL)) LEMMAS ((REWRITE-RULE ORDERED-SORT-LP ((ORDERED Y)) (ORDERED (SORT-LP X Y)) NIL) (REWRITE-RULE ORDERED-ADDTOLIST ((ORDERED Y)) (ORDERED (ADDTOLIST X Y)) NIL) (REWRITE-RULE CROCK-DUE-TO-LACK-OF-BOUNCE ((EQUAL X (SORT L))) (ORDERED X) NIL) (REWRITE-RULE ORDERED-SORT NIL (ORDERED (SORT X)) NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (L) (IF (LISTP L) (IF (LISTP (CDR L)) (IF (LESSP (CAR (CDR L)) (CAR L)) (QUOTE 1FALSE) (ORDERED (CDR L))) (QUOTE 1TRUE)) (QUOTE 1TRUE))) LISP-CODE 1ORDERED INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP L) (LISTP (CDR L)) (LESSP (CAR (CDR L)) (CAR L))) NIL) (TESTS-AND-CASES ((LISTP L) (LISTP (CDR L)) (NOT (LESSP (CAR (CDR L)) (CAR L)))) (((CDR L)))) (TESTS-AND-CASES ((LISTP L) (NOT (LISTP (CDR L)))) NIL) (TESTS-AND-CASES ((NOT (LISTP L))) NIL)) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (L) (COUNT L) LESSP (ZERO CDR-LESSP))) IDATE 840117182047. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1ORDERED) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (ORDERED-SORT-LP ORDERED-ADDTOLIST SORT-ORDERED CROCK-DUE-TO-LACK-OF-BOUNCE SORT-OF-ORDERED-NUMBER-LIST ADDTOLIST-OF-ORDERED-NUMBER-LIST ORDERED-SORT ORDERED-APPEND) EVENT (DEFN ORDERED (L) (IF (LISTP L) (IF (LISTP (CDR L)) (IF (LESSP (CADR L) (CAR L)) F (ORDERED (CDR L))) T) T)) LOCAL-UNDO-TUPLES ((DCELL . 1ORDERED))))) 
(PUT1-LST (QUOTE TRANSITIVITY-OF-LEQ) (QUOTE (IDATE 840117182046. EVENT (PROVE-LEMMA TRANSITIVITY-OF-LEQ NIL (IMPLIES (AND (LEQ X Y) (LEQ Y Z)) (LEQ X Z)))))) 
(PUT1-LST (QUOTE 1GREATEREQP) (QUOTE NIL)) 
(PUT1-LST (QUOTE GREATEREQP) (QUOTE (TYPE-PRESCRIPTION-LST ((GREATEREQP 3. NIL NIL)) SDEFN (LAMBDA (X Y) (IF (LESSP X Y) (QUOTE 1FALSE) (QUOTE 1TRUE))) LISP-CODE 1GREATEREQP LEVEL-NO 0. JUSTIFICATIONS NIL IDATE 840117182046. SATELLITES (1GREATEREQP) EVENT (DEFN GREATEREQP (X Y) (NOT (LESSP X Y))) LOCAL-UNDO-TUPLES ((DCELL . 1GREATEREQP))))) 
(PUT1-LST (QUOTE 1NTH) (QUOTE NIL)) 
(PUT1-LST (QUOTE NTH) (QUOTE (TYPE-PRESCRIPTION-LST ((NTH -1. T NIL)) LEMMAS ((REWRITE-RULE NTH-APPEND NIL (EQUAL (NTH (APPEND A B) I) (APPEND (NTH A I) (NTH B (DIFFERENCE I (LENGTH A))))) NIL) (REWRITE-RULE NTH-APPEND1 NIL (EQUAL (NTH A (PLUS I J)) (NTH (NTH A I) J)) NIL) (REWRITE-RULE NTH-NIL NIL (EQUAL (NTH (QUOTE NIL) I) (IF (EQUAL I (QUOTE 0.)) (QUOTE NIL) (IF (NUMBERP I) (QUOTE 0.) (QUOTE NIL)))) NIL) (REWRITE-RULE NTH-0 NIL (EQUAL (NTH (QUOTE 0.) I) (QUOTE 0.)) NIL)) LINEAR-LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE SELF-REFLEXIVE) SDEFN (LAMBDA (X N) (IF (EQUAL N (QUOTE 0.)) X (IF (NUMBERP N) (NTH (CDR X) (SUB1 N)) X))) LISP-CODE 1NTH INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP N)) NIL) (TESTS-AND-CASES ((NOT (ZEROP N))) (((CDR X) (SUB1 N))))) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (N) (COUNT N) LESSP (ZERO ZEROP COUNT-NUMBERP))) IDATE 840117182045. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (2.) SATELLITES (1NTH) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (NTH-APPEND LEQ-NTH NTH-APPEND1 NTH-NIL NTH-0) EVENT (DEFN NTH (X N) (IF (ZEROP N) X (NTH (CDR X) (SUB1 N)))) LOCAL-UNDO-TUPLES ((DCELL . 1NTH))))) 
(PUT1-LST (QUOTE SUBSETP-INTERSECT) (QUOTE (IDATE 840117182045. EVENT (PROVE-LEMMA SUBSETP-INTERSECT NIL (IMPLIES (AND (PLISTP A) (SUBSETP A B)) (EQUAL (INTERSECT A B) A))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 INTERSECT . SUBSETP-INTERSECT) (IMMEDIATE-DEPENDENTS0 PLISTP . SUBSETP-INTERSECT))))) 
(PUT1-LST (QUOTE SUBSETP-UNION) (QUOTE (IDATE 840117182041. EVENT (PROVE-LEMMA SUBSETP-UNION NIL (IMPLIES (SUBSETP A B) (EQUAL (UNION A B) B))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 UNION . SUBSETP-UNION))))) 
(PUT1-LST (QUOTE MEMBER-UNION) (QUOTE (IDATE 840117182039. EVENT (PROVE-LEMMA MEMBER-UNION NIL (EQUAL (MEMBER A (UNION B C)) (OR (MEMBER A B) (MEMBER A C)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 UNION . MEMBER-UNION))))) 
(PUT1-LST (QUOTE 1UNION) (QUOTE NIL)) 
(PUT1-LST (QUOTE UNION) (QUOTE (TYPE-PRESCRIPTION-LST ((UNION 16. NIL T)) LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE UNCHANGING) SDEFN (LAMBDA (X Y) (IF (LISTP X) (IF (MEMBER (CAR X) Y) (UNION (CDR X) Y) (CONS (CAR X) (UNION (CDR X) Y))) Y)) LISP-CODE 1UNION INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP X) (MEMBER (CAR X) Y)) (((CDR X) Y))) (TESTS-AND-CASES ((LISTP X) (NOT (MEMBER (CAR X) Y))) (((CDR X) Y))) (TESTS-AND-CASES ((NOT (LISTP X))) NIL)) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (X) (COUNT X) LESSP (ZERO CDR-LESSP))) IDATE 840117182033. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1UNION) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (SUBSETP-UNION MEMBER-UNION) EVENT (DEFN UNION (X Y) (IF (LISTP X) (IF (MEMBER (CAR X) Y) (UNION (CDR X) Y) (CONS (CAR X) (UNION (CDR X) Y))) Y)) LOCAL-UNDO-TUPLES ((DCELL . 1UNION))))) 
(PUT1-LST (QUOTE MEMBER-INTERSECT) (QUOTE (IDATE 840117182033. EVENT (PROVE-LEMMA MEMBER-INTERSECT (REWRITE) (EQUAL (MEMBER A (INTERSECT B C)) (AND (MEMBER A B) (MEMBER A C)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 INTERSECT . MEMBER-INTERSECT) (LEMMAS MEMBER . MEMBER-INTERSECT))))) 
(PUT1-LST (QUOTE 1INTERSECT) (QUOTE NIL)) 
(PUT1-LST (QUOTE INTERSECT) (QUOTE (TYPE-PRESCRIPTION-LST ((INTERSECT 24. NIL NIL)) LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE UNCHANGING) SDEFN (LAMBDA (X Y) (IF (LISTP X) (IF (MEMBER (CAR X) Y) (CONS (CAR X) (INTERSECT (CDR X) Y)) (INTERSECT (CDR X) Y)) (QUOTE NIL))) LISP-CODE 1INTERSECT INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP X) (MEMBER (CAR X) Y)) (((CDR X) Y))) (TESTS-AND-CASES ((LISTP X) (NOT (MEMBER (CAR X) Y))) (((CDR X) Y))) (TESTS-AND-CASES ((NOT (LISTP X))) NIL)) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (X) (COUNT X) LESSP (ZERO CDR-LESSP))) IDATE 840117182024. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1INTERSECT) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EMPTY-INTERSECT-MULTS A-WINNER-EVERY-TIME WIN-SOME-LOSE-SOME-2 SUBSETP-INTERSECT MEMBER-INTERSECT) EVENT (DEFN INTERSECT (X Y) (IF (LISTP X) (IF (MEMBER (CAR X) Y) (CONS (CAR X) (INTERSECT (CDR X) Y)) (INTERSECT (CDR X) Y)) NIL)) LOCAL-UNDO-TUPLES ((DCELL . 1INTERSECT))))) 
(PUT1-LST (QUOTE LENGTH-REVERSE) (QUOTE (IDATE 840117182024. EVENT (PROVE-LEMMA LENGTH-REVERSE (REWRITE) (EQUAL (LENGTH (REVERSE X)) (LENGTH X))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 APPEND . LENGTH-REVERSE) (IMMEDIATE-DEPENDENTS0 PLISTP . LENGTH-REVERSE) (IMMEDIATE-DEPENDENTS0 PLISTP-REVERSE . LENGTH-REVERSE) (IMMEDIATE-DEPENDENTS0 REVERSE . LENGTH-REVERSE) (LEMMAS LENGTH . LENGTH-REVERSE))))) 
(PUT1-LST (QUOTE MEMBER-REVERSE) (QUOTE (IDATE 840117182019. EVENT (PROVE-LEMMA MEMBER-REVERSE (REWRITE) (EQUAL (MEMBER X (REVERSE Y)) (MEMBER X Y))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 MEMBER-APPEND . MEMBER-REVERSE) (IMMEDIATE-DEPENDENTS0 REVERSE . MEMBER-REVERSE) (LEMMAS MEMBER . MEMBER-REVERSE))))) 
(PUT1-LST (QUOTE MEMBER-APPEND) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182017. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (MEMBER-REVERSE) EVENT (PROVE-LEMMA MEMBER-APPEND (REWRITE) (EQUAL (MEMBER X (APPEND A B)) (OR (MEMBER X A) (MEMBER X B)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 APPEND . MEMBER-APPEND) (LEMMAS MEMBER . MEMBER-APPEND))))) 
(PUT1-LST (QUOTE FLATTEN-MC-FLATTEN) (QUOTE (IDATE 840117182014. EVENT (PROVE-LEMMA FLATTEN-MC-FLATTEN (REWRITE) (EQUAL (MC-FLATTEN X Y) (APPEND (FLATTEN X) Y))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-APPEND . FLATTEN-MC-FLATTEN) (IMMEDIATE-DEPENDENTS0 FLATTEN . FLATTEN-MC-FLATTEN) (IMMEDIATE-DEPENDENTS0 APPEND . FLATTEN-MC-FLATTEN) (IMMEDIATE-DEPENDENTS0 MC-FLATTEN . FLATTEN-MC-FLATTEN) (LEMMAS MC-FLATTEN . FLATTEN-MC-FLATTEN))))) 
(PUT1-LST (QUOTE 1MC-FLATTEN) (QUOTE NIL)) 
(PUT1-LST (QUOTE MC-FLATTEN) (QUOTE (TYPE-PRESCRIPTION-LST ((MC-FLATTEN 16. NIL NIL)) LEMMAS ((REWRITE-RULE FLATTEN-MC-FLATTEN NIL (EQUAL (MC-FLATTEN X Y) (APPEND (FLATTEN X) Y)) NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE QUESTIONABLE) SDEFN (LAMBDA (X Y) (IF (LISTP X) (MC-FLATTEN (CAR X) (MC-FLATTEN (CDR X) Y)) (CONS X Y))) LISP-CODE 1MC-FLATTEN INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP X)) (((CAR X) (MC-FLATTEN (CDR X) Y)) ((CDR X) Y))) (TESTS-AND-CASES ((NOT (LISTP X))) NIL)) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (X) (COUNT X) LESSP (CDR-LESSP ZERO CAR-LESSP))) IDATE 840117182013. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1MC-FLATTEN) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (FLATTEN-MC-FLATTEN) EVENT (DEFN MC-FLATTEN (X Y) (IF (LISTP X) (MC-FLATTEN (CAR X) (MC-FLATTEN (CDR X) Y)) (CONS X Y))) LOCAL-UNDO-TUPLES ((DCELL . 1MC-FLATTEN))))) 
(PUT1-LST (QUOTE 1FLATTEN) (QUOTE NIL)) 
(PUT1-LST (QUOTE FLATTEN) (QUOTE (TYPE-PRESCRIPTION-LST ((FLATTEN 16. NIL)) LEMMAS ((REWRITE-RULE GOPHER-RETURNS-CORRECT-STATE NIL (EQUAL (FLATTEN (CDR (GOPHER X))) (IF (LISTP X) (CDR (FLATTEN X)) (QUOTE (0.)))) NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (X) (IF (LISTP X) (APPEND (FLATTEN (CAR X)) (FLATTEN (CDR X))) (CONS X (QUOTE NIL)))) LISP-CODE 1FLATTEN INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP X)) (((CDR X)) ((CAR X)))) (TESTS-AND-CASES ((NOT (LISTP X))) NIL)) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (X) (COUNT X) LESSP (CAR-LESSP ZERO CDR-LESSP))) IDATE 840117182012. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1FLATTEN) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-SAMEFRINGE GOPHER-RETURNS-CORRECT-STATE GOPHER-RETURNS-LEFTMOST-ATOM FLATTEN-SINGLETON FLATTEN-MC-FLATTEN) EVENT (DEFN FLATTEN (X) (IF (LISTP X) (APPEND (FLATTEN (CAR X)) (FLATTEN (CDR X))) (CONS X NIL))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 APPEND . FLATTEN) (DCELL . 1FLATTEN))))) 
(PUT1-LST (QUOTE REVERSE-REVERSE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182012. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (REVERSE-REVERSE-) EVENT (PROVE-LEMMA REVERSE-REVERSE (REWRITE) (IMPLIES (PLISTP X) (EQUAL (REVERSE (REVERSE X)) X))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 APPEND . REVERSE-REVERSE) (IMMEDIATE-DEPENDENTS0 APPEND-REVERSE . REVERSE-REVERSE) (IMMEDIATE-DEPENDENTS0 REVERSE . REVERSE-REVERSE) (IMMEDIATE-DEPENDENTS0 PLISTP . REVERSE-REVERSE) (LEMMAS REVERSE . REVERSE-REVERSE))))) 
(PUT1-LST (QUOTE TRICHOTOMY-OF-LESSP) (QUOTE (IDATE 840117182011. EVENT (PROVE-LEMMA TRICHOTOMY-OF-LESSP NIL (IMPLIES (AND (NOT (EQP X Y)) (NOT (LESSP Y X))) (LESSP X Y))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQP . TRICHOTOMY-OF-LESSP))))) 
(PUT1-LST (QUOTE 1EQP) (QUOTE NIL)) 
(PUT1-LST (QUOTE EQP) (QUOTE (TYPE-PRESCRIPTION-LST ((EQP 3. NIL NIL)) LEMMAS NIL QUICK-BLOCK-INFO NIL SDEFN (LAMBDA (X Y) (IF (NUMBERP X) (IF (NUMBERP Y) (EQUAL X Y) (EQUAL X (QUOTE 0.))) (IF (NUMBERP Y) (EQUAL (QUOTE 0.) Y) (QUOTE 1TRUE)))) LISP-CODE 1EQP INDUCTION-MACHINE NIL LEVEL-NO 0. JUSTIFICATIONS NIL IDATE 840117182009. CONTROLLER-POCKETS NIL SATELLITES (1EQP) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (GET-SET TRICHOTOMY-OF-LESSP) EVENT (DEFN EQP (X Y) (EQUAL (FIX X) (FIX Y))) LOCAL-UNDO-TUPLES ((DCELL . 1EQP))))) 
(PUT1-LST (QUOTE LESSP-NOT-REFLEXIVE) (QUOTE (IDATE 840117182009. EVENT (PROVE-LEMMA LESSP-NOT-REFLEXIVE NIL (NOT (LESSP X X)))))) 
(PUT1-LST (QUOTE TRANSITIVITY-OF-LESSP) (QUOTE (IDATE 840117182009. EVENT (PROVE-LEMMA TRANSITIVITY-OF-LESSP NIL (IMPLIES (AND (LESSP X Y) (LESSP Y Z)) (LESSP X Z)))))) 
(PUT1-LST (QUOTE CORRECTNESS-OF-OPTIMIZING-COMPILER) (QUOTE (IDATE 840117182009. EVENT (PROVE-LEMMA CORRECTNESS-OF-OPTIMIZING-COMPILER NIL (IMPLIES (EXPRESSIONP X) (EQUAL (EXEC (COMPILE X) PDS ENVRN) (PUSH (EVAL X ENVRN) PDS)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 FORMP-OPTIMIZE . CORRECTNESS-OF-OPTIMIZING-COMPILER) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-OPTIMIZE . CORRECTNESS-OF-OPTIMIZING-COMPILER) (IMMEDIATE-DEPENDENTS0 REVERSE . CORRECTNESS-OF-OPTIMIZING-COMPILER) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CODEGEN . CORRECTNESS-OF-OPTIMIZING-COMPILER) (IMMEDIATE-DEPENDENTS0 EVAL . CORRECTNESS-OF-OPTIMIZING-COMPILER) (IMMEDIATE-DEPENDENTS0 PUSH . CORRECTNESS-OF-OPTIMIZING-COMPILER) (IMMEDIATE-DEPENDENTS0 COMPILE . CORRECTNESS-OF-OPTIMIZING-COMPILER) (IMMEDIATE-DEPENDENTS0 EXEC . CORRECTNESS-OF-OPTIMIZING-COMPILER) (IMMEDIATE-DEPENDENTS0 EXPRESSIONP . CORRECTNESS-OF-OPTIMIZING-COMPILER))))) 
(PUT1-LST (QUOTE CORRECTNESS-OF-CODEGEN) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117182008. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-OPTIMIZING-COMPILER) EVENT (PROVE-LEMMA CORRECTNESS-OF-CODEGEN (REWRITE) (IMPLIES (EXPRESSIONP X) (EQUAL (EXEC (REVERSE (CODEGEN X INS)) PDS ENVRN) (PUSH (EVAL X ENVRN) (EXEC (REVERSE INS) PDS ENVRN))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PUSH . CORRECTNESS-OF-CODEGEN) (IMMEDIATE-DEPENDENTS0 SEQUENTIAL-EXECUTION . CORRECTNESS-OF-CODEGEN) (IMMEDIATE-DEPENDENTS0 EVAL . CORRECTNESS-OF-CODEGEN) (IMMEDIATE-DEPENDENTS0 CODEGEN . CORRECTNESS-OF-CODEGEN) (IMMEDIATE-DEPENDENTS0 REVERSE . CORRECTNESS-OF-CODEGEN) (IMMEDIATE-DEPENDENTS0 EXEC . CORRECTNESS-OF-CODEGEN) (IMMEDIATE-DEPENDENTS0 EXPRESSIONP . CORRECTNESS-OF-CODEGEN) (LEMMAS EXEC . CORRECTNESS-OF-CODEGEN))))) 
(PUT1-LST (QUOTE SEQUENTIAL-EXECUTION) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117181935. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-CODEGEN) EVENT (PROVE-LEMMA SEQUENTIAL-EXECUTION (REWRITE) (EQUAL (EXEC (APPEND X Y) PDS ENVRN) (EXEC Y (EXEC X PDS ENVRN) ENVRN))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 APPEND . SEQUENTIAL-EXECUTION) (IMMEDIATE-DEPENDENTS0 EXEC . SEQUENTIAL-EXECUTION) (LEMMAS EXEC . SEQUENTIAL-EXECUTION))))) 
(PUT1-LST (QUOTE EXEC) (QUOTE (TYPE-PRESCRIPTION-LST ((EXEC 64. NIL T NIL)) LEMMAS ((REWRITE-RULE CORRECTNESS-OF-CODEGEN ((EXPRESSIONP X)) (EQUAL (EXEC (REVERSE (CODEGEN X INS)) PDS ENVRN) (PUSH (EVAL X ENVRN) (EXEC (REVERSE INS) PDS ENVRN))) NIL) (REWRITE-RULE SEQUENTIAL-EXECUTION NIL (EQUAL (EXEC (APPEND X Y) PDS ENVRN) (EXEC Y (EXEC X PDS ENVRN) ENVRN)) NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE SELF-REFLEXIVE UNCHANGING) SDEFN (LAMBDA (PC PDS ENVRN) (IF (LISTP PC) (IF (LISTP (CAR PC)) (IF (EQUAL (CAR (CAR PC)) (QUOTE PUSHI)) (EXEC (CDR PC) (PUSH (CAR (CDR (CAR PC))) PDS) ENVRN) (EXEC (CDR PC) (PUSH (GETVALUE (CAR (CDR (CAR PC))) ENVRN) PDS) ENVRN)) (EXEC (CDR PC) (PUSH (CALL (CAR PC) (TOP (POP PDS)) (TOP PDS)) (POP (POP PDS))) ENVRN)) PDS)) INDUCTION-MACHINE ((TESTS-AND-CASES ((NLISTP PC)) NIL) (TESTS-AND-CASES ((NOT (NLISTP PC)) (LISTP (CAR PC)) (EQUAL (CAR (CAR PC)) (QUOTE PUSHI))) (((CDR PC) (PUSH (CAR (CDR (CAR PC))) PDS) ENVRN))) (TESTS-AND-CASES ((NOT (NLISTP PC)) (LISTP (CAR PC)) (NOT (EQUAL (CAR (CAR PC)) (QUOTE PUSHI)))) (((CDR PC) (PUSH (GETVALUE (CAR (CDR (CAR PC))) ENVRN) PDS) ENVRN))) (TESTS-AND-CASES ((NOT (NLISTP PC)) (NOT (LISTP (CAR PC)))) (((CDR PC) (PUSH (CALL (CAR PC) (TOP (POP PDS)) (TOP PDS)) (POP (POP PDS))) ENVRN)))) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (PC) (COUNT PC) LESSP (CDR-LESSP NLISTP ZERO CDR-LESSEQP))) IDATE 840117181925. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-OPTIMIZING-COMPILER CORRECTNESS-OF-CODEGEN SEQUENTIAL-EXECUTION) EVENT (DEFN EXEC (PC PDS ENVRN) (IF (NLISTP PC) PDS (IF (LISTP (CAR PC)) (IF (EQUAL (CAAR PC) (QUOTE PUSHI)) (EXEC (CDR PC) (PUSH (CADAR PC) PDS) ENVRN) (EXEC (CDR PC) (PUSH (GETVALUE (CADAR PC) ENVRN) PDS) ENVRN)) (EXEC (CDR PC) (PUSH (CALL (CAR PC) (TOP (POP PDS)) (TOP PDS)) (POP (POP PDS))) ENVRN)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PUSH . EXEC) (IMMEDIATE-DEPENDENTS0 CALL . EXEC) (IMMEDIATE-DEPENDENTS0 GETVALUE . EXEC))))) 
(PUT1-LST (QUOTE CORRECTNESS-OF-OPTIMIZE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117181925. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-OPTIMIZING-COMPILER) EVENT (PROVE-LEMMA CORRECTNESS-OF-OPTIMIZE (REWRITE) (IMPLIES (EXPRESSIONP X) (EQUAL (EVAL (OPTIMIZE X) ENVRN) (EVAL X ENVRN)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 OPTIMIZE . CORRECTNESS-OF-OPTIMIZE) (IMMEDIATE-DEPENDENTS0 EVAL . CORRECTNESS-OF-OPTIMIZE) (IMMEDIATE-DEPENDENTS0 EXPRESSIONP . CORRECTNESS-OF-OPTIMIZE) (LEMMAS EVAL . CORRECTNESS-OF-OPTIMIZE))))) 
(PUT1-LST (QUOTE FORMP-OPTIMIZE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117181919. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-OPTIMIZING-COMPILER) EVENT (PROVE-LEMMA FORMP-OPTIMIZE (REWRITE) (IMPLIES (EXPRESSIONP X) (EXPRESSIONP (OPTIMIZE X)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 OPTIMIZE . FORMP-OPTIMIZE) (IMMEDIATE-DEPENDENTS0 EXPRESSIONP . FORMP-OPTIMIZE) (LEMMAS EXPRESSIONP . FORMP-OPTIMIZE))))) 
(PUT1-LST (QUOTE COMPILE) (QUOTE (TYPE-PRESCRIPTION-LST ((COMPILE 24. NIL)) SDEFN (LAMBDA (FORM) (REVERSE (CODEGEN (OPTIMIZE FORM) (QUOTE NIL)))) INDUCTION-MACHINE NIL LEVEL-NO 2. JUSTIFICATIONS NIL IDATE 840117181915. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-OPTIMIZING-COMPILER) EVENT (DEFN COMPILE (FORM) (REVERSE (CODEGEN (OPTIMIZE FORM) NIL))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 OPTIMIZE . COMPILE) (IMMEDIATE-DEPENDENTS0 CODEGEN . COMPILE) (IMMEDIATE-DEPENDENTS0 REVERSE . COMPILE))))) 
(PUT1-LST (QUOTE 1CODEGEN) (QUOTE NIL)) 
(PUT1-LST (QUOTE CODEGEN) (QUOTE (TYPE-PRESCRIPTION-LST ((CODEGEN 16. NIL NIL)) LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE QUESTIONABLE) SDEFN (LAMBDA (FORM INS) (IF (NUMBERP FORM) (CONS (CONS (QUOTE PUSHI) (CONS FORM (QUOTE NIL))) INS) (IF (LISTP (CDR (CDR FORM))) (CONS (CAR FORM) (CODEGEN (CAR (CDR (CDR FORM))) (CODEGEN (CAR (CDR FORM)) INS))) (CONS (CONS (QUOTE PUSHV) (CONS FORM (QUOTE NIL))) INS)))) LISP-CODE 1CODEGEN INDUCTION-MACHINE ((TESTS-AND-CASES ((NUMBERP FORM)) NIL) (TESTS-AND-CASES ((NOT (NUMBERP FORM)) (LISTP (CDR (CDR FORM)))) (((CAR (CDR (CDR FORM))) (CODEGEN (CAR (CDR FORM)) INS)) ((CAR (CDR FORM)) INS))) (TESTS-AND-CASES ((NOT (NUMBERP FORM)) (NOT (LISTP (CDR (CDR FORM))))) NIL)) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (FORM) (COUNT FORM) LESSP (CADR-CROCK ZERO CDR-LESSEQP CAR-LESSP))) IDATE 840117181914. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1CODEGEN) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-CODEGEN COMPILE) EVENT (DEFN CODEGEN (FORM INS) (IF (NUMBERP FORM) (CONS (LIST (QUOTE PUSHI) FORM) INS) (IF (LISTP (CDDR FORM)) (CONS (CAR FORM) (CODEGEN (CADDR FORM) (CODEGEN (CADR FORM) INS))) (CONS (LIST (QUOTE PUSHV) FORM) INS)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 CADR-CROCK . CODEGEN) (DCELL . 1CODEGEN))))) 
(PUT1-LST (QUOTE OPTIMIZE) (QUOTE (TYPE-PRESCRIPTION-LST ((OPTIMIZE 20. T)) LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (FORM) (IF (LISTP (CDR (CDR FORM))) (IF (NUMBERP (OPTIMIZE (CAR (CDR FORM)))) (IF (NUMBERP (OPTIMIZE (CAR (CDR (CDR FORM))))) (CALL (CAR FORM) (OPTIMIZE (CAR (CDR FORM))) (OPTIMIZE (CAR (CDR (CDR FORM))))) (CONS (CAR FORM) (CONS (OPTIMIZE (CAR (CDR FORM))) (CONS (OPTIMIZE (CAR (CDR (CDR FORM)))) (QUOTE NIL))))) (CONS (CAR FORM) (CONS (OPTIMIZE (CAR (CDR FORM))) (CONS (OPTIMIZE (CAR (CDR (CDR FORM)))) (QUOTE NIL))))) FORM)) LISP-CODE NIL INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP (CDR (CDR FORM))) (NUMBERP (OPTIMIZE (CAR (CDR FORM)))) (NUMBERP (OPTIMIZE (CAR (CDR (CDR FORM)))))) (((CAR (CDR (CDR FORM)))) ((CAR (CDR FORM))))) (TESTS-AND-CASES ((LISTP (CDR (CDR FORM))) (NUMBERP (OPTIMIZE (CAR (CDR FORM)))) (NOT (NUMBERP (OPTIMIZE (CAR (CDR (CDR FORM))))))) (((CAR (CDR (CDR FORM)))) ((CAR (CDR FORM))))) (TESTS-AND-CASES ((LISTP (CDR (CDR FORM))) (NOT (NUMBERP (OPTIMIZE (CAR (CDR FORM)))))) (((CAR (CDR (CDR FORM)))) ((CAR (CDR FORM))))) (TESTS-AND-CASES ((NOT (LISTP (CDR (CDR FORM))))) NIL)) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (FORM) (COUNT FORM) LESSP (CDR-LESSEQP CAR-LESSP ZERO CADR-CROCK))) IDATE 840117181912. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-OPTIMIZE FORMP-OPTIMIZE COMPILE) EVENT (DEFN OPTIMIZE (FORM) (IF (LISTP (CDDR FORM)) (IF (NUMBERP (OPTIMIZE (CADR FORM))) (IF (NUMBERP (OPTIMIZE (CADDR FORM))) (CALL (CAR FORM) (OPTIMIZE (CADR FORM)) (OPTIMIZE (CADDR FORM))) (LIST (CAR FORM) (OPTIMIZE (CADR FORM)) (OPTIMIZE (CADDR FORM)))) (LIST (CAR FORM) (OPTIMIZE (CADR FORM)) (OPTIMIZE (CADDR FORM)))) FORM)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 CALL . OPTIMIZE) (IMMEDIATE-DEPENDENTS0 CADR-CROCK . OPTIMIZE))))) 
(PUT1-LST (QUOTE EVAL) (QUOTE (TYPE-PRESCRIPTION-LST ((EVAL -1. NIL NIL)) LEMMAS ((REWRITE-RULE CORRECTNESS-OF-OPTIMIZE ((EXPRESSIONP X)) (EQUAL (EVAL (OPTIMIZE X) ENVRN) (EVAL X ENVRN)) NIL)) LINEAR-LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE UNCHANGING) SDEFN (LAMBDA (FORM ENVRN) (IF (NUMBERP FORM) FORM (IF (LISTP (CDR (CDR FORM))) (CALL (CAR FORM) (EVAL (CAR (CDR FORM)) ENVRN) (EVAL (CAR (CDR (CDR FORM))) ENVRN)) (GETVALUE FORM ENVRN)))) INDUCTION-MACHINE ((TESTS-AND-CASES ((NUMBERP FORM)) NIL) (TESTS-AND-CASES ((NOT (NUMBERP FORM)) (LISTP (CDR (CDR FORM)))) (((CAR (CDR (CDR FORM))) ENVRN) ((CAR (CDR FORM)) ENVRN))) (TESTS-AND-CASES ((NOT (NUMBERP FORM)) (NOT (LISTP (CDR (CDR FORM))))) NIL)) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (FORM) (COUNT FORM) LESSP (CADR-CROCK ZERO CDR-LESSEQP CAR-LESSP))) IDATE 840117181912. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-OPTIMIZING-COMPILER CORRECTNESS-OF-CODEGEN CORRECTNESS-OF-OPTIMIZE) EVENT (DEFN EVAL (FORM ENVRN) (IF (NUMBERP FORM) FORM (IF (LISTP (CDDR FORM)) (CALL (CAR FORM) (EVAL (CADR FORM) ENVRN) (EVAL (CADDR FORM) ENVRN)) (GETVALUE FORM ENVRN)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 GETVALUE . EVAL) (IMMEDIATE-DEPENDENTS0 CALL . EVAL) (IMMEDIATE-DEPENDENTS0 CADR-CROCK . EVAL))))) 
(PUT1-LST (QUOTE CADR-CROCK) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117181911. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CODEGEN OPTIMIZE EVAL) EVENT (PROVE-LEMMA CADR-CROCK (REWRITE) (IMPLIES (LISTP (CDDR X)) (LESSP (COUNT (CADR X)) (COUNT X)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-PLUS . CADR-CROCK) (IMMEDIATE-DEPENDENTS0 PLUS-ADD1 . CADR-CROCK) (LINEAR-LEMMAS COUNT . CADR-CROCK))))) 
(PUT1-LST (QUOTE 1EXPRESSIONP) (QUOTE NIL)) 
(PUT1-LST (QUOTE EXPRESSIONP) (QUOTE (TYPE-PRESCRIPTION-LST ((EXPRESSIONP 3. NIL)) LEMMAS ((REWRITE-RULE FORMP-OPTIMIZE ((EXPRESSIONP X)) (EXPRESSIONP (OPTIMIZE X)) NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (X) (IF (LISTP X) (IF (LISTP (CAR X)) (QUOTE 1FALSE) (IF (LISTP (CDR X)) (IF (LISTP (CDR (CDR X))) (IF (EXPRESSIONP (CAR (CDR X))) (EXPRESSIONP (CAR (CDR (CDR X)))) (QUOTE 1FALSE)) (QUOTE 1FALSE)) (QUOTE 1FALSE))) (QUOTE 1TRUE))) LISP-CODE 1EXPRESSIONP INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP X) (LISTP (CAR X))) NIL) (TESTS-AND-CASES ((LISTP X) (NOT (LISTP (CAR X))) (LISTP (CDR X)) (LISTP (CDR (CDR X))) (EXPRESSIONP (CAR (CDR X)))) (((CAR (CDR X))) ((CAR (CDR (CDR X)))))) (TESTS-AND-CASES ((LISTP X) (NOT (LISTP (CAR X))) (LISTP (CDR X)) (LISTP (CDR (CDR X))) (NOT (EXPRESSIONP (CAR (CDR X))))) (((CAR (CDR X))))) (TESTS-AND-CASES ((LISTP X) (NOT (LISTP (CAR X))) (LISTP (CDR X)) (NOT (LISTP (CDR (CDR X))))) NIL) (TESTS-AND-CASES ((LISTP X) (NOT (LISTP (CAR X))) (NOT (LISTP (CDR X)))) NIL) (TESTS-AND-CASES ((NOT (LISTP X))) NIL)) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (X) (COUNT X) LESSP (CDR-LESSP ZERO CDR-LESSEQP CAR-LESSP))) IDATE 840117181904. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1EXPRESSIONP) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-OPTIMIZING-COMPILER CORRECTNESS-OF-CODEGEN CORRECTNESS-OF-OPTIMIZE FORMP-OPTIMIZE) EVENT (DEFN EXPRESSIONP (X) (IF (LISTP X) (IF (LISTP (CAR X)) F (IF (LISTP (CDR X)) (IF (LISTP (CDDR X)) (IF (EXPRESSIONP (CADR X)) (EXPRESSIONP (CADDR X)) F) F) F)) T)) LOCAL-UNDO-TUPLES ((DCELL . 1EXPRESSIONP))))) 
(PUT1-LST (QUOTE NUMBERP-CALL) (QUOTE (IDATE 840117181904. EVENT (ADD-AXIOM NUMBERP-CALL (REWRITE) (NUMBERP (CALL FN X Y))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 CALL . NUMBERP-CALL) (TYPE-PRESCRIPTION-LST CALL . NUMBERP-CALL) (NONCONSTRUCTIVE-AXIOM-NAMES NIL . NUMBERP-CALL))))) 
(PUT1-LST (QUOTE GETVALUE) (QUOTE (TYPE-PRESCRIPTION-LST ((GETVALUE -1. NIL NIL)) LEMMAS NIL SDEFN NIL LISP-CODE NIL LEVEL-NO 0. IDATE 840117181904. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EXEC EVAL) EVENT (DCL GETVALUE (VAR ENVRN))))) 
(PUT1-LST (QUOTE CALL) (QUOTE (TYPE-PRESCRIPTION-LST ((NUMBERP-CALL 4. NIL NIL NIL) (CALL -1. NIL NIL NIL)) LEMMAS NIL LINEAR-LEMMAS NIL SDEFN NIL LISP-CODE NIL INDUCTION-MACHINE NIL LEVEL-NO 0. IDATE 840117181904. ELIMINATE-DESTRUCTORS-SEQ NIL MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (COUNTPS COUNTPS-LOOP EXEC OPTIMIZE EVAL NUMBERP-CALL) EVENT (DCL CALL (FN X Y))))) 
(PUT1-LST (QUOTE COUNT-PUSH) (QUOTE (MAIN-EVENT PUSH EVENT NIL))) 
(PUT1-LST (QUOTE TOP-POP-ELIM) (QUOTE (MAIN-EVENT PUSH EVENT NIL))) 
(PUT1-LST (QUOTE PUSH-TOP-POP) (QUOTE (MAIN-EVENT PUSH EVENT NIL))) 
(PUT1-LST (QUOTE PUSH-EQUAL) (QUOTE (TYPE-PRESCRIPTION-LST NIL MAIN-EVENT PUSH EVENT NIL))) 
(PUT1-LST (QUOTE POP-LESSEQP) (QUOTE (MAIN-EVENT PUSH EVENT NIL))) 
(PUT1-LST (QUOTE POP-LESSP) (QUOTE (MAIN-EVENT PUSH EVENT NIL))) 
(PUT1-LST (QUOTE POP-NSTACKP) (QUOTE (MAIN-EVENT PUSH EVENT NIL))) 
(PUT1-LST (QUOTE POP-PUSH) (QUOTE (TYPE-PRESCRIPTION-LST NIL MAIN-EVENT PUSH EVENT NIL))) 
(PUT1-LST (QUOTE TOP-LESSEQP) (QUOTE (MAIN-EVENT PUSH EVENT NIL))) 
(PUT1-LST (QUOTE TOP-LESSP) (QUOTE (MAIN-EVENT PUSH EVENT NIL))) 
(PUT1-LST (QUOTE TOP-NSTACKP) (QUOTE (MAIN-EVENT PUSH EVENT NIL))) 
(PUT1-LST (QUOTE TOP-PUSH) (QUOTE (TYPE-PRESCRIPTION-LST NIL MAIN-EVENT PUSH EVENT NIL))) 
(PUT1-LST (QUOTE 1POP) (QUOTE NIL)) 
(PUT1-LST (QUOTE POP) (QUOTE (TYPE-PRESCRIPTION-LST ((PUSH -1. NIL)) LEMMAS ((REWRITE-RULE POP-NSTACKP ((NOT (STACKP X))) (EQUAL (POP X) (QUOTE 0.)) NIL) (REWRITE-RULE POP-PUSH NIL (EQUAL (POP (PUSH TOP POP)) POP) NIL)) SDEFN NIL LISP-CODE 1POP INDUCTION-MACHINE NIL LEVEL-NO NIL ELIMINATE-DESTRUCTORS-SEQ (REWRITE-RULE TOP-POP-ELIM ((STACKP X)) (EQUAL (PUSH (TOP X) (POP X)) X) NIL) ELIMINATE-DESTRUCTORS-DESTS ((POP X) (TOP X)) MAIN-EVENT PUSH EVENT NIL))) 
(PUT1-LST (QUOTE 1TOP) (QUOTE NIL)) 
(PUT1-LST (QUOTE TOP) (QUOTE (TYPE-PRESCRIPTION-LST ((PUSH -1. NIL)) LEMMAS ((REWRITE-RULE TOP-NSTACKP ((NOT (STACKP X))) (EQUAL (TOP X) (QUOTE 0.)) NIL) (REWRITE-RULE TOP-PUSH NIL (EQUAL (TOP (PUSH TOP POP)) TOP) NIL)) SDEFN NIL LISP-CODE 1TOP INDUCTION-MACHINE NIL LEVEL-NO NIL ELIMINATE-DESTRUCTORS-SEQ (REWRITE-RULE TOP-POP-ELIM ((STACKP X)) (EQUAL (PUSH (TOP X) (POP X)) X) NIL) ELIMINATE-DESTRUCTORS-DESTS ((TOP X) (POP X)) MAIN-EVENT PUSH EVENT NIL))) 
(PUT1-LST (QUOTE 1STACKP) (QUOTE NIL)) 
(PUT1-LST (QUOTE STACKP) (QUOTE (TYPE-PRESCRIPTION-LST ((PUSH 3. NIL)) LEMMAS NIL SDEFN NIL LISP-CODE 1STACKP INDUCTION-MACHINE NIL MAIN-EVENT PUSH EVENT NIL))) 
(PUT1-LST (QUOTE 1PUSH) (QUOTE NIL)) 
(PUT1-LST (QUOTE PUSH) (QUOTE (TYPE-PRESCRIPTION-LST ((PUSH 64. NIL NIL)) LEMMAS ((REWRITE-RULE PUSH-TOP-POP NIL (EQUAL (PUSH (TOP X) (POP X)) (IF (STACKP X) X (QUOTE (1QUOTE PUSH 0. 0.)))) NIL)) QUICK-BLOCK-INFO NIL SDEFN NIL LISP-CODE 1PUSH TYPE-RESTRICTIONS ((TYPE-RESTRICTION (QUOTE 1TRUE) -1. (QUOTE 0.)) (TYPE-RESTRICTION (QUOTE 1TRUE) -1. (QUOTE 0.))) INDUCTION-MACHINE NIL LEVEL-NO NIL JUSTIFICATIONS NIL IDATE 840117181903. ELIMINATE-DESTRUCTORS-SEQ NIL SATELLITES (COUNT-PUSH TOP-POP-ELIM PUSH-TOP-POP PUSH-EQUAL POP-LESSEQP POP-LESSP POP-NSTACKP POP-PUSH TOP-LESSEQP TOP-LESSP TOP-NSTACKP TOP-PUSH 1POP POP 1TOP TOP 1STACKP STACKP 1PUSH) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-OPTIMIZING-COMPILER CORRECTNESS-OF-CODEGEN EXEC) EVENT (ADD-SHELL PUSH NIL STACKP ((TOP (NONE-OF) ZERO) (POP (NONE-OF) ZERO))) LOCAL-UNDO-TUPLES ((LEMMAS COUNT . COUNT-PUSH) (LEMMAS EQUAL . PUSH-EQUAL) (LINEAR-LEMMAS COUNT . POP-LESSEQP) (LINEAR-LEMMAS COUNT . POP-LESSP) (LINEAR-LEMMAS COUNT . TOP-LESSEQP) (LINEAR-LEMMAS COUNT . TOP-LESSP) (RECOGNIZER-ALIST NIL STACKP . 64.) (SHELL-POCKETS NIL PUSH TOP POP) (SHELL-ALIST NIL PUSH . 6.) (DCELL . 1POP) (DCELL . 1TOP) (DCELL . 1STACKP) (DCELL . 1PUSH))))) 
(PUT1-LST (QUOTE EQUAL-TIMES-0) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117181903. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (ALL-NON-ZEROP-MULTS LEQ-WINS1 LEQ-WINS1-WINS2 LEQ-QUOT-WINS1 LEQ-QUOT-TIMES-2 LEQ-TIMES-QUOT LEQ-N-WINS1 EVEN3-TIMES ALL-DISTINCT-REFLECT-LIST-3 REFLECT-COMMUTES-WITH-TIMES-1 TIMES-COMP-LIST-2 COMPLEMENT-IS-UNIQUE COMPLEMENT-WORKS T-I-L-LEMMA N-Z-I-LEMMA INVERSE-IS-UNIQUE CRYPT-INVERTS-STEP-2 COROLLARY-55 COROLLARY-53 PRODUCT-DIVIDES PRODUCT-DIVIDES-LEMMA EQUAL-MODS-TRICK-2 CRYPT-CORRECT REMAINDER-PLUS-TIMES-1 HACK1 PRIME-BASIC TIMES-ID-IFF-1 NORMALIZE-NORMALIZES NORMALIZE-IS-SOUND NORMALIZE IF-COMPLEXITY-NOT-0 GCD-IS-THE-GREATEST DISTRIBUTIVITY-OF-TIMES-OVER-GCD LESSP-TIMES-CANCELLATION DIVIDES-TIMES TIMES-DIFFERENCE LESSP-REMAINDER1 LESSP-QUOTIENT1) EVENT (PROVE-LEMMA EQUAL-TIMES-0 (REWRITE) (EQUAL (EQUAL (TIMES X Y) 0.) (OR (ZEROP X) (ZEROP Y)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PLUS-EQUAL-0 . EQUAL-TIMES-0) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . EQUAL-TIMES-0) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO2 . EQUAL-TIMES-0) (LEMMAS EQUAL . EQUAL-TIMES-0))))) 
(PUT1-LST (QUOTE ASSOCIATIVITY-OF-TIMES) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117181900. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LEQ-QUOT-TIMES TIMES-EXP-FACT TIMES-MOD-4 COMPLEMENT-IS-UNIQUE COMPLEMENT-WORKS T-I-L-LEMMA1 INVERSE-IS-UNIQUE CRYPT-INVERTS-STEP-2 CRYPT-INVERTS-STEP-1B CRYPT-INVERTS-STEP-1A REMAINDER-TIMES-LIST-S PRODUCT-DIVIDES-LEMMA TIMES-MOD-2 PRIME-KEY-REWRITE EXP-TIMES TIMES-LIST-APPEND FACT-LOOP-FACT EXP-PLUS) EVENT (PROVE-LEMMA ASSOCIATIVITY-OF-TIMES (REWRITE) (EQUAL (TIMES (TIMES X Y) Z) (TIMES X (TIMES Y Z)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . ASSOCIATIVITY-OF-TIMES) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-TIMES . ASSOCIATIVITY-OF-TIMES) (LEMMAS TIMES . ASSOCIATIVITY-OF-TIMES))))) 
(PUT1-LST (QUOTE COMMUTATIVITY2-OF-TIMES) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117181859. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (TIMES-EXP-FACT COMPLEMENT-WORKS CRYPT-INVERTS-STEP-2 ALL-NON-ZEROP-S ALL-DISTINCT-S REMAINDER-TIMES-LIST-S REMAINDER-EXP-LEMMA CRYPT-CORRECT TIMES-MOD-1 TIMES-TIMES-LIST-DELETE PRIME-KEY-REWRITE REMAINDER-TIMES-1 EXP-TIMES DISTRIBUTIVITY-OF-DIVIDES DIVIDES-TIMES-LIST NORMALIZE-NORMALIZES NORMALIZE-IS-SOUND NORMALIZE ASSOCIATIVITY-OF-TIMES) EVENT (PROVE-LEMMA COMMUTATIVITY2-OF-TIMES (REWRITE) (EQUAL (TIMES X (TIMES Y Z)) (TIMES Y (TIMES X Z)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-TIMES-OVER-PLUS . COMMUTATIVITY2-OF-TIMES) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . COMMUTATIVITY2-OF-TIMES) (LEMMAS TIMES . COMMUTATIVITY2-OF-TIMES))))) 
(PUT1-LST (QUOTE COMMUTATIVITY-OF-TIMES) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117181855. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EQUAL-WINS-PLUS-QUOT-LIST LEQ-WINS1-QUOT LEQ-WINS1 LEQ-WINS2 LEQ-QUOT-WINS1 LEQ-QUOT-WINS1-2 LEQ-QUOT-WINS1-1 LEQ-QUOT-TIMES-2 LEQ-QUOT-TIMES LEQ-TIMES-QUOT LEQ-N-WINS1 WIN-SOME-LOSE-SOME-2 EVEN3-TIMES REM-QUOT-LIST RES1-REM-2 RES1-REM-1 PLUS-MOD-1 TIMES-EXP-FACT REFLECT-COMMUTES-WITH-TIMES-2 REFLECT-COMMUTES-WITH-TIMES-1 REM-DIFF-TIMES DIFF-MOD-1 TIMES-MOD-4 COMPLEMENT-OF-COMPLEMENT NON-ZEROP-COMPLEMENT BOUNDED-COMPLEMENT COMPLEMENT-WORKS ALL-SQUARES-1 WILSON-THM T-I-L-LEMMA3 T-I-L-LEMMA T-I-L-LEMMA1 N-Z-I-LEMMA INVERSE-OF-INVERSE I-O-I-LEMMA N-O-I-LEMMA1 S-P-I-I-LEMMA1 INVERSE-IS-UNIQUE INVERSE-INVERTS INVERSE-INVERTS-LEMMA CRYPT-INVERTS CRYPT-INVERTS-STEP-2 CRYPT-INVERTS-STEP-1A ALL-NON-ZEROP-S ALL-DISTINCT-S COROLLARY-55 PRODUCT-DIVIDES-LEMMA PRIME-KEY-TRICK TIMES-DISTRIBUTES-OVER-PDIFFERENCE EXP-MOD-IS-1 REMAINDER-EXP-LEMMA TIMES-MOD-3 CRYPT-CORRECT TIMES-MOD-1 PRIME-KEY-REWRITE REMAINDER-DIFFERENCE-TIMES REMAINDER-PLUS-TIMES-2 REMAINDER-PLUS-TIMES-1 SIGMA-IS-HALF-PRODUCT TIMES-EQUAL-1 DISTRIBUTIVITY-OF-DIVIDES QUOTIENT-TIMES DIVIDES-TIMES-LIST REMAINDER-TIMES QUOTIENT-DIVIDES PRIME-KEY HACK1 TIMES-IDENTITY DIVIDES-TIMES1 PRIME-BASIC TIMES-ID-IFF-1 ENOUGH-FACTORS QUOTIENT-LESSP TIMES-LIST-APPEND NORMALIZE-NORMALIZES NORMALIZE-IS-SOUND NORMALIZE IF-COMPLEXITY-GOES-DOWN2 IF-COMPLEXITY-GOES-DOWN1 IF-COMPLEXITY-NOT-0 GCD-IS-THE-GREATEST DISTRIBUTIVITY-OF-TIMES-OVER-GCD LESSP-TIMES-CANCELLATION EUCLID DIVIDES-PLUS-REWRITE2 DIVIDES-PLUS-REWRITE1 REMAINDER-ADD1 DIVIDES-TIMES TIMES-DIFFERENCE LESSP-REMAINDER1 LESSP-TIMES-2 POWER-EVAL-BIG-PLUS1 REMAINDER-QUOTIENT FACT-LOOP-FACT EXP-PLUS EQUAL-TIMES-0 ASSOCIATIVITY-OF-TIMES COMMUTATIVITY2-OF-TIMES) EVENT (PROVE-LEMMA COMMUTATIVITY-OF-TIMES (REWRITE) (EQUAL (TIMES X Y) (TIMES Y X))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-ADD1 . COMMUTATIVITY-OF-TIMES) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO2 . COMMUTATIVITY-OF-TIMES) (LEMMAS TIMES . COMMUTATIVITY-OF-TIMES))))) 
(PUT1-LST (QUOTE TIMES-ADD1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117181849. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LEQ-TIMES-QUOT LEQ-N-WINS1 WIN-SOME-LOSE-SOME-2 EVEN3-TIMES REM-QUOT-LIST REM-DIFF-TIMES ALL-SQUARES-1 I-O-I-LEMMA N-O-I-LEMMA1 S-P-I-I-LEMMA1 ALL-NON-ZEROP-S ALL-DISTINCT-S CRYPT-CORRECT SIGMA-IS-HALF-PRODUCT REMAINDER-QUOTIENT DOUBLE-TIMES-2 COMMUTATIVITY-OF-TIMES) EVENT (PROVE-LEMMA TIMES-ADD1 (REWRITE) (EQUAL (TIMES X (ADD1 Y)) (IF (NUMBERP Y) (PLUS X (TIMES X Y)) (FIX X)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PLUS-RIGHT-ID2 . TIMES-ADD1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . TIMES-ADD1) (LEMMAS TIMES . TIMES-ADD1))))) 
(PUT1-LST (QUOTE DISTRIBUTIVITY-OF-TIMES-OVER-PLUS) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117181844. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (LEQ-QUOT-WINS1 LEQ-QUOT-TIMES LEQ-TIMES-QUOT REM-QUOT-LIST RES1-REM-2 ALL-DISTINCT-REFLECT-LIST-5 REM-DIFF-TIMES INVERSE-IS-UNIQUE ALL-NON-ZEROP-S ALL-DISTINCT-S REMAINDER-EXP-LEMMA CRYPT-CORRECT TIMES-MOD-1 HACK1 NORMALIZE-NORMALIZES NORMALIZE-IS-SOUND NORMALIZE IF-COMPLEXITY-GOES-DOWN2 IF-COMPLEXITY-GOES-DOWN1 IF-COMPLEXITY-NOT-0 DISTRIBUTIVITY-OF-TIMES-OVER-GCD POWER-EVAL-BIG-PLUS POWER-EVAL-BIG-PLUS1 FACT-LOOP-FACT COMMUTATIVITY2-OF-TIMES) EVENT (PROVE-LEMMA DISTRIBUTIVITY-OF-TIMES-OVER-PLUS (REWRITE) (EQUAL (TIMES X (PLUS Y Z)) (PLUS (TIMES X Y) (TIMES X Z)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-PLUS . DISTRIBUTIVITY-OF-TIMES-OVER-PLUS) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-PLUS . DISTRIBUTIVITY-OF-TIMES-OVER-PLUS) (LEMMAS TIMES . DISTRIBUTIVITY-OF-TIMES-OVER-PLUS))))) 
(PUT1-LST (QUOTE TIMES-ZERO2) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117181842. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (EMPTY-INTERSECT-MULTS LEQ-QUOT-WINS1 LEQ-QUOT-WINS1-1 LEQ-QUOT-TIMES-2 LEQ-TIMES-QUOT REFLECT-COMMUTES-WITH-TIMES-1 DIFF-MOD-1 COMPLEMENT-IS-UNIQUE EULER-1-7 ALL-SQUARES-1 T-I-L-LEMMA1 N-O-I-LEMMA1 INVERSE-INVERTS-LEMMA PRODUCT-DIVIDES-LEMMA TIMES-DISTRIBUTES-OVER-PDIFFERENCE REMAINDER-EXP-LEMMA CRYPT-CORRECT TIMES-MOD-1 PRIME-KEY-REWRITE REMAINDER-PLUS-TIMES-1 TIMES-1 DISTRIBUTIVITY-OF-DIVIDES QUOTIENT-TIMES QUOTIENT-DIVIDES HACK1 TIMES-ID-IFF-1 DISTRIBUTIVITY-OF-TIMES-OVER-GCD LESSP-TIMES-CANCELLATION REMAINDER-QUOTIENT DOUBLE-TIMES-2 EQUAL-TIMES-0 COMMUTATIVITY-OF-TIMES) EVENT (PROVE-LEMMA TIMES-ZERO2 (REWRITE) (IMPLIES (NOT (NUMBERP Y)) (EQUAL (TIMES X Y) 0.))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PLUS-RIGHT-ID2 . TIMES-ZERO2) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . TIMES-ZERO2) (LEMMAS TIMES . TIMES-ZERO2))))) 
(PUT1-LST (QUOTE APPEND-REVERSE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117181840. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (REVERSE-APPEND REVERSE-REVERSE) EVENT (PROVE-LEMMA APPEND-REVERSE (REWRITE) (EQUAL (REVERSE (APPEND A B)) (APPEND (REVERSE B) (REVERSE A)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PLISTP-REVERSE . APPEND-REVERSE) (IMMEDIATE-DEPENDENTS0 APPEND-RIGHT-ID . APPEND-REVERSE) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-APPEND . APPEND-REVERSE) (IMMEDIATE-DEPENDENTS0 APPEND . APPEND-REVERSE) (IMMEDIATE-DEPENDENTS0 REVERSE . APPEND-REVERSE) (LEMMAS REVERSE . APPEND-REVERSE))))) 
(PUT1-LST (QUOTE PLISTP-REVERSE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117181834. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (REVERSE-LOOP-REVERSE LENGTH-REVERSE APPEND-REVERSE) EVENT (PROVE-LEMMA PLISTP-REVERSE (GENERALIZE REWRITE) (PLISTP (REVERSE X))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 APPEND . PLISTP-REVERSE) (IMMEDIATE-DEPENDENTS0 REVERSE . PLISTP-REVERSE) (IMMEDIATE-DEPENDENTS0 PLISTP . PLISTP-REVERSE) (LEMMAS PLISTP . PLISTP-REVERSE) (GENERALIZE-LEMMAS NIL . PLISTP-REVERSE))))) 
(PUT1-LST (QUOTE APPEND-RIGHT-ID) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117181831. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (REVERSE-LOOP-REVERSE APPEND-REVERSE) EVENT (PROVE-LEMMA APPEND-RIGHT-ID (REWRITE) (IMPLIES (PLISTP X) (EQUAL (APPEND X NIL) X))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 APPEND . APPEND-RIGHT-ID) (IMMEDIATE-DEPENDENTS0 PLISTP . APPEND-RIGHT-ID) (LEMMAS APPEND . APPEND-RIGHT-ID))))) 
(PUT1-LST (QUOTE 1PLISTP) (QUOTE NIL)) 
(PUT1-LST (QUOTE PLISTP) (QUOTE (TYPE-PRESCRIPTION-LST ((PLISTP 3. NIL)) LEMMAS ((REWRITE-RULE SORT2-GEN-1 NIL (PLISTP (SORT2 X)) NIL) (REWRITE-RULE PLISTP-REVERSE NIL (PLISTP (REVERSE X)) NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (X) (IF (LISTP X) (PLISTP (CDR X)) (EQUAL X (QUOTE NIL)))) LISP-CODE 1PLISTP INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP X)) (((CDR X)))) (TESTS-AND-CASES ((NOT (LISTP X))) NIL)) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (X) (COUNT X) LESSP (ZERO CDR-LESSP))) IDATE 840117181829. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1PLISTP) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (COUNT-LIST-SORT2 SORT2-DELETE-CONS DELETE-ADDTOLIST2 ADDTOLIST2-DELETE SORT2-GEN SORT2-GEN-1 REVERSE-REVERSE- SUBSETP-INTERSECT LENGTH-REVERSE REVERSE-REVERSE PLISTP-REVERSE APPEND-RIGHT-ID) EVENT (DEFN PLISTP (X) (IF (LISTP X) (PLISTP (CDR X)) (EQUAL X NIL))) LOCAL-UNDO-TUPLES ((DCELL . 1PLISTP))))) 
(PUT1-LST (QUOTE ASSOCIATIVITY-OF-APPEND) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117181829. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (GOPHER-RETURNS-CORRECT-STATE GOPHER-RETURNS-LEFTMOST-ATOM REVERSE-LOOP-APPEND-REVERSE FLATTEN-MC-FLATTEN APPEND-REVERSE) EVENT (PROVE-LEMMA ASSOCIATIVITY-OF-APPEND (REWRITE) (EQUAL (APPEND (APPEND X Y) Z) (APPEND X (APPEND Y Z)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 APPEND . ASSOCIATIVITY-OF-APPEND) (LEMMAS APPEND . ASSOCIATIVITY-OF-APPEND))))) 
(PUT1-LST (QUOTE 1REVERSE) (QUOTE NIL)) 
(PUT1-LST (QUOTE REVERSE) (QUOTE (TYPE-PRESCRIPTION-LST ((REVERSE 24. NIL)) LEMMAS ((REWRITE-RULE REVERSE-REVERSE ((PLISTP X)) (EQUAL (REVERSE (REVERSE X)) X) NIL) (REWRITE-RULE APPEND-REVERSE NIL (EQUAL (REVERSE (APPEND A B)) (APPEND (REVERSE B) (REVERSE A))) NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (X) (IF (LISTP X) (APPEND (REVERSE (CDR X)) (CONS (CAR X) (QUOTE NIL))) (QUOTE NIL))) LISP-CODE 1REVERSE INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP X)) (((CDR X)))) (TESTS-AND-CASES ((NOT (LISTP X))) NIL)) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (X) (COUNT X) LESSP (ZERO CDR-LESSP))) IDATE 840117181828. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1REVERSE) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (REVERSE-LOOP-REVERSE REVERSE-LOOP-APPEND-REVERSE LAST-REVERSE LENGTH-REVERSE MEMBER-REVERSE REVERSE-REVERSE CORRECTNESS-OF-OPTIMIZING-COMPILER CORRECTNESS-OF-CODEGEN COMPILE APPEND-REVERSE PLISTP-REVERSE) EVENT (DEFN REVERSE (X) (IF (LISTP X) (APPEND (REVERSE (CDR X)) (CONS (CAR X) NIL)) NIL)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 APPEND . REVERSE) (DCELL . 1REVERSE))))) 
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(PUT1-LST (QUOTE SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117181219. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (BRIDGE-TO-SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP PLUS-TREE-BAGDIFF) EVENT (PROVE-LEMMA SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP (REWRITE) (IMPLIES (SUBBAGP X Y) (NOT (LESSP (MEANING (PLUS-TREE Y) A) (MEANING (PLUS-TREE X) A))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SUBBAGP-CDR2 . SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP) (IMMEDIATE-DEPENDENTS0 PLUS-RIGHT-ID2 . SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP) (IMMEDIATE-DEPENDENTS0 MEMBER-IMPLIES-PLUS-TREE-GREATEREQP . SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP) (IMMEDIATE-DEPENDENTS0 PLUS-TREE-DELETE . SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP) (IMMEDIATE-DEPENDENTS0 PLUS-TREE . SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP) (IMMEDIATE-DEPENDENTS0 SUBBAGP . SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP) (LINEAR-LEMMAS MEANING . SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP) (LINEAR-LEMMAS MEANING . SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP))))) 
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(PUT1-LST (QUOTE MEMBER-IMPLIES-PLUS-TREE-GREATEREQP) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117181016. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-CANCEL PLUS-TREE-BAGDIFF SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP PLUS-TREE-DELETE) EVENT (PROVE-LEMMA MEMBER-IMPLIES-PLUS-TREE-GREATEREQP (REWRITE) (IMPLIES (MEMBER X Y) (NOT (LESSP (MEANING (PLUS-TREE Y) A) (MEANING X A))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PLUS-RIGHT-ID2 . MEMBER-IMPLIES-PLUS-TREE-GREATEREQP) (IMMEDIATE-DEPENDENTS0 PLUS-TREE . MEMBER-IMPLIES-PLUS-TREE-GREATEREQP) (LINEAR-LEMMAS MEANING . MEMBER-IMPLIES-PLUS-TREE-GREATEREQP) (LINEAR-LEMMAS MEANING . MEMBER-IMPLIES-PLUS-TREE-GREATEREQP))))) 
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(PUT1-LST (QUOTE CANCEL) (QUOTE (TYPE-PRESCRIPTION-LST ((CANCEL 16. T)) LEMMAS NIL SDEFN (LAMBDA (X) (IF (LISTP X) (IF (EQUAL (CAR X) (QUOTE EQUAL)) (IF (LISTP (CAR (CDR X))) (IF (EQUAL (CAR (CAR (CDR X))) (QUOTE PLUS)) (IF (LISTP (CAR (CDR (CDR X)))) (IF (EQUAL (CAR (CAR (CDR (CDR X)))) (QUOTE PLUS)) (CONS (QUOTE EQUAL) (CONS (PLUS-TREE (BAGDIFF (PLUS-FRINGE (CAR (CDR X))) (BAGINT (PLUS-FRINGE (CAR (CDR X))) (PLUS-FRINGE (CAR (CDR (CDR X))))))) (CONS (PLUS-TREE (BAGDIFF (PLUS-FRINGE (CAR (CDR (CDR X)))) (BAGINT (PLUS-FRINGE (CAR (CDR X))) (PLUS-FRINGE (CAR (CDR (CDR X))))))) (QUOTE NIL)))) (IF (MEMBER (CAR (CDR (CDR X))) (PLUS-FRINGE (CAR (CDR X)))) (CONS (QUOTE IF) (CONS (CONS (QUOTE NUMBERP) (CONS (CAR (CDR (CDR X))) (QUOTE NIL))) (CONS (CONS (QUOTE EQUAL) (CONS (PLUS-TREE (DELETE (CAR (CDR (CDR X))) (PLUS-FRINGE (CAR (CDR X))))) (QUOTE ((QUOTE 0.))))) (QUOTE ((QUOTE 1FALSE)))))) X)) (IF (MEMBER (CAR (CDR (CDR X))) (PLUS-FRINGE (CAR (CDR X)))) (CONS (QUOTE IF) (CONS (CONS (QUOTE NUMBERP) (CONS (CAR (CDR (CDR X))) (QUOTE NIL))) (CONS (CONS (QUOTE EQUAL) (CONS (PLUS-TREE (DELETE (CAR (CDR (CDR X))) (PLUS-FRINGE (CAR (CDR X))))) (QUOTE ((QUOTE 0.))))) (QUOTE ((QUOTE 1FALSE)))))) X)) (IF (LISTP (CAR (CDR (CDR X)))) (IF (EQUAL (CAR (CAR (CDR (CDR X)))) (QUOTE PLUS)) (IF (MEMBER (CAR (CDR X)) (PLUS-FRINGE (CAR (CDR (CDR X))))) (CONS (QUOTE IF) (CONS (CONS (QUOTE NUMBERP) (CONS (CAR (CDR X)) (QUOTE NIL))) (CONS (CONS (QUOTE EQUAL) (CONS (QUOTE (QUOTE 0.)) (CONS (PLUS-TREE (DELETE (CAR (CDR X)) (PLUS-FRINGE (CAR (CDR (CDR X)))))) (QUOTE NIL)))) (QUOTE ((QUOTE 1FALSE)))))) X) X) X)) (IF (LISTP (CAR (CDR (CDR X)))) (IF (EQUAL (CAR (CAR (CDR (CDR X)))) (QUOTE PLUS)) (IF (MEMBER (CAR (CDR X)) (PLUS-FRINGE (CAR (CDR (CDR X))))) (CONS (QUOTE IF) (CONS (CONS (QUOTE NUMBERP) (CONS (CAR (CDR X)) (QUOTE NIL))) (CONS (CONS (QUOTE EQUAL) (CONS (QUOTE (QUOTE 0.)) (CONS (PLUS-TREE (DELETE (CAR (CDR X)) (PLUS-FRINGE (CAR (CDR (CDR X)))))) (QUOTE NIL)))) (QUOTE ((QUOTE 1FALSE)))))) X) X) X)) X) X)) LISP-CODE 1CANCEL INDUCTION-MACHINE NIL LEVEL-NO 2. JUSTIFICATIONS NIL IDATE 840117180927. CONTROLLER-POCKETS NIL SATELLITES (1CANCEL) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-CANCEL) EVENT (DEFN CANCEL (X) (IF (AND (LISTP X) (EQUAL (CAR X) (QUOTE EQUAL))) (IF (AND (LISTP (CADR X)) (EQUAL (CAADR X) (QUOTE PLUS)) (LISTP (CADDR X)) (EQUAL (CAADDR X) (QUOTE PLUS))) (LIST (QUOTE EQUAL) (PLUS-TREE (BAGDIFF (PLUS-FRINGE (CADR X)) (BAGINT (PLUS-FRINGE (CADR X)) (PLUS-FRINGE (CADDR X))))) (PLUS-TREE (BAGDIFF (PLUS-FRINGE (CADDR X)) (BAGINT (PLUS-FRINGE (CADR X)) (PLUS-FRINGE (CADDR X)))))) (IF (AND (LISTP (CADR X)) (EQUAL (CAADR X) (QUOTE PLUS)) (MEMBER (CADDR X) (PLUS-FRINGE (CADR X)))) (LIST (QUOTE IF) (LIST (QUOTE NUMBERP) (CADDR X)) (LIST (QUOTE EQUAL) (PLUS-TREE (DELETE (CADDR X) (PLUS-FRINGE (CADR X)))) (QUOTE (QUOTE 0.))) (LIST (QUOTE QUOTE) F)) (IF (AND (LISTP (CADDR X)) (EQUAL (CAADDR X) (QUOTE PLUS)) (MEMBER (CADR X) (PLUS-FRINGE (CADDR X)))) (LIST (QUOTE IF) (LIST (QUOTE NUMBERP) (CADR X)) (LIST (QUOTE EQUAL) (QUOTE (QUOTE 0.)) (PLUS-TREE (DELETE (CADR X) (PLUS-FRINGE (CADDR X))))) (LIST (QUOTE QUOTE) F)) X))) X)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DELETE . CANCEL) (IMMEDIATE-DEPENDENTS0 BAGINT . CANCEL) (IMMEDIATE-DEPENDENTS0 PLUS-FRINGE . CANCEL) (IMMEDIATE-DEPENDENTS0 BAGDIFF . CANCEL) (IMMEDIATE-DEPENDENTS0 PLUS-TREE . CANCEL) (DCELL . 1CANCEL))))) 
(PUT1-LST (QUOTE 1PLUS-TREE) (QUOTE NIL)) 
(PUT1-LST (QUOTE PLUS-TREE) (QUOTE (TYPE-PRESCRIPTION-LST ((PLUS-TREE 16. NIL)) LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (L) (IF (LISTP L) (IF (LISTP (CDR L)) (IF (LISTP (CDR (CDR L))) (CONS (QUOTE PLUS) (CONS (CAR L) (CONS (PLUS-TREE (CDR L)) (QUOTE NIL)))) (CONS (QUOTE PLUS) (CONS (CAR L) (CONS (CAR (CDR L)) (QUOTE NIL))))) (CONS (QUOTE FIX) (CONS (CAR L) (QUOTE NIL)))) (QUOTE (QUOTE 0.)))) LISP-CODE 1PLUS-TREE INDUCTION-MACHINE ((TESTS-AND-CASES ((NLISTP L)) NIL) (TESTS-AND-CASES ((NOT (NLISTP L)) (NLISTP (CDR L))) NIL) (TESTS-AND-CASES ((NOT (NLISTP L)) (NOT (NLISTP (CDR L))) (NLISTP (CDR (CDR L)))) NIL) (TESTS-AND-CASES ((NOT (NLISTP L)) (NOT (NLISTP (CDR L))) (NOT (NLISTP (CDR (CDR L))))) (((CDR L))))) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (L) (COUNT L) LESSP (CDR-LESSP NLISTP ZERO CDR-LESSEQP))) IDATE 840117180924. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1PLUS-TREE) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PLUS-TREE-PLUS-FRINGE MEANING-PLUS-TREE-APPEND BRIDGE-TO-SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP NUMBERP-MEANING-BRIDGE PLUS-TREE-BAGDIFF SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP PLUS-TREE-DELETE MEMBER-IMPLIES-PLUS-TREE-GREATEREQP NUMBERP-MEANING-PLUS-TREE FORMP-PLUS-TREE CANCEL) EVENT (DEFN PLUS-TREE (L) (IF (NLISTP L) (QUOTE (QUOTE 0.)) (IF (NLISTP (CDR L)) (LIST (QUOTE FIX) (CAR L)) (IF (NLISTP (CDDR L)) (LIST (QUOTE PLUS) (CAR L) (CADR L)) (LIST (QUOTE PLUS) (CAR L) (PLUS-TREE (CDR L))))))) LOCAL-UNDO-TUPLES ((DCELL . 1PLUS-TREE))))) 
(PUT1-LST (QUOTE 1PLUS-FRINGE) (QUOTE NIL)) 
(PUT1-LST (QUOTE PLUS-FRINGE) (QUOTE (TYPE-PRESCRIPTION-LST ((PLUS-FRINGE 16. NIL)) LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (X) (IF (LISTP X) (IF (EQUAL (CAR X) (QUOTE PLUS)) (APPEND (PLUS-FRINGE (CAR (CDR X))) (PLUS-FRINGE (CAR (CDR (CDR X))))) (CONS X (QUOTE NIL))) (CONS X (QUOTE NIL)))) LISP-CODE 1PLUS-FRINGE INDUCTION-MACHINE ((TESTS-AND-CASES ((AND (LISTP X) (EQUAL (CAR X) (QUOTE PLUS)))) (((CAR (CDR (CDR X)))) ((CAR (CDR X))))) (TESTS-AND-CASES ((NOT (AND (LISTP X) (EQUAL (CAR X) (QUOTE PLUS))))) NIL)) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (X) (COUNT X) LESSP (CDR-LESSP AND ZERO CDR-LESSEQP CAR-LESSEQP))) IDATE 840117180920. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1PLUS-FRINGE) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (MEMBER-IMPLIES-NUMBERP PLUS-TREE-PLUS-FRINGE BRIDGE-TO-SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP FORM-LSTP-PLUS-FRINGE CANCEL) EVENT (DEFN PLUS-FRINGE (X) (IF (AND (LISTP X) (EQUAL (CAR X) (QUOTE PLUS))) (APPEND (PLUS-FRINGE (CADR X)) (PLUS-FRINGE (CADDR X))) (CONS X NIL))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 APPEND . PLUS-FRINGE) (DCELL . 1PLUS-FRINGE))))) 
(PUT1-LST (QUOTE SUBBAGP-BAGINT2) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117180920. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-CANCEL) EVENT (PROVE-LEMMA SUBBAGP-BAGINT2 (REWRITE) (SUBBAGP (BAGINT X Y) Y)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SUBBAGP-CDR2 . SUBBAGP-BAGINT2) (IMMEDIATE-DEPENDENTS0 BAGINT . SUBBAGP-BAGINT2) (IMMEDIATE-DEPENDENTS0 SUBBAGP . SUBBAGP-BAGINT2) (LEMMAS SUBBAGP . SUBBAGP-BAGINT2))))) 
(PUT1-LST (QUOTE SUBBAGP-BAGINT1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117180915. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-CANCEL) EVENT (PROVE-LEMMA SUBBAGP-BAGINT1 (REWRITE) (SUBBAGP (BAGINT X Y) X)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SUBBAGP-CDR2 . SUBBAGP-BAGINT1) (IMMEDIATE-DEPENDENTS0 DELETE . SUBBAGP-BAGINT1) (IMMEDIATE-DEPENDENTS0 BAGINT . SUBBAGP-BAGINT1) (IMMEDIATE-DEPENDENTS0 SUBBAGP . SUBBAGP-BAGINT1) (LEMMAS SUBBAGP . SUBBAGP-BAGINT1))))) 
(PUT1-LST (QUOTE SUBBAGP-CDR2) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117180911. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PLUS-TREE-BAGDIFF SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP SUBBAGP-BAGINT2 SUBBAGP-BAGINT1) EVENT (PROVE-LEMMA SUBBAGP-CDR2 (REWRITE) (IMPLIES (SUBBAGP X (CDR Y)) (SUBBAGP X Y))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DELETE . SUBBAGP-CDR2) (IMMEDIATE-DEPENDENTS0 DELETE-NON-MEMBER . SUBBAGP-CDR2) (IMMEDIATE-DEPENDENTS0 SUBBAGP-CDR1 . SUBBAGP-CDR2) (IMMEDIATE-DEPENDENTS0 SUBBAGP . SUBBAGP-CDR2) (LEMMAS SUBBAGP . SUBBAGP-CDR2))))) 
(PUT1-LST (QUOTE SUBBAGP-CDR1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117180855. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (SUBBAGP-CDR2) EVENT (PROVE-LEMMA SUBBAGP-CDR1 (REWRITE) (IMPLIES (SUBBAGP X Y) (SUBBAGP (CDR X) Y))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SUBBAGP-DELETE . SUBBAGP-CDR1) (IMMEDIATE-DEPENDENTS0 SUBBAGP . SUBBAGP-CDR1) (LEMMAS SUBBAGP . SUBBAGP-CDR1))))) 
(PUT1-LST (QUOTE SUBBAGP-DELETE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117180852. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (SUBBAGP-CDR1) EVENT (PROVE-LEMMA SUBBAGP-DELETE (REWRITE) (IMPLIES (SUBBAGP X (DELETE U Y)) (SUBBAGP X Y))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 MEMBER-DELETE . SUBBAGP-DELETE) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-DELETE . SUBBAGP-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE . SUBBAGP-DELETE) (IMMEDIATE-DEPENDENTS0 SUBBAGP . SUBBAGP-DELETE) (LEMMAS SUBBAGP . SUBBAGP-DELETE))))) 
(PUT1-LST (QUOTE COMMUTATIVITY-OF-DELETE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117180845. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (SUBBAGP-DELETE) EVENT (PROVE-LEMMA COMMUTATIVITY-OF-DELETE (REWRITE) (EQUAL (DELETE X (DELETE Y Z)) (DELETE Y (DELETE X Z)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DELETE-NON-MEMBER . COMMUTATIVITY-OF-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE . COMMUTATIVITY-OF-DELETE) (LEMMAS DELETE . COMMUTATIVITY-OF-DELETE))))) 
(PUT1-LST (QUOTE MEMBER-DELETE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117180840. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PERM-MEMBER ALL-DISTINCT-DELETE SUBBAGP-DELETE) EVENT (PROVE-LEMMA MEMBER-DELETE (REWRITE) (IMPLIES (MEMBER X (DELETE U V)) (MEMBER X V))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DELETE-NON-MEMBER . MEMBER-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE . MEMBER-DELETE) (LEMMAS MEMBER . MEMBER-DELETE))))) 
(PUT1-LST (QUOTE DELETE-NON-MEMBER) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117180838. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (ALL-LESSEQP-DELETE PIGEON-HOLE-PRINCIPLE-LEMMA-1 ALL-DISTINCT-DELETE ALL-NON-ZEROP-DELETE LENGTH-DELETE SORT2-DELETE SORT2-DELETE-CONS ADDTOLIST2-DELETE LESSP-DELETE-REWRITE PRIME-LIST-DELETE PLUS-TREE-DELETE FORM-LSTP-DELETE SUBBAGP-CDR2 COMMUTATIVITY-OF-DELETE MEMBER-DELETE) EVENT (PROVE-LEMMA DELETE-NON-MEMBER (REWRITE) (IMPLIES (NOT (MEMBER X Y)) (EQUAL (DELETE X Y) Y))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DELETE . DELETE-NON-MEMBER) (LEMMAS DELETE . DELETE-NON-MEMBER))))) 
(PUT1-LST (QUOTE 1BAGINT) (QUOTE NIL)) 
(PUT1-LST (QUOTE BAGINT) (QUOTE (TYPE-PRESCRIPTION-LST ((BAGINT 24. NIL NIL)) LEMMAS NIL QUICK-BLOCK-INFO (SELF-REFLEXIVE QUESTIONABLE) SDEFN (LAMBDA (X Y) (IF (LISTP X) (IF (MEMBER (CAR X) Y) (CONS (CAR X) (BAGINT (CDR X) (DELETE (CAR X) Y))) (BAGINT (CDR X) Y)) (QUOTE NIL))) LISP-CODE 1BAGINT INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP X) (MEMBER (CAR X) Y)) (((CDR X) (DELETE (CAR X) Y)))) (TESTS-AND-CASES ((LISTP X) (NOT (MEMBER (CAR X) Y))) (((CDR X) Y))) (TESTS-AND-CASES ((NOT (LISTP X))) NIL)) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (X) (COUNT X) LESSP (ZERO CDR-LESSP))) IDATE 840117180834. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1BAGINT) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CANCEL SUBBAGP-BAGINT2 SUBBAGP-BAGINT1) EVENT (DEFN BAGINT (X Y) (IF (LISTP X) (IF (MEMBER (CAR X) Y) (CONS (CAR X) (BAGINT (CDR X) (DELETE (CAR X) Y))) (BAGINT (CDR X) Y)) NIL)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DELETE . BAGINT) (DCELL . 1BAGINT))))) 
(PUT1-LST (QUOTE 1BAGDIFF) (QUOTE NIL)) 
(PUT1-LST (QUOTE BAGDIFF) (QUOTE (TYPE-PRESCRIPTION-LST ((BAGDIFF -1. T NIL)) LEMMAS NIL QUICK-BLOCK-INFO (QUESTIONABLE SELF-REFLEXIVE) SDEFN (LAMBDA (X Y) (IF (LISTP Y) (IF (MEMBER (CAR Y) X) (BAGDIFF (DELETE (CAR Y) X) (CDR Y)) (BAGDIFF X (CDR Y))) X)) LISP-CODE 1BAGDIFF INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP Y) (MEMBER (CAR Y) X)) (((DELETE (CAR Y) X) (CDR Y)))) (TESTS-AND-CASES ((LISTP Y) (NOT (MEMBER (CAR Y) X))) ((X (CDR Y)))) (TESTS-AND-CASES ((NOT (LISTP Y))) NIL)) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (Y) (COUNT Y) LESSP (ZERO CDR-LESSP))) IDATE 840117180833. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (2.) SATELLITES (1BAGDIFF) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PLUS-TREE-BAGDIFF FORM-LSTP-BAGDIFF CANCEL) EVENT (DEFN BAGDIFF (X Y) (IF (LISTP Y) (IF (MEMBER (CAR Y) X) (BAGDIFF (DELETE (CAR Y) X) (CDR Y)) (BAGDIFF X (CDR Y))) X)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DELETE . BAGDIFF) (DCELL . 1BAGDIFF))))) 
(PUT1-LST (QUOTE 1SUBBAGP) (QUOTE NIL)) 
(PUT1-LST (QUOTE SUBBAGP) (QUOTE (TYPE-PRESCRIPTION-LST ((SUBBAGP 3. NIL NIL)) LEMMAS ((REWRITE-RULE SUBBAGP-BAGINT2 NIL (SUBBAGP (BAGINT X Y) Y) NIL) (REWRITE-RULE SUBBAGP-BAGINT1 NIL (SUBBAGP (BAGINT X Y) X) NIL) (REWRITE-RULE SUBBAGP-CDR2 ((SUBBAGP X (CDR Y))) (SUBBAGP X Y) NIL) (REWRITE-RULE SUBBAGP-CDR1 ((SUBBAGP X Y)) (SUBBAGP (CDR X) Y) NIL) (REWRITE-RULE SUBBAGP-DELETE ((SUBBAGP X (DELETE U Y))) (SUBBAGP X Y) NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE SELF-REFLEXIVE) SDEFN (LAMBDA (X Y) (IF (LISTP X) (IF (MEMBER (CAR X) Y) (SUBBAGP (CDR X) (DELETE (CAR X) Y)) (QUOTE 1FALSE)) (QUOTE 1TRUE))) LISP-CODE 1SUBBAGP INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP X) (MEMBER (CAR X) Y)) (((CDR X) (DELETE (CAR X) Y)))) (TESTS-AND-CASES ((LISTP X) (NOT (MEMBER (CAR X) Y))) NIL) (TESTS-AND-CASES ((NOT (LISTP X))) NIL)) LEVEL-NO 2. JUSTIFICATIONS ((JUSTIFICATION (X) (COUNT X) LESSP (ZERO CDR-LESSP))) IDATE 840117180830. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1SUBBAGP) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (BRIDGE-TO-SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP PLUS-TREE-BAGDIFF SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP SUBBAGP-BAGINT2 SUBBAGP-BAGINT1 SUBBAGP-CDR2 SUBBAGP-CDR1 SUBBAGP-DELETE) EVENT (DEFN SUBBAGP (X Y) (IF (LISTP X) (IF (MEMBER (CAR X) Y) (SUBBAGP (CDR X) (DELETE (CAR X) Y)) F) T)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DELETE . SUBBAGP) (DCELL . 1SUBBAGP))))) 
(PUT1-LST (QUOTE 1DELETE) (QUOTE NIL)) 
(PUT1-LST (QUOTE DELETE) (QUOTE (TYPE-PRESCRIPTION-LST ((DELETE -1. NIL T)) LEMMAS ((REWRITE-RULE DELETE-ADDTOLIST2 ((PLISTP Y)) (EQUAL (DELETE V (ADDTOLIST2 V Y)) Y) NIL) (REWRITE-RULE COMMUTATIVITY-OF-DELETE NIL (EQUAL (DELETE X (DELETE Y Z)) (DELETE Y (DELETE X Z))) ((X . Y))) (REWRITE-RULE DELETE-NON-MEMBER ((NOT (MEMBER X Y))) (EQUAL (DELETE X Y) Y) NIL)) LINEAR-LEMMAS NIL QUICK-BLOCK-INFO (UNCHANGING SELF-REFLEXIVE) SDEFN (LAMBDA (X Y) (IF (LISTP Y) (IF (EQUAL X (CAR Y)) (CDR Y) (CONS (CAR Y) (DELETE X (CDR Y)))) Y)) LISP-CODE 1DELETE INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP Y) (EQUAL X (CAR Y))) NIL) (TESTS-AND-CASES ((LISTP Y) (NOT (EQUAL X (CAR Y)))) ((X (CDR Y)))) (TESTS-AND-CASES ((NOT (LISTP Y))) NIL)) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (Y) (COUNT Y) LESSP (ZERO CDR-LESSP))) IDATE 840117180829. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (2.) SATELLITES (1DELETE) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PERM-PLUS-LIST-1 SUB1-LENGTH-DELETE PIGEONHOLE2-INDUCTION SUBSETP-POSITIVES-DELETE ALL-LESSEQP-DELETE DELETE-MEMBER-LEAVE-SUBSET DELETE-X-LEAVE-A PIGEON-HOLE-INDUCTION PIGEON-HOLE-PRINCIPLE-LEMMA-1 ALL-DISTINCT-DELETE ALL-NON-ZEROP-DELETE TIMES-TIMES-LIST-DELETE LENGTH-DELETE SORT2-DELETE SORT2-DELETE-CONS DELETE-ADDTOLIST2 ADDTOLIST2-DELETE DSORT LESSP-DELETE-REWRITE TIMES-LIST-DELETE PRIME-LIST-DELETE PERM LESSP-COUNT-DELETE PLUS-TREE-DELETE FORM-LSTP-DELETE CANCEL SUBBAGP-BAGINT1 SUBBAGP-CDR2 SUBBAGP-DELETE COMMUTATIVITY-OF-DELETE MEMBER-DELETE DELETE-NON-MEMBER BAGINT BAGDIFF SUBBAGP) EVENT (DEFN DELETE (X Y) (IF (LISTP Y) (IF (EQUAL X (CAR Y)) (CDR Y) (CONS (CAR Y) (DELETE X (CDR Y)))) Y)) LOCAL-UNDO-TUPLES ((DCELL . 1DELETE))))) 
(PUT1-LST (QUOTE 1APPEND) (QUOTE NIL)) 
(PUT1-LST (QUOTE APPEND) (QUOTE (TYPE-PRESCRIPTION-LST ((APPEND 16. NIL T)) LEMMAS ((REWRITE-RULE APPEND-RIGHT-ID ((PLISTP X)) (EQUAL (APPEND X (QUOTE NIL)) X) NIL) (REWRITE-RULE ASSOCIATIVITY-OF-APPEND NIL (EQUAL (APPEND (APPEND X Y) Z) (APPEND X (APPEND Y Z))) NIL)) QUICK-BLOCK-INFO (SELF-REFLEXIVE UNCHANGING) SDEFN (LAMBDA (X Y) (IF (LISTP X) (CONS (CAR X) (APPEND (CDR X) Y)) Y)) LISP-CODE 1APPEND INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP X)) (((CDR X) Y))) (TESTS-AND-CASES ((NOT (LISTP X))) NIL)) LEVEL-NO 1. JUSTIFICATIONS ((JUSTIFICATION (X) (COUNT X) LESSP (ZERO CDR-LESSP))) IDATE 840117180824. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1APPEND) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-INTERPRETED-SIGMA PRIME-LIST-APPEND TIMES-LIST-APPEND PRIME-FACTORS GOPHER-RETURNS-CORRECT-STATE GOPHER-RETURNS-LEFTMOST-ATOM FLATTEN-SINGLETON TAUTOLOGY-CHECKER-IS-SOUND TAUTOLOGY-CHECKER-SOUNDNESS-BRIDGE TAUTOLOGYP-IS-SOUND ASSIGNMENT-APPEND NTH-APPEND APPEND-CANCELLATION REVERSE-APPEND REVERSE-LOOP-APPEND-REVERSE ORDERED-APPEND LAST-APPEND LENGTH-REVERSE MEMBER-APPEND FLATTEN-MC-FLATTEN FLATTEN REVERSE-REVERSE SEQUENTIAL-EXECUTION APPEND-REVERSE PLISTP-REVERSE APPEND-RIGHT-ID ASSOCIATIVITY-OF-APPEND REVERSE MEANING-PLUS-TREE-APPEND FORM-LSTP-APPEND PLUS-FRINGE) EVENT (DEFN APPEND (X Y) (IF (LISTP X) (CONS (CAR X) (APPEND (CDR X) Y)) Y)) LOCAL-UNDO-TUPLES ((DCELL . 1APPEND))))) 
(PUT1-LST (QUOTE DIFFERENCE-CANCELLATION-1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117180824. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-CANCEL) EVENT (PROVE-LEMMA DIFFERENCE-CANCELLATION-1 (REWRITE) (EQUAL (EQUAL (DIFFERENCE X Y) (DIFFERENCE Z Y)) (IF (LESSP X Y) (NOT (LESSP Y Z)) (IF (LESSP Z Y) (NOT (LESSP Y X)) (EQUAL (FIX X) (FIX Z)))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . DIFFERENCE-CANCELLATION-1) (IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE-0 . DIFFERENCE-CANCELLATION-1) (LEMMAS EQUAL . DIFFERENCE-CANCELLATION-1))))) 
(PUT1-LST (QUOTE DIFFERENCE-CANCELLATION-0) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840117180817. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (GCD-DIVIDES-BOTH DISTRIBUTIVITY-OF-TIMES-OVER-GCD COMMUTATIVITY-OF-GCD GCD-EQUAL-0 GCD PLUS-TREE-BAGDIFF PLUS-TREE-DELETE) EVENT (PROVE-LEMMA DIFFERENCE-CANCELLATION-0 (REWRITE) (EQUAL (EQUAL X (DIFFERENCE X Y)) (AND (NUMBERP X) (OR (EQUAL X 0.) (ZEROP Y))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . DIFFERENCE-CANCELLATION-0) (LEMMAS EQUAL . DIFFERENCE-CANCELLATION-0))))) 
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(PUT1-LST (QUOTE 1EXECUTE1) (QUOTE (SEXPR (LAMBDA (3PC 3MEM 3MAX) (LET ((2TEMP1 (QUOTE 1X)) (2TEMP2 (QUOTE 1X)) (2TEMP3 (QUOTE 1X)) (2TEMP4 (QUOTE 1X))) (COND ((NEQ (1NOT (1LESSP 3PC 3MAX)) 1F) (CONS (QUOTE 1FALSE) (CONS 3MEM (QUOTE NIL)))) ((EQUAL (SETQ 2TEMP4 (1GET 3PC 3MEM)) (QUOTE (STOP))) (CONS (QUOTE 1FALSE) (CONS 3MEM (QUOTE NIL)))) ((EQ (SETQ 2TEMP3 (1CAR 2TEMP4)) (QUOTE JUMPA)) (CONS (1CAR (1CDR 2TEMP4)) (CONS 3MEM (QUOTE NIL)))) ((EQ 2TEMP3 (QUOTE SKIPNE)) (COND ((NEQ (1ZEROP (1GET (1CAR (1CDR 2TEMP4)) 3MEM)) 1F) (1EXECUTE1 (1ADD1 3PC) 3MEM 3MAX)) (T (1EXECUTE1 (1ADD1 (1ADD1 3PC)) 3MEM 3MAX)))) ((EQ 2TEMP3 (QUOTE SUBI)) (1EXECUTE1 (1ADD1 3PC) (1SET (SETQ 2TEMP2 (1CAR (SETQ 2TEMP1 (1CDR 2TEMP4)))) (1DIFFERENCE (1GET 2TEMP2 3MEM) (1CAR (1CDR 2TEMP1))) 3MEM) 3MAX)) ((EQ 2TEMP3 (QUOTE ADDI)) (1EXECUTE1 (1ADD1 3PC) (1SET (SETQ 2TEMP2 (1CAR (SETQ 2TEMP1 (1CDR 2TEMP4)))) (1PLUS (1CAR (1CDR 2TEMP1)) (1GET 2TEMP2 3MEM)) 3MEM) 3MAX)) ((EQ 2TEMP3 (QUOTE ADD)) (1EXECUTE1 (1ADD1 3PC) (1SET (SETQ 2TEMP2 (1CAR (SETQ 2TEMP1 (1CDR 2TEMP4)))) (1PLUS (1GET (1CAR (1CDR 2TEMP1)) 3MEM) (1GET 2TEMP2 3MEM)) 3MEM) 3MAX)) ((EQ 2TEMP3 (QUOTE MOVEI)) (1EXECUTE1 (1ADD1 3PC) (1SET (1CAR (SETQ 2TEMP1 (1CDR 2TEMP4))) (1CAR (1CDR 2TEMP1)) 3MEM) 3MAX)) (T (CONS (QUOTE 1FALSE) (CONS 3MEM (QUOTE NIL)))))))))) 
(PUT1-LST (QUOTE 1EXECUTE) (QUOTE (SEXPR (LAMBDA (3PC 3MEM 3CLK) (LET ((2TEMP1 (QUOTE 1X))) (COND ((NEQ (1ZEROP 3CLK) 1F) 3MEM) ((NEQ (1NUMBERP 3PC) 1F) (1EXECUTE (1CAR (SETQ 2TEMP1 (1EXECUTE1 3PC 3MEM (1LENGTH 3MEM)))) (1CAR (1CDR 2TEMP1)) (1SUB1 3CLK))) (T 3MEM))))))) 
(PUT1-LST (QUOTE 1GET-SIMPLIFIER) (QUOTE (SEXPR (LAMBDA (3X) (LET ((2TEMP1 (QUOTE 1X)) (2TEMP2 (QUOTE 1X)) (2TEMP3 (QUOTE 1X))) (COND ((NEQ (1AND (COND ((AND (PAIRP 3X) (NEQ (CAR 3X) (QUOTE 1QUOTE))) (QUOTE 1TRUE)) (T (QUOTE 1FALSE))) (1AND (COND ((EQ (1CAR 3X) (QUOTE GET)) (QUOTE 1TRUE)) (T (QUOTE 1FALSE))) (1AND (COND ((AND (PAIRP (SETQ 2TEMP3 (1CAR (SETQ 2TEMP2 (1CDR 3X))))) (NEQ (CAR 2TEMP3) (QUOTE 1QUOTE))) (QUOTE 1TRUE)) (T (QUOTE 1FALSE))) (COND ((EQ (1CAR 2TEMP3) (QUOTE QUOTE)) (QUOTE 1TRUE)) (T (QUOTE 1FALSE)))))) 1F) (COND ((NEQ (1ZEROP (SETQ 2TEMP1 (1CAR (1CDR 2TEMP3)))) 1F) (CONS (QUOTE CAR) (CONS (1CAR (1CDR 2TEMP2)) (QUOTE NIL)))) (T (CONS (QUOTE GET) (CONS (CONS (QUOTE QUOTE) (CONS (1SUB1 2TEMP1) (QUOTE NIL))) (CONS (CONS (QUOTE CDR) (CONS (1CAR (1CDR 2TEMP2)) (QUOTE NIL))) (QUOTE NIL))))))) (T 3X))))))) 
(PUT1-LST (QUOTE 1SET-SIMPLIFIER) (QUOTE (SEXPR (LAMBDA (3X) (LET ((2TEMP1 (QUOTE 1X)) (2TEMP2 (QUOTE 1X)) (2TEMP3 (QUOTE 1X)) (2TEMP4 (QUOTE 1X)) (2TEMP5 (QUOTE 1X))) (COND ((NEQ (1AND (COND ((AND (PAIRP 3X) (NEQ (CAR 3X) (QUOTE 1QUOTE))) (QUOTE 1TRUE)) (T (QUOTE 1FALSE))) (1AND (COND ((EQ (1CAR 3X) (QUOTE SET)) (QUOTE 1TRUE)) (T (QUOTE 1FALSE))) (1AND (COND ((AND (PAIRP (SETQ 2TEMP5 (1CAR (SETQ 2TEMP4 (1CDR 3X))))) (NEQ (CAR 2TEMP5) (QUOTE 1QUOTE))) (QUOTE 1TRUE)) (T (QUOTE 1FALSE))) (COND ((EQ (1CAR 2TEMP5) (QUOTE QUOTE)) (QUOTE 1TRUE)) (T (QUOTE 1FALSE)))))) 1F) (COND ((NEQ (1ZEROP (SETQ 2TEMP3 (1CAR (1CDR 2TEMP5)))) 1F) (CONS (QUOTE CONS) (CONS (1CAR (SETQ 2TEMP2 (1CDR 2TEMP4))) (CONS (CONS (QUOTE CDR) (CONS (1CAR (1CDR 2TEMP2)) (QUOTE NIL))) (QUOTE NIL))))) (T (CONS (QUOTE CONS) (CONS (CONS (QUOTE CAR) (SETQ 2TEMP1 (CONS (1CAR (1CDR (SETQ 2TEMP2 (1CDR 2TEMP4)))) (QUOTE NIL)))) (CONS (CONS (QUOTE SET) (CONS (CONS (QUOTE QUOTE) (CONS (1SUB1 2TEMP3) (QUOTE NIL))) (CONS (1CAR 2TEMP2) (CONS (CONS (QUOTE CDR) 2TEMP1) (QUOTE NIL))))) (QUOTE NIL))))))) (T 3X))))))) 
(PUT1-LST (QUOTE 1F0) (QUOTE (SEXPR (LAMBDA (3X) (COND ((NEQ (1LESSP (QUOTE 100.) 3X) 1F) (1DIFFERENCE 3X (QUOTE 10.))) (T (QUOTE 91.))))))) 
