(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 NIL)) 
(SETQ CHRONOLOGY (QUOTE (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 (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 (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))) 
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(PUT1-LST (QUOTE 1SUBST2) (QUOTE (MAIN-EVENT SUBST2 EVENT NIL))) 
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(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 840609133436. 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 (MAIN-EVENT EXECUTE EVENT 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 840609133430. 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 (MAIN-EVENT EXECUTE1 EVENT 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 (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))) (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 (CAR (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 840609133421. 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 840609133420. 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 (MAIN-EVENT GET EVENT 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 840609133407. 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 (MAIN-EVENT SET EVENT 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 840609133406. 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 840609133406. 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 840609133404. 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 840609133334. 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 840609133333. 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 840609133332. 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 (MAIN-EVENT PROG-TRANS-OF-SIGMA EVENT 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 840609133325. 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 840609133325. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (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 (MAIN-EVENT SIGMA EVENT 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 840609133323. 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 840609133323. 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 840609133201. 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 840609133156. 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 840609133142. 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 840609132957. 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 840609132946. 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 840609132935. 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 840609132932. 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 840609132853. 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 840609132853. 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 840609132832. 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 (MAIN-EVENT SORT2 EVENT 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 840609132823. 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 (MAIN-EVENT ADDTOLIST2 EVENT 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 840609132823. 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 (MAIN-EVENT DSORT EVENT 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 840609132822. 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 (MAIN-EVENT ORDERED2 EVENT 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 840609132822. 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 840609132821. 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 840609132820. 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 (MAIN-EVENT MAXIMUM EVENT 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 840609132814. 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 840609132814. 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 840609132607. 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 840609132606. 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))))) 
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(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 840609130651. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (2.) SATELLITES (1PRIME1) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (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 840609130650. 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 840609130643. 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 840609130637. 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 (MAIN-EVENT SAMEFRINGE EVENT 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 840609130631. 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 840609130631. 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 840609130629. 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 (MAIN-EVENT GOPHER EVENT 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 840609130607. 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 (MAIN-EVENT LEFTCOUNT EVENT 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 840609130601. 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 840609130556. 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 840609130334. 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 840609130331. 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 840609130328. 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 840609130327. 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 840609130325. 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 840609130324. 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 840609130315. 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 840609130252. 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 840609125325. 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 840609125240. 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 840609125237. 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 840609125237. 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 840609125237. 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 840609125148. 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 840609125147. 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 840609125146. 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 840609125119. 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 840609125113. 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 840609125113. 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 840609125113. 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 840609125111. 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))))) 
