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T) (RDIFFERENCE-RDIFFERENCE-ARG2 RDIFFERENCE-RDIFFERENCE-ARG2-OFF . T) (RPLUS-RNEG-ARG1 RPLUS-RNEG-ARG1-OFF . T) (RPLUS-RNEG-ARG2 RPLUS-RNEG-ARG2-OFF . T) (COMMUTATIVITY-OF-SIMPLE-RTIMES COMMUTATIVITY-OF-SIMPLE-RTIMES-OFF . T) (COMMUTATIVITY-OF-RTIMES COMMUTATIVITY-OF-RTIMES-OFF . T) (RZEROP RZEROP-OFF . T) (SIMPLE-RTIMES-RZEROP SIMPLE-RTIMES-RZEROP-OFF . T) (ASSOCIATIVITY-OF-SIMPLE-RTIMES-WHEN-NOT-RZEROP ASSOCIATIVITY-OF-SIMPLE-RTIMES-WHEN-NOT-RZEROP-OFF . T) (NUMERATOR-ZERO-RZEROP-BRIDGE NUMERATOR-ZERO-RZEROP-BRIDGE-OFF . T) (ASSOCIATIVITY-OF-SIMPLE-RTIMES ASSOCIATIVITY-OF-SIMPLE-RTIMES-OFF . T) (REQUAL-SIMPLE-RTIMES-REQUAL-ARG1 REQUAL-SIMPLE-RTIMES-REQUAL-ARG1-OFF . T) (REQUAL-SIMPLE-RTIMES-REQUAL-ARG2 REQUAL-SIMPLE-RTIMES-REQUAL-ARG2-OFF . T) (REQUAL-SIMPLE-RTIMES-REDUCE-ARG1 REQUAL-SIMPLE-RTIMES-REDUCE-ARG1-OFF . T) (REQUAL-SIMPLE-RTIMES-REDUCE-ARG2 REQUAL-SIMPLE-RTIMES-REDUCE-ARG2-OFF . T) (REQUAL-SIMPLE-RTIMES-BRIDGE REQUAL-SIMPLE-RTIMES-BRIDGE-OFF . 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T) (REQUAL-RTIMES-RNEG REQUAL-RTIMES-RNEG-OFF . T) (RTIMES-RNEG-ARG1 RTIMES-RNEG-ARG1-OFF . T) (RTIMES-RNEG-ARG2 RTIMES-RNEG-ARG2-OFF . T) (RTIMES-RDIFFERENCE-ARG1 RTIMES-RDIFFERENCE-ARG1-OFF . T) (RTIMES-RDIFFERENCE-ARG2 RTIMES-RDIFFERENCE-ARG2-OFF . T) (RNEG-RDIFFERENCE RNEG-RDIFFERENCE-OFF . T) (RDIFFERENCE-RNEG-ARG2 RDIFFERENCE-RNEG-ARG2-OFF . T) (EQUAL-REQUAL-REWRITE EQUAL-REQUAL-REWRITE-OFF . T) (TRANSITIVITY-OF-REQUAL-BRIDGE TRANSITIVITY-OF-REQUAL-BRIDGE-OFF . T) (RPLUS-REQUAL-ARG1 RPLUS-REQUAL-ARG1-OFF . T) (RPLUS-OPEN-UP RPLUS-OPEN-UP-OFF . T) (REQUAL-REDUCE-REDUCE-EQUAL REQUAL-REDUCE-REDUCE-EQUAL-OFF . T) (NEGATIVEP-IF-INTEGERP-AND-NOT-NUMBERP NEGATIVEP-IF-INTEGERP-AND-NOT-NUMBERP-OFF . T) (NUMBERP-IF-INTEGERP-AND-NOT-NEGATIVEP NUMBERP-IF-INTEGERP-AND-NOT-NEGATIVEP-OFF . T) (IQUOTIENT IQUOTIENT-OFF1 . T) (IREMAINDER IREMAINDER-OFF1 . T) (IZEROP IZEROP-OFF1 . T) (FIX-INT FIX-INT-OFF1 . T) (INEG INEG-OFF1 . T) (ITIMES ITIMES-OFF1 . T) (IPLUS IPLUS-OFF1 . T) (IDIFFERENCE IDIFFERENCE-OFF1 . T) (ILESSP ILESSP-OFF1 . T) (IDIFFERENCE-IPLUS-CANONICALIZER1 IDIFFERENCE-IPLUS-CANONICALIZER1-ON) (GCD-FACTORS GCD-FACTORS-OFF . T) (GCD-FACTORS-GIVES-LINEAR-COMBINATION GCD-FACTORS-GIVES-LINEAR-COMBINATION-OFF . T) (GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE-OFF . T) (DPR-HACK5 DPR-HACK5-OFF . T) (DPR-HACK4 DPR-HACK4-OFF . T) (DPR-HACK3 DPR-HACK3-OFF . T) (DPR-HACK2 DPR-HACK2-OFF . T) (DPR-HACK1 DPR-HACK1-OFF . T) (REMAINDER-0-SUFFICIENCY REMAINDER-0-SUFFICIENCY-OFF . T) (IQUOTIENT IQUOTIENT-ON) (IREMAINDER IREMAINDER-ON) (IZEROP IZEROP-ON) (FIX-INT FIX-INT-ON) (INTEGERP INTEGERP-ON) (INEG INEG-ON) (ITIMES ITIMES-ON) (IPLUS IPLUS-ON) (IDIFFERENCE IDIFFERENCE-ON) (ILESSP ILESSP-ON) (IDIFFERENCE-IPLUS-CANONICALIZER1 IDIFFERENCE-IPLUS-CANONICALIZER1-OFF . T) (CANCEL-EQUAL-TIMES-PRESERVES-INEQUALITY-BRIDGE CANCEL-EQUAL-TIMES-PRESERVES-INEQUALITY-BRIDGE-OFF . T) (CANCEL-EQUAL-TIMES-PRESERVES-INEQUALITY CANCEL-EQUAL-TIMES-PRESERVES-INEQUALITY-OFF . T) (EVAL$-EQUAL-TIMES-TREE-BAGDIFF EVAL$-EQUAL-TIMES-TREE-BAGDIFF-OFF . T) (ZEROP-MAKES-EQUAL-TRUE-BRIDGE ZEROP-MAKES-EQUAL-TRUE-BRIDGE-OFF . T) (EVAL$-QUOTIENT-TIMES-TREE-BAGDIFF EVAL$-QUOTIENT-TIMES-TREE-BAGDIFF-OFF . T) (ZEROP-MAKES-QUOTIENT-ZERO-BRIDGE ZEROP-MAKES-QUOTIENT-ZERO-BRIDGE-OFF . T) (ZEROP-MAKES-LESSP-FALSE-BRIDGE ZEROP-MAKES-LESSP-FALSE-BRIDGE-OFF . T) (EVAL$-LESSP-TIMES-TREE-BAGDIFF EVAL$-LESSP-TIMES-TREE-BAGDIFF-OFF . T) (TIMES-TREE-OF-TIMES-FRINGE TIMES-TREE-OF-TIMES-FRINGE-OFF . T) (TIMES-TREE-APPEND TIMES-TREE-APPEND-OFF . T) (ZEROP-MAKES-TIMES-TREE-ZERO2 ZEROP-MAKES-TIMES-TREE-ZERO2-OFF . T) (OR-ZEROP-TREE-IS-NOT-ZEROP-TREE OR-ZEROP-TREE-IS-NOT-ZEROP-TREE-OFF . T) (ZEROP-MAKES-TIMES-TREE-ZERO ZEROP-MAKES-TIMES-TREE-ZERO-OFF . T) (EVAL$-TIMES-MEMBER EVAL$-TIMES-MEMBER-OFF . T) (EQUAL-TIMES-BRIDGE EQUAL-TIMES-BRIDGE-OFF . T) (EQUAL-TIMES-ARG1 EQUAL-TIMES-ARG1-OFF . T) (STUPID-HACK STUPID-HACK-OFF . T) (LESSP-TIMES-ARG1 LESSP-TIMES-ARG1-OFF . T) (BAGDIFF-DELETE