(PUT1-LST (QUOTE 1F91) (QUOTE (SEXPR (LAMBDA (3X) (COND ((NEQ (1LESSP (QUOTE 100.) 3X) 1F) (1DIFFERENCE 3X (QUOTE 10.))) (T (1F91 (1F91 (1PLUS 3X (QUOTE 11.)))))))))) 
(PUT1-LST (QUOTE 1EVEN) (QUOTE (SEXPR (LAMBDA (3X) (COND ((EQUAL (QUOTE 0.) (1REMAINDER 3X (QUOTE 2.))) (QUOTE 1TRUE)) (T (QUOTE 1FALSE))))))) 
(PUT1-LST (QUOTE 1SQUARE) (QUOTE (SEXPR (LAMBDA (3X) (1TIMES 3X 3X))))) 
(PUT1-LST (QUOTE 1SUBST2) (QUOTE (SEXPR (LAMBDA (3NEW 3OLD 3TERM) (COND ((NEQ (1NUMBERP 3TERM) 1F) 3TERM) ((NEQ (1LITATOM 3TERM) 1F) (COND ((EQUAL 3OLD 3TERM) 3NEW) (T 3TERM))) ((AND (PAIRP 3TERM) (NEQ (CAR 3TERM) (QUOTE 1QUOTE))) (CONS (CAR 3TERM) (CONS (1SUBST2 3NEW 3OLD (1CAR (CDR 3TERM))) (CONS (1SUBST2 3NEW 3OLD (1CAR (1CDR (CDR 3TERM)))) (QUOTE NIL))))) (T 3TERM)))))) 
(PUT1-LST (QUOTE 1CRYPT) (QUOTE (SEXPR (LAMBDA (3M 3E 3N) (LET NIL (COND ((NEQ (1ZEROP 3E) 1F) (QUOTE 1.)) ((NEQ (1EVEN 3E) 1F) (1REMAINDER (1SQUARE (1CRYPT 3M (1QUOTIENT 3E (QUOTE 2.)) 3N)) 3N)) (T (1REMAINDER (1TIMES 3M (1REMAINDER (1SQUARE (1CRYPT 3M (1QUOTIENT 3E (QUOTE 2.)) 3N)) 3N)) 3N)))))))) 
(PUT1-LST (QUOTE 1PDIFFERENCE) (QUOTE (SEXPR (LAMBDA (3A 3B) (COND ((NEQ (1LESSP 3A 3B) 1F) (1DIFFERENCE 3B 3A)) (T (1DIFFERENCE 3A 3B))))))) 
(PUT1-LST (QUOTE 1ALL-DISTINCT) (QUOTE (SEXPR (LAMBDA (3L) (LET ((2TEMP1 (QUOTE 1X))) (COND ((NEQ (1NLISTP 3L) 1F) (QUOTE 1TRUE)) (T (1AND (1NOT (1MEMBER (1CAR 3L) (SETQ 2TEMP1 (1CDR 3L)))) (1ALL-DISTINCT 2TEMP1))))))))) 
(PUT1-LST (QUOTE 1ALL-LESSEQP) (QUOTE (SEXPR (LAMBDA (3L 3N) (COND ((NEQ (1NLISTP 3L) 1F) (QUOTE 1TRUE)) (T (1AND (1NOT (1LESSP 3N (1CAR 3L))) (1ALL-LESSEQP (1CDR 3L) 3N)))))))) 
(PUT1-LST (QUOTE 1ALL-NON-ZEROP) (QUOTE (SEXPR (LAMBDA (3L) (COND ((NEQ (1NLISTP 3L) 1F) (QUOTE 1TRUE)) (T (1AND (1NOT (1ZEROP (1CAR 3L))) (1ALL-NON-ZEROP (1CDR 3L))))))))) 
(PUT1-LST (QUOTE 1POSITIVES) (QUOTE (SEXPR (LAMBDA (3N) (COND ((NEQ (1ZEROP 3N) 1F) (QUOTE NIL)) (T (CONS 3N (1POSITIVES (1SUB1 3N))))))))) 
(PUT1-LST (QUOTE 1PIGEON-HOLE-INDUCTION) (QUOTE (SEXPR (LAMBDA (3L) (LET ((2TEMP1 (QUOTE 1X))) (COND ((AND (PAIRP 3L) (NEQ (CAR 3L) (QUOTE 1QUOTE))) (COND ((NEQ (1MEMBER (SETQ 2TEMP1 (1LENGTH 3L)) 3L) 1F) (1PIGEON-HOLE-INDUCTION (1DELETE 2TEMP1 3L))) (T (1PIGEON-HOLE-INDUCTION (CDR 3L))))) (T (QUOTE 1TRUE)))))))) 
(PUT1-LST (QUOTE 1S) (QUOTE (SEXPR (LAMBDA (3N 3M 3P) (COND ((NEQ (1ZEROP 3N) 1F) (QUOTE NIL)) (T (CONS (1REMAINDER (1TIMES 3M 3N) 3P) (1S (1SUB1 3N) 3M 3P)))))))) 
(PUT1-LST (QUOTE 1INVERSE) (QUOTE (SEXPR (LAMBDA (3J 3P) (COND ((EQUAL 3P (QUOTE 2.)) (1REMAINDER 3J (QUOTE 2.))) (T (1REMAINDER (1EXP 3J (1DIFFERENCE 3P (QUOTE 2.))) 3P))))))) 
(PUT1-LST (QUOTE 1INVERSE-LIST) (QUOTE (SEXPR (LAMBDA (3I 3P) (LET ((2TEMP1 (QUOTE 1X))) (COND ((NEQ (1ZEROP 3I) 1F) (QUOTE NIL)) ((EQUAL 3I (QUOTE 1.)) (QUOTE (1.))) ((NEQ (1MEMBER 3I (SETQ 2TEMP1 (1INVERSE-LIST (1SUB1 3I) 3P))) 1F) 2TEMP1) (T (CONS 3I (CONS (1INVERSE 3I 3P) 2TEMP1))))))))) 
(PUT1-LST (QUOTE 1PIGEONHOLE2-INDUCTION) (QUOTE (SEXPR (LAMBDA (3L 3N) (COND ((NEQ (1ZEROP 3N) 1F) (QUOTE 1TRUE)) (T (1PIGEONHOLE2-INDUCTION (1DELETE 3N 3L) (1SUB1 3N)))))))) 
(PUT1-LST (QUOTE 1SQUARES) (QUOTE (SEXPR (LAMBDA (3N 3P) (COND ((NEQ (1ZEROP 3N) 1F) (QUOTE (0.))) (T (CONS (1REMAINDER (1TIMES 3N 3N) 3P) (1SQUARES (1SUB1 3N) 3P)))))))) 
(PUT1-LST (QUOTE 1RESIDUE) (QUOTE (SEXPR (LAMBDA (3A 3P) (1AND (1NOT (1DIVIDES 3P 3A)) (1MEMBER (1REMAINDER 3A 3P) (1SQUARES 3P 3P))))))) 
(PUT1-LST (QUOTE 1COMPLEMENT) (QUOTE (SEXPR (LAMBDA (3J 3A 3P) (1REMAINDER (1TIMES (1INVERSE 3J 3P) 3A) 3P))))) 
(PUT1-LST (QUOTE 1COMP-LIST) (QUOTE (SEXPR (LAMBDA (3I 3A 3P) (LET ((2TEMP1 (QUOTE 1X))) (COND ((NEQ (1ZEROP 3I) 1F) (QUOTE NIL)) ((NEQ (1MEMBER 3I (SETQ 2TEMP1 (1COMP-LIST (1SUB1 3I) 3A 3P))) 1F) 2TEMP1) (T (CONS 3I (CONS (1COMPLEMENT 3I 3A 3P) 2TEMP1))))))))) 
(PUT1-LST (QUOTE 1RES1) (QUOTE (SEXPR (LAMBDA (3N 3A 3P) (LET NIL (COND ((NEQ (1ZEROP 3N) 1F) (QUOTE 1TRUE)) ((NEQ (1LESSP (1QUOTIENT 3P (QUOTE 2.)) (1REMAINDER (1TIMES 3A 3N) 3P)) 1F) (1NOT (1RES1 (1SUB1 3N) 3A 3P))) (T (1RES1 (1SUB1 3N) 3A 3P)))))))) 
(PUT1-LST (QUOTE 1REFLECT) (QUOTE (SEXPR (LAMBDA (3X 3P) (1DIFFERENCE 3P 3X))))) 
(PUT1-LST (QUOTE 1REFLECT-LIST) (QUOTE (SEXPR (LAMBDA (3N 3A 3P) (LET ((2TEMP1 (QUOTE 1X))) (COND ((NEQ (1ZEROP 3N) 1F) (QUOTE NIL)) ((NEQ (1LESSP (1QUOTIENT 3P (QUOTE 2.)) (SETQ 2TEMP1 (1REMAINDER (1TIMES 3A 3N) 3P))) 1F) (CONS (1REFLECT 2TEMP1 3P) (1REFLECT-LIST (1SUB1 3N) 3A 3P))) (T (CONS 2TEMP1 (1REFLECT-LIST (1SUB1 3N) 3A 3P))))))))) 
(PUT1-LST (QUOTE 1PLUS-LIST) (QUOTE (SEXPR (LAMBDA (3L) (COND ((NEQ (1NLISTP 3L) 1F) (QUOTE 0.)) (T (1PLUS (1CAR 3L) (1PLUS-LIST (1CDR 3L))))))))) 
(PUT1-LST (QUOTE 1QUOT-LIST) (QUOTE (SEXPR (LAMBDA (3N 3A 3P) (COND ((NEQ (1ZEROP 3N) 1F) (QUOTE NIL)) (T (CONS (1QUOTIENT (1TIMES 3A 3N) 3P) (1QUOT-LIST (1SUB1 3N) 3A 3P)))))))) 
(PUT1-LST (QUOTE 1REM-LIST) (QUOTE (SEXPR (LAMBDA (3N 3A 3P) (COND ((NEQ (1ZEROP 3N) 1F) (QUOTE NIL)) (T (CONS (1REMAINDER (1TIMES 3A 3N) 3P) (1REM-LIST (1SUB1 3N) 3A 3P)))))))) 
(PUT1-LST (QUOTE 1EVEN3) (QUOTE (SEXPR (LAMBDA (3X) (COND ((NEQ (1ZEROP 3X) 1F) (QUOTE 1TRUE)) (T (1NOT (1EVEN3 (1SUB1 3X))))))))) 
(PUT1-LST (QUOTE 1WINS1) (QUOTE (SEXPR (LAMBDA (3X 3L) (LET NIL (COND ((NEQ (1NLISTP 3L) 1F) (QUOTE 0.)) ((NEQ (1LESSP (1CAR 3L) 3X) 1F) (1ADD1 (1WINS1 3X (1CDR 3L)))) (T (1WINS1 3X (1CDR 3L))))))))) 
(PUT1-LST (QUOTE 1WINS) (QUOTE (SEXPR (LAMBDA (3K 3L) (COND ((NEQ (1NLISTP 3K) 1F) (QUOTE 0.)) (T (1PLUS (1WINS1 (1CAR 3K) 3L) (1WINS (1CDR 3K) 3L)))))))) 
(PUT1-LST (QUOTE 1LOSSES1) (QUOTE (SEXPR (LAMBDA (3X 3L) (LET NIL (COND ((NEQ (1NLISTP 3L) 1F) (QUOTE 0.)) ((NEQ (1LESSP 3X (1CAR 3L)) 1F) (1ADD1 (1LOSSES1 3X (1CDR 3L)))) (T (1LOSSES1 3X (1CDR 3L))))))))) 
(PUT1-LST (QUOTE 1LOSSES) (QUOTE (SEXPR (LAMBDA (3K 3L) (COND ((NEQ (1NLISTP 3K) 1F) (QUOTE 0.)) (T (1PLUS (1LOSSES1 (1CAR 3K) 3L) (1LOSSES (1CDR 3K) 3L)))))))) 
(PUT1-LST (QUOTE 1MULTS) (QUOTE (SEXPR (LAMBDA (3N 3P) (COND ((NEQ (1ZEROP 3N) 1F) (QUOTE NIL)) (T (CONS (1TIMES 3N 3P) (1MULTS (1SUB1 3N) 3P)))))))) 
(PUT1-LST (QUOTE 1QUOT-QUOT-INDUCTION) (QUOTE (SEXPR (LAMBDA (3A 3B 3C 3D) (COND ((NEQ (1ZEROP 3B) 1F) (QUOTE 1TRUE)) ((NEQ (1ZEROP 3D) 1F) (QUOTE 1TRUE)) ((NEQ (1LESSP 3A 3D) 1F) (QUOTE 1TRUE)) ((NEQ (1LESSP 3C 3B) 1F) (QUOTE 1TRUE)) (T (1QUOT-QUOT-INDUCTION (1DIFFERENCE 3A 3D) 3B (1DIFFERENCE 3C 3B) 3D))))))) 
(PUT1-LST (QUOTE 1MONOTONE-QUOT-INDUCTION) (QUOTE (SEXPR (LAMBDA (3I 3J 3P) (COND ((NEQ (1ZEROP 3P) 1F) (QUOTE 1TRUE)) ((NEQ (1LESSP 3I 3P) 1F) (QUOTE 1TRUE)) ((NEQ (1LESSP 3J 3P) 1F) (QUOTE 1TRUE)) (T (1MONOTONE-QUOT-INDUCTION (1DIFFERENCE 3I 3P) (1DIFFERENCE 3J 3P) 3P))))))) 
(PUT1-LST (QUOTE 1WINS2) (QUOTE (SEXPR (LAMBDA (3A 3N 3P) (COND ((NEQ (1ZEROP 3N) 1F) (QUOTE 0.)) ((NEQ (1LESSP (1TIMES 3N 3P) 3A) 1F) 3N) (T (1WINS2 3A (1SUB1 3N) 3P)))))))