(PUT1-LST (QUOTE 1NORMALIZED-IF-EXPRP) (QUOTE NIL)) 
(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 840609125110. 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))))) 
(PUT1-LST (QUOTE 1NORMALIZE) (QUOTE NIL)) 
(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 840609125050. 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))))) 
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(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 840609124411. 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 840609124411. 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 840609124407. 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 840609124358. 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 840609124358. 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 840609124348. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (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 840609124324. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (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 840609124323. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (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 840609124321. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (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 840609124319. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (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 840609124319. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (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 840609124315. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (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))))) 
(PUT1-LST (QUOTE REMAINDER-WRT-1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840609124314. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (HACK1) EVENT (PROVE-LEMMA REMAINDER-WRT-1 (REWRITE) (EQUAL (REMAINDER Y 1.) 0.)) LOCAL-UNDO-TUPLES ((LEMMAS REMAINDER . REMAINDER-WRT-1))))) 
(PUT1-LST (QUOTE POWER-EVAL-BIG-PLUS) (QUOTE (IDATE 840609124313. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-BIG-PLUS) EVENT (PROVE-LEMMA POWER-EVAL-BIG-PLUS (REWRITE) (EQUAL (POWER-EVAL (BIG-PLUS X Y I BASE) BASE) (PLUS I (PLUS (POWER-EVAL X BASE) (POWER-EVAL Y BASE))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL . POWER-EVAL-BIG-PLUS) (IMMEDIATE-DEPENDENTS0 POWER-EVAL-BIG-PLUS1 . POWER-EVAL-BIG-PLUS) (IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-TIMES-OVER-PLUS . POWER-EVAL-BIG-PLUS) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT . POWER-EVAL-BIG-PLUS) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-PLUS . POWER-EVAL-BIG-PLUS) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . POWER-EVAL-BIG-PLUS) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-PLUS . POWER-EVAL-BIG-PLUS) (IMMEDIATE-DEPENDENTS0 BIG-PLUS . POWER-EVAL-BIG-PLUS) (IMMEDIATE-DEPENDENTS0 POWER-EVAL . POWER-EVAL-BIG-PLUS) (LEMMAS POWER-EVAL . POWER-EVAL-BIG-PLUS))))) 
(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 840609124055. 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))))) 
(PUT1-LST (QUOTE POWER-EVAL-BIG-PLUS1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840609124054. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (POWER-EVAL-BIG-PLUS) EVENT (PROVE-LEMMA POWER-EVAL-BIG-PLUS1 (REWRITE) (EQUAL (POWER-EVAL (BIG-PLUS1 L I BASE) BASE) (PLUS (POWER-EVAL L BASE) I))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . POWER-EVAL-BIG-PLUS1) (IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-TIMES-OVER-PLUS . POWER-EVAL-BIG-PLUS1) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT . POWER-EVAL-BIG-PLUS1) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL . POWER-EVAL-BIG-PLUS1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . POWER-EVAL-BIG-PLUS1) (IMMEDIATE-DEPENDENTS0 BIG-PLUS1 . POWER-EVAL-BIG-PLUS1) (IMMEDIATE-DEPENDENTS0 POWER-EVAL . POWER-EVAL-BIG-PLUS1) (LEMMAS POWER-EVAL . POWER-EVAL-BIG-PLUS1))))) 
(PUT1-LST (QUOTE REMAINDER-QUOTIENT) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840609124041. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (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))))) 
(PUT1-LST (QUOTE 1BIG-PLUS1) (QUOTE NIL)) 
(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 840609124029. 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))))) 
(PUT1-LST (QUOTE 1POWER-EVAL) (QUOTE NIL)) 
(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 840609124028. 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 840609124028. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (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 840609124027. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (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 840609124026. 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 840609124024. 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))))) 
(PUT1-LST (QUOTE ORDERED-SORT-LP) (QUOTE (IDATE 840609123937. EVENT (PROVE-LEMMA ORDERED-SORT-LP (REWRITE) (IMPLIES (ORDERED Y) (ORDERED (SORT-LP X Y)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ORDERED-ADDTOLIST . ORDERED-SORT-LP) (IMMEDIATE-DEPENDENTS0 SORT-LP . ORDERED-SORT-LP) (IMMEDIATE-DEPENDENTS0 ORDERED . ORDERED-SORT-LP) (LEMMAS ORDERED . ORDERED-SORT-LP))))) 
(PUT1-LST (QUOTE ORDERED-ADDTOLIST) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840609123934. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (ORDERED-SORT-LP) EVENT (PROVE-LEMMA ORDERED-ADDTOLIST (REWRITE) (IMPLIES (ORDERED Y) (ORDERED (ADDTOLIST X Y)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ADDTOLIST . ORDERED-ADDTOLIST) (IMMEDIATE-DEPENDENTS0 ORDERED . ORDERED-ADDTOLIST) (LEMMAS ORDERED . ORDERED-ADDTOLIST))))) 
(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 840609123918. 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 840609123918. 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-))))) 
(PUT1-LST (QUOTE REVERSE-APPEND) (QUOTE (IDATE 840609123918. EVENT (PROVE-LEMMA REVERSE-APPEND NIL (EQUAL (REVERSE- (APPEND A B)) (APPEND (REVERSE- B) (REVERSE- A)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 APPEND-REVERSE . REVERSE-APPEND) (IMMEDIATE-DEPENDENTS0 REVERSE-LOOP-REVERSE . REVERSE-APPEND) (IMMEDIATE-DEPENDENTS0 APPEND . REVERSE-APPEND) (IMMEDIATE-DEPENDENTS0 REVERSE- . REVERSE-APPEND))))) 
(PUT1-LST (QUOTE REVERSE-LOOP-REVERSE) (QUOTE (IDATE 840609123918. 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))))) 
(PUT1-LST (QUOTE REVERSE-LOOP-APPEND-REVERSE) (QUOTE (IDATE 840609123917. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (REVERSE-LOOP-REVERSE) EVENT (PROVE-LEMMA REVERSE-LOOP-APPEND-REVERSE (REWRITE) (EQUAL (REVERSE-LOOP X Y) (APPEND (REVERSE X) Y))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-APPEND . REVERSE-LOOP-APPEND-REVERSE) (IMMEDIATE-DEPENDENTS0 REVERSE . REVERSE-LOOP-APPEND-REVERSE) (IMMEDIATE-DEPENDENTS0 APPEND . REVERSE-LOOP-APPEND-REVERSE) (IMMEDIATE-DEPENDENTS0 REVERSE-LOOP . REVERSE-LOOP-APPEND-REVERSE) (LEMMAS REVERSE-LOOP . REVERSE-LOOP-APPEND-REVERSE))))) 
(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 840609123916. 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 840609123916. 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-LOOP-FACT) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840609123915. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (FACT-FACT) EVENT (PROVE-LEMMA FACT-LOOP-FACT (REWRITE) (IMPLIES (NUMBERP I) (EQUAL (FACT-LOOP J I) (TIMES I (FACT J))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-TIMES-OVER-PLUS . FACT-LOOP-FACT) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-TIMES . FACT-LOOP-FACT) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . FACT-LOOP-FACT) (IMMEDIATE-DEPENDENTS0 FACT . FACT-LOOP-FACT) (IMMEDIATE-DEPENDENTS0 FACT-LOOP . FACT-LOOP-FACT) (LEMMAS FACT-LOOP . FACT-LOOP-FACT))))) 
(PUT1-LST (QUOTE 1FACT-) (QUOTE NIL)) 
(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 840609123911. 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 840609123910. 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 840609123909. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1FACT) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (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 840609123909. 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 840609123908. 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 840609123908. 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 840609123908. 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 840609123908. 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 840609123906. 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 840609123906. 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 840609123904. 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))))) 
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(PUT1-LST (QUOTE CROCK-DUE-TO-LACK-OF-BOUNCE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840609123901. 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 840609123901. SATELLITES (1XOR) EVENT (DEFN XOR (P Q) (IF Q (IF P F T) (EQUAL P T))) LOCAL-UNDO-TUPLES ((DCELL . 1XOR))))) 
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(PUT1-LST (QUOTE ORDERED-SORT) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840609123843. 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 840609123823. 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 840609123823. 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 840609123821. 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 840609123814. 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 840609123757. 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 840609123757. 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 840609123750. 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 840609123734. 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 840609123730. 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 840609123727. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (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 840609123721. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (2.) SATELLITES (1EXP) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (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 840609123721. 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 840609123720. 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 (IDATE 840609123713. 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 840609123712. 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 840609123708. 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 840609123705. 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 840609123701. 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 840609123701. 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 840609123659. 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 840609123658. 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 840609123658. 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 840609123657. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1ODD) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (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 840609123657. 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 840609123656. 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 840609123647. 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 840609123647. 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 840609123644. 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 840609123642. CONTROLLER-POCKETS NIL SATELLITES (1IFF) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (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 840609123642. 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 840609123642. 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 840609123641. 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 840609123639. 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 840609123639. 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 840609123639. 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 840609123638. 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 840609123637. 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 840609123637. 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 840609123633. 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 840609123627. 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 840609123613. 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 840609123613. 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 840609123603. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (1.) SATELLITES (1INTERSECT) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (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 840609123603. 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 840609123555. 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 840609123552. 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 840609123547. 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 840609123544. 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 840609123543. 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 840609123543. 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 840609123540. 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 840609123538. 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 840609123538. EVENT (PROVE-LEMMA LESSP-NOT-REFLEXIVE NIL (NOT (LESSP X X)))))) 
(PUT1-LST (QUOTE TRANSITIVITY-OF-LESSP) (QUOTE (IDATE 840609123535. 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 840609123535. 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 840609123534. 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 840609123440. 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 840609123425. 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 840609123425. 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 840609123412. 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 840609123406. 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 840609123405. 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 840609123402. 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 840609123400. 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 840609123400. 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 840609123353. 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 840609123353. 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 840609123353. 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 840609123353. 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 840609123351. 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 840609123351. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (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 840609123348. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (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 840609123346. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (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))))) 
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(PUT1-LST (QUOTE TIMES-ADD1) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840609123337. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (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 840609123331. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (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 840609123329. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (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 840609123326. 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 840609123320. 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))))) 
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(PUT1-LST (QUOTE BRIDGE-TO-SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840609122829. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-CANCEL) EVENT (PROVE-LEMMA BRIDGE-TO-SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP (REWRITE) (IMPLIES (AND (SUBBAGP Y (PLUS-FRINGE Z)) (EQUAL (MEANING Z A) (MEANING (PLUS-TREE (PLUS-FRINGE Z)) A))) (EQUAL (LESSP (MEANING Z A) (MEANING (PLUS-TREE Y) A)) F))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP . BRIDGE-TO-SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP) (IMMEDIATE-DEPENDENTS0 PLUS-TREE . BRIDGE-TO-SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP) (IMMEDIATE-DEPENDENTS0 PLUS-FRINGE . BRIDGE-TO-SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP) (IMMEDIATE-DEPENDENTS0 SUBBAGP . BRIDGE-TO-SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP) (LEMMAS LESSP . BRIDGE-TO-SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP))))) 
(PUT1-LST (QUOTE NUMBERP-MEANING-BRIDGE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840609122827. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (PLUS-TREE-PLUS-FRINGE MEANING-PLUS-TREE-APPEND) EVENT (PROVE-LEMMA NUMBERP-MEANING-BRIDGE (REWRITE) (IMPLIES (EQUAL (MEANING Z A) (MEANING (PLUS-TREE X) A)) (NUMBERP (MEANING Z A)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PLUS-TREE . NUMBERP-MEANING-BRIDGE) (LEMMAS NUMBERP . NUMBERP-MEANING-BRIDGE))))) 
(PUT1-LST (QUOTE PLUS-TREE-BAGDIFF) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840609122825. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-CANCEL) EVENT (PROVE-LEMMA PLUS-TREE-BAGDIFF (REWRITE) (IMPLIES (SUBBAGP X Y) (EQUAL (MEANING (PLUS-TREE (BAGDIFF Y X)) A) (DIFFERENCE (MEANING (PLUS-TREE Y) A) (MEANING (PLUS-TREE X) A))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PLUS-RIGHT-ID2 . PLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 MEMBER-IMPLIES-PLUS-TREE-GREATEREQP . PLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP . PLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE-0 . PLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 SUBBAGP-CDR2 . PLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 NUMBERP-MEANING-PLUS-TREE . PLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-CANCELLATION-0 . PLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . PLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 PLUS-TREE-DELETE . PLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 BAGDIFF . PLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 PLUS-TREE . PLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 SUBBAGP . PLUS-TREE-BAGDIFF) (LEMMAS MEANING . PLUS-TREE-BAGDIFF))))) 
(PUT1-LST (QUOTE SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840609122655. 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))))) 
(PUT1-LST (QUOTE PLUS-TREE-DELETE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840609122640. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-CANCEL PLUS-TREE-BAGDIFF SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP) EVENT (PROVE-LEMMA PLUS-TREE-DELETE (REWRITE) (EQUAL (MEANING (PLUS-TREE (DELETE X Y)) A) (IF (MEMBER X Y) (DIFFERENCE (MEANING (PLUS-TREE Y) A) (MEANING X A)) (MEANING (PLUS-TREE Y) A)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PLUS-EQUAL-0 . PLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . PLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 PLUS-RIGHT-ID2 . PLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 MEMBER-IMPLIES-PLUS-TREE-GREATEREQP . PLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE-0 . PLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-CANCELLATION-0 . PLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 NUMBERP-MEANING-PLUS-TREE . PLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-PLUS . PLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-0 . PLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE-NON-MEMBER . PLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE . PLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 PLUS-TREE . PLUS-TREE-DELETE) (LEMMAS MEANING . PLUS-TREE-DELETE))))) 
(PUT1-LST (QUOTE MEMBER-IMPLIES-PLUS-TREE-GREATEREQP) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840609122445. 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 FORM-LSTP-BAGDIFF) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840609122417. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-CANCEL) EVENT (PROVE-LEMMA FORM-LSTP-BAGDIFF (REWRITE) (IMPLIES (FORM-LSTP X) (FORM-LSTP (BAGDIFF X Y)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 FORM-LSTP-DELETE . FORM-LSTP-BAGDIFF) (IMMEDIATE-DEPENDENTS0 BAGDIFF . FORM-LSTP-BAGDIFF) (LEMMAS FORM-LSTP . FORM-LSTP-BAGDIFF))))) 
(PUT1-LST (QUOTE FORM-LSTP-DELETE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840609122413. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-CANCEL FORM-LSTP-BAGDIFF) EVENT (PROVE-LEMMA FORM-LSTP-DELETE (REWRITE) (IMPLIES (FORM-LSTP X) (FORM-LSTP (DELETE Y X)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DELETE-NON-MEMBER . FORM-LSTP-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE . FORM-LSTP-DELETE) (LEMMAS FORM-LSTP . FORM-LSTP-DELETE))))) 
(PUT1-LST (QUOTE FORM-LSTP-PLUS-FRINGE) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840609122409. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-CANCEL) EVENT (PROVE-LEMMA FORM-LSTP-PLUS-FRINGE (REWRITE) (IMPLIES (FORMP X) (FORM-LSTP (PLUS-FRINGE X)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 FORM-LSTP-APPEND . FORM-LSTP-PLUS-FRINGE) (IMMEDIATE-DEPENDENTS0 PLUS-FRINGE . FORM-LSTP-PLUS-FRINGE) (LEMMAS FORM-LSTP . FORM-LSTP-PLUS-FRINGE))))) 
(PUT1-LST (QUOTE FORM-LSTP-APPEND) (QUOTE (TYPE-PRESCRIPTION-LST NIL IDATE 840609122358. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (FORM-LSTP-PLUS-FRINGE) EVENT (PROVE-LEMMA FORM-LSTP-APPEND (REWRITE) (IMPLIES (AND (FORM-LSTP A) (FORM-LSTP B)) (FORM-LSTP (APPEND A B)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 APPEND . FORM-LSTP-APPEND) (LEMMAS FORM-LSTP . FORM-LSTP-APPEND))))) 
(PUT1-LST (QUOTE 1CANCEL) (QUOTE NIL)) 
(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 840609122351. 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 840609122349. 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 840609122345. 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 840609122345. 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 840609122340. 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 840609122334. 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 840609122318. 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 840609122314. 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 840609122309. 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 840609122304. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (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 840609122302. MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (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 840609122259. 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 840609122259. 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 840609122255. 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 840609122255. ELIMINATE-DESTRUCTORS-SEQ NIL CONTROLLER-POCKETS (2.) SATELLITES (1DELETE) MAIN-EVENT NIL IMMEDIATE-DEPENDENTS0 (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 840609122249. 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))))) 
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(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))))))