BAGDIFF-DELETE-OFF . T) (NUMBERP-EVAL$-TIMES-TREE NUMBERP-EVAL$-TIMES-TREE-OFF . T) (EVAL$-QUOTIENT2 EVAL$-QUOTIENT2-OFF . T) (EVAL$-QUOTIENT EVAL$-QUOTIENT-OFF . T) (EVAL$-IF2 EVAL$-IF2-OFF . T) (EVAL$-IF EVAL$-IF-OFF . T) (EVAL$-LESSP2 EVAL$-LESSP2-OFF . T) (EVAL$-LESSP EVAL$-LESSP-OFF . T) (EVAL$-EQUAL EVAL$-EQUAL-OFF . T) (EVAL$-OR2 EVAL$-OR2-OFF . T) (EVAL$-OR EVAL$-OR-OFF . T) (EVAL$-TIMES2 EVAL$-TIMES2-OFF . T) (EVAL$-TIMES EVAL$-TIMES-OFF . T) (NUMBERP-EVAL$-TIMES NUMBERP-EVAL$-TIMES-OFF . T) (INTEGERP INTEGERP-OFF . T) (FIX-INT FIX-INT-OFF . T) (IZEROP IZEROP-OFF . T) (ILESSP ILESSP-OFF . T) (ILEQ ILEQ-OFF . T) (IPLUS IPLUS-OFF . T) (INEG INEG-OFF . T) (IDIFFERENCE IDIFFERENCE-OFF . T) (IABS IABS-OFF . T) (ITIMES ITIMES-OFF . T) (CANCEL-IPLUS CANCEL-IPLUS-OFF . T) (INTEGERP-EVAL$-IPLUS INTEGERP-EVAL$-IPLUS-OFF . T) (INTEGERP-EVAL$-IPLUS-TREE INTEGERP-EVAL$-IPLUS-TREE-OFF . T) (INTEGERP-EVAL$-BRIDGE INTEGERP-EVAL$-BRIDGE-OFF . T) (EVAL$-IPLUS-TREE-APPEND EVAL$-IPLUS-TREE-APPEND-OFF . T) (IPLUS-TREE-IPLUS-FRINGE IPLUS-TREE-IPLUS-FRINGE-OFF . T) (IPLUS-TREE-DELETE IPLUS-TREE-DELETE-OFF . T) (IPLUS-TREE-BAGDIFF IPLUS-TREE-BAGDIFF-OFF . T) (NOT-INTEGERP-IMPLIES-NOT-EQUAL-IPLUS NOT-INTEGERP-IMPLIES-NOT-EQUAL-IPLUS-OFF . T) (CANCEL-IDIFFERENCE CANCEL-IDIFFERENCE-OFF . T) (IQUOTIENT IQUOTIENT-OFF . T) (IREMAINDER IREMAINDER-OFF . T) (QUOTIENT-DIFFERENCE-LESSP-ARG2 QUOTIENT-DIFFERENCE-LESSP-ARG2-OFF . T) (IDIV IDIV-OFF . T) (IMOD IMOD-OFF . T) (IQUO IQUO-OFF . T) (IREM IREM-OFF . T) (REMAINDER-EQUALS-ITS-FIRST-ARGUMENT REMAINDER-EQUALS-ITS-FIRST-ARGUMENT-OFF . T) (QUOTIENT-TIMES-INSTANCE-TEMP QUOTIENT-TIMES-INSTANCE-TEMP-OFF . T) (PLUS-REMAINDER-TIMES-QUOTIENT PLUS-REMAINDER-TIMES-QUOTIENT-OFF . T) (EQUAL-REMAINDER-PLUS-REMAINDER EQUAL-REMAINDER-PLUS-REMAINDER-OFF . T) (REMAINDER-TIMES-TIMES REMAINDER-TIMES-TIMES-OFF . T) (REMAINDER-DIFFERENCE3 REMAINDER-DIFFERENCE3-OFF . T) (EQUAL-REMAINDER-DIFFERENCE-0 EQUAL-REMAINDER-DIFFERENCE-0-OFF . T) (LESSP-PLUS-FACT LESSP-PLUS-FACT-OFF . T) (OPEN-PLUS OPEN-PLUS-OFF . T) (PLUS-CANCELLATION PLUS-CANCELLATION-OFF . T) (DIFFERENCE-X-X DIFFERENCE-X-X-OFF . T) (DIFFERENCE-PLUS DIFFERENCE-PLUS-OFF . T) (DIFFERENCE-PLUS-CANCELLATION1 DIFFERENCE-PLUS-CANCELLATION1-OFF . T) (DIFFERENCE-PLUS-CANCELLATION2 DIFFERENCE-PLUS-CANCELLATION2-OFF . T) (DIFFERENCE-CANCELLATION-0 DIFFERENCE-CANCELLATION-0-OFF . T) (DIFFERENCE-CANCELLATION-1 DIFFERENCE-CANCELLATION-1-OFF . T) (DIFFERENCE-1 DIFFERENCE-1-OFF . T) (DIFFERENCE-2 DIFFERENCE-2-OFF . T) (DIFFERENCE-ADD1-PLUS-CANCELLATION DIFFERENCE-ADD1-PLUS-CANCELLATION-OFF . T) (DIFFERENCE-SUB1-ARG2 DIFFERENCE-SUB1-ARG2-OFF . T) (DIFFERENCE-DIFFERENCE-ARG1 DIFFERENCE-DIFFERENCE-ARG1-OFF . T) (DIFFERENCE-DIFFERENCE-ARG2 DIFFERENCE-DIFFERENCE-ARG2-OFF . T) (DIFFERENCE-DIFFERENCE-DIFFERENCE DIFFERENCE-DIFFERENCE-DIFFERENCE-OFF . T) (DIFFERENCE-PLUS-CANCELLATION3 DIFFERENCE-PLUS-CANCELLATION3-OFF . T) (NUMBERP-EVAL$-PLUS NUMBERP-EVAL$-PLUS-OFF . T) (NUMBERP-EVAL$-PLUS-TREE NUMBERP-EVAL$-PLUS-TREE-OFF . T) (MEMBER-IMPLIES-PLUS-TREE-GREATEREQP MEMBER-IMPLIES-PLUS-TREE-GREATEREQP-OFF . T) (PLUS-TREE-DELETE PLUS-TREE-DELETE-OFF . T) (SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP-OFF . T) (PLUS-TREE-BAGDIFF PLUS-TREE-BAGDIFF-OFF . T) (NUMBERP-EVAL$-BRIDGE NUMBERP-EVAL$-BRIDGE-OFF . T) (BRIDGE-TO-SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP BRIDGE-TO-SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP-OFF . T) (EVAL$-PLUS-TREE-APPEND EVAL$-PLUS-TREE-APPEND-OFF . T) (PLUS-TREE-PLUS-FRINGE PLUS-TREE-PLUS-FRINGE-OFF . T) (MEMBER-IMPLIES-NUMBERP MEMBER-IMPLIES-NUMBERP-OFF . T) (CADR-EVAL$-LIST CADR-EVAL$-LIST-OFF . T) (EVAL$-QUOTE EVAL$-QUOTE-OFF . T) (LISTP-EVAL$ LISTP-EVAL$-OFF . T) (CANCEL-EQUAL-PLUS CANCEL-EQUAL-PLUS-OFF . T) (CANCEL-DIFFERENCE-PLUS CANCEL-DIFFERENCE-PLUS-OFF . T) (LESSP-DIFFERENCE-CANCELLATION LESSP-DIFFERENCE-CANCELLATION-OFF . T) (CANCEL-LESSP-PLUS CANCEL-LESSP-PLUS-OFF . T) (APPLY$ GROUND-ZERO . T) (V&C-APPLY$ GROUND-ZERO . T)))) (SETQ *1*THM-MODE$ (QUOTE NQTHM)) (SETQ FREE-VARS-IN-REWRITE-RHSS (QUOTE NIL)) (SETQ STATE-STACK-LIST (QUOTE NIL)) (SETQ CHRONOLOGY (QUOTE (R2 CANCEL-RPLUS-OFF CORRECTNESS-OF-CANCEL-RPLUS-OFF CORRECTNESS-OF-CANCEL-RPLUS CANCEL-RPLUS RPLUS-RZEROP-BRIDGE-OFF RPLUS-RZEROP-BRIDGE2-OFF RPLUS-RZEROP-OFF EVAL$-RPLUS-OFF EVAL$-REDUCE-OFF MEMBER-APPEND-OFF DELETE-APPEND-OFF MEMBER-SUBBAGP-OFF OCCURRENCES-DELETE2-OFF OCCURRENCES-APPEND-OFF SUBBAGP-APPEND-OFF SUBBAGP-DELETE-SAME-OFF SUBBAGP-DELETE-SAME-MEANS-OFF SUBBAGP-DELETE-CAR-OFF SUBBAGP-DELETE-CAR2-OFF SUBBAGP-PERMUTATION-OFF PERMUTATION-A-B-OFF NOT-SUBBAGP-NOT-PERMUTATION-OFF SUBBAGP-NECC-OFF SUBBAGP-TRANSITIVE-OFF NOT-MEMBER-MAKE-NEGS-FACT-OFF MAKE-NEGS-DELETE-OFF MAKE-NEGS-BAGDIFF-OFF APPEND-BAGDIFF-ARG1-OFF APPEND-BAGDIFF-ARG2-OFF BAGDIFF-BAGDIFF-OFF MEMBER-RNEG-MAKE-NEGS-OFF SUBBAGP-MAKE-NEGS-OFF RDIFFERENCE-REDUCE-OFF REQUAL-SIMPLE-RPLUS-X-SIMPLE-RNEG-X-OFF REQUAL-RPLUS-X-SIMPLE-RNEG-X-OFF RPLUS-X-RNEG-X-OFF RDIFFERENCE-X-X-OFF RDIFFERENCE-RPLUS-HACK-OFF RDIFFERENCE-RPLUS-HACK2-OFF RPLUS-RDIFFERENCE-HACK-OFF EQUAL-DIFFERENCE-HACK1-OFF EQUAL-DIFFERENCE-HACK2-OFF EQUAL-DIFFERENCE-REWRITE-OFF EQUAL-DIFFERENCE-REWRITE2-OFF EQUAL-TIMES-BRIDGE5-OFF EQUAL-PLUS-DIFFERENCE-REWRITE-OFF LESSP-TIMES-BRIDGE1-OFF EQUAL-DIFFERENCE-OFF REQUAL-SIMPLE-RPLUS-X-X-REWRITE-OFF EQUAL-RPLUS-X-X-REWRITE-OFF EQUAL-RPLUS-RDIFFERENCE-HACK-OFF MEMBER-CAR-X-X-OFF MEMBER-BAGDIFF-APPEND-OFF PERMUTATION-TRANSITIVE-OFF BAGDIFF-X-X-OFF BAGDIFF-APPEND-ARG1-OFF BAGDIFF-CONS-Z-Z-OFF BAGDIFF-NOT-LISTP-OFF BAGDIFF-CAR-IN-OFF LAST-CDR-DELETE-OFF MEMBER-SUBBAGP2-OFF MEMBER-SUBBAGP-DELETE-OFF SUBBAGP-BAGDIFF-OFF PERMUTATION-BAGDIFF-OFF PERMUTATION-APPEND-ARG1-ARG2-BRIDGE-OFF SUBBAGP-TRANSITIVE-BRIDGE-HELPER-OFF SUBBAGP-TRANSITIVE-BRIDGE-OFF EQUAL-PERMUTATION-OFF PERMUTATION-BAGDIFF-APPEND-HELPER-OFF PERMUTATION-BAGDIFF-APPEND-OFF SUBBAGP-APPEND-SIMPLIFY1-OFF SUBBAGP-PERMUTATION-EQUIV-OFF SUBBAGP-APPEND-SIMPLIFY2-OFF SUBBAGP-APPEND-BRIDGE-OFF SUBBAGP-APPEND-BRIDGE2-OFF SUBBAGP-X-X-OFF RNEGS-NOT-CAR-SPLIT-BY-PARITY-OFF PERMUTATION-APPEND-SPLIT-BY-PARITY-BRIDGE-OFF MEMBER-CDR-SPLIT-BY-PARITY-OFF ALL-RNEGS-MAKE-NEGS-BAGINT-FACT-OFF ALL-RNEGS-MAKE-NEGS-BAGINT-OFF BAGINT-ALL-RNEGS-CAR-SPLIT-BY-PARITY-OFF BAGINT-MAKE-NEGS-SPLIT-BY-PARITY-OFF REDUCE-EVAL$-RPLUS-TREE-OFF RPLUS-EVAL$-RPLUS-TREE-OFF EVAL$-RPLUS-TREE-DELETE-OFF PERMUTATION-DOES-NOT-EFFECT-RPLUS-OFF EVAL$-RPLUS-TREE-ZERO-OFF CANCEL-ZERO-FACT-OFF CANCEL-ZERO-FACT-BRIDGE-OFF RNEGS-CANCEL-LIST-OFF CANCELLING-FROM-RPLUS-OFF EVAL$-RPLUS-TREE-RPLUS-FRINGE-OFF COMMUTATIVITY2-OF-RTIMES BAGINT-MAKE-NEGS-SPLIT-BY-PARITY BAGINT-ALL-RNEGS-CAR-SPLIT-BY-PARITY ALL-RNEGS-MAKE-NEGS-BAGINT ALL-RNEGS-MAKE-NEGS-BAGINT-FACT ALL-RNEGS MEMBER-CDR-SPLIT-BY-PARITY PERMUTATION-APPEND-SPLIT-BY-PARITY-BRIDGE RNEGS-NOT-CAR-SPLIT-BY-PARITY SUBBAGP-X-X EVAL$-RPLUS-TREE-RPLUS-FRINGE CANCELLING-FROM-RPLUS SUBBAGP-APPEND-BRIDGE2 SUBBAGP-APPEND-BRIDGE SUBBAGP-APPEND-SIMPLIFY2 SUBBAGP-PERMUTATION-EQUIV SUBBAGP-APPEND-SIMPLIFY1 RNEGS-CANCEL-LIST CANCEL-ZERO-FACT-BRIDGE PERMUTATION-BAGDIFF-APPEND PERMUTATION-BAGDIFF-APPEND-HELPER EQUAL-PERMUTATION SUBBAGP-TRANSITIVE-BRIDGE SUBBAGP-TRANSITIVE-BRIDGE-HELPER PERMUTATION-APPEND-ARG1-ARG2-BRIDGE PERMUTATION-BAGDIFF SUBBAGP-BAGDIFF MEMBER-SUBBAGP-DELETE MEMBER-SUBBAGP2 LAST-CDR-DELETE BAGDIFF-CAR-IN BAGDIFF-NOT-LISTP BAGDIFF-CONS-Z-Z BAGDIFF-APPEND-ARG1 BAGDIFF-X-X LAST-CDR PERMUTATION-TRANSITIVE MEMBER-BAGDIFF-APPEND MEMBER-CAR-X-X CANCEL-ZERO-FACT EVAL$-RPLUS-TREE-ZERO PERMUTATION-DOES-NOT-EFFECT-RPLUS EVAL$-RPLUS-TREE-DELETE EQUAL-RPLUS-RDIFFERENCE-HACK EQUAL-RPLUS-X-X-REWRITE REQUAL-SIMPLE-RPLUS-X-X-REWRITE EQUAL-DIFFERENCE LESSP-TIMES-BRIDGE1 EQUAL-PLUS-DIFFERENCE-REWRITE EQUAL-TIMES-BRIDGE5 EQUAL-DIFFERENCE-REWRITE2 EQUAL-DIFFERENCE-REWRITE EQUAL-DIFFERENCE-HACK2 EQUAL-DIFFERENCE-HACK1 RPLUS-RDIFFERENCE-HACK RDIFFERENCE-RPLUS-HACK2 RDIFFERENCE-RPLUS-HACK RDIFFERENCE-X-X RPLUS-X-RNEG-X REQUAL-RPLUS-X-SIMPLE-RNEG-X REQUAL-SIMPLE-RPLUS-X-SIMPLE-RNEG-X RDIFFERENCE-REDUCE SUBBAGP-MAKE-NEGS MEMBER-RNEG-MAKE-NEGS BAGDIFF-BAGDIFF APPEND-BAGDIFF-ARG2 APPEND-BAGDIFF-ARG1 MAKE-NEGS-BAGDIFF MAKE-NEGS-DELETE NOT-MEMBER-MAKE-NEGS-FACT SUBBAGP-TRANSITIVE SUBBAGP-NECC PERMUTATION-AS-SUBBAGP-OFF PERMUTATION-AS-SUBBAGP-HELPER-OFF PERMUTATION-AS-SUBBAGP PERMUTATION-AS-SUBBAGP-HELPER NOT-SUBBAGP-NOT-PERMUTATION PERMUTATION-A-B SUBBAGP-PERMUTATION SUBBAGP-DELETE-CAR2 SUBBAGP-DELETE-CAR SUBBAGP-DELETE-SAME-MEANS SUBBAGP-DELETE-SAME SUBBAGP-WIT-LEMMA-OFF MEMBER-OCCUR-OFF SUBBAGP-APPEND OCCURRENCES-APPEND SUBBAGP-WIT-LEMMA OCCURRENCES-DELETE2 MEMBER-OCCUR BADGUY MEMBER-SUBBAGP DELETE-APPEND MEMBER-APPEND RPLUS-EVAL$-RPLUS-TREE REDUCE-EVAL$-RPLUS-TREE EVAL$-REDUCE EVAL$-RPLUS RPLUS-RZEROP RPLUS-RZEROP-BRIDGE2 RPLUS-RZEROP-BRIDGE MAKE-NEGS SPLIT-BY-PARITY RPLUS-FRINGE RPLUS-TREE R1 RATIONALP-OFF FIX-RATIONAL-OFF REDUCE-OFF SIMPLE-RPLUS-OFF RPLUS-OFF SIMPLE-RNEG-OFF RNEG-OFF RDIFFERENCE-OFF SIMPLE-RTIMES-OFF RTIMES-OFF RQUOTIENT-OFF SIMPLE-RMAGNITUDE-OFF RMAGNITUDE-OFF RLESSP-OFF REQUAL-OFF INTEGERP-MINUS-OFF FIX-INT-ON-INTEGERS-OFF ITIMES-INEG-ARG1-OFF ITIMES-INEG-ARG2-OFF INTEGERP-IF-NEGATIVEP-NON-ZERO-OFF INTEGERP-IF-NUMBERP-OFF ITIMES-NEGATIVEP-ARG1-OFF ITIMES-NEGATIVEP-ARG2-OFF EQUAL-INEG-INEG-OFF ITIMES-IS-TIMES-OFF IPLUS-IS-PLUS-OFF RATIONALP-REDUCE-OFF RATIONALP-RPLUS-OFF RATIONALP-FIX-RATIONAL-OFF RATIONALP-RTIMES-OFF RATIONALP-RNEG-OFF RATIONALP-RDIFFERENCE-OFF RATIONALP-RQUOTIENT-OFF RATIONALP-RMAGNITUDE-OFF FIX-RATIONAL-REDUCE-OFF FIX-RATIONAL-RPLUS-OFF FIX-RATIONAL-FIX-RATIONAL-OFF FIX-RATIONAL-RTIMES-OFF FIX-RATIONAL-RNEG-OFF FIX-RATIONAL-RDIFFERENCE-OFF FIX-RATIONAL-RQUOTIENT-OFF FIX-RATIONAL-RMAGNITUDE-OFF RATIONAL-GENERALIZATION-OFF GCD-REMAINDER-FACT1-OFF GCD-REMAINDER-FACT2-OFF GCD-TIMES1-INDUCT-OFF GCD-TIMES1-OFF GCD-TIMES2-OFF GCD-QUOTIENT-QUOTIENT-OFF DIVIDES-EACH-EQUALITY-OFF GCD-FACTORS-OFF1 GCD-FACTORS-GIVES-LINEAR-COMBINATION-OFF1 GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE-OFF1 DPR-HACK1-OFF1 DPR-HACK2-OFF1 DPR-HACK3-OFF1 DPR-HACK4-OFF1 DPR-HACK5-OFF1 REMAINDER-0-SUFFICIENCY-OFF1 DIVIDES-PRODUCT-REDUCTION-OFF GCD-REMAINDER-TIMES-FACT1-PROOF-OFF TIMES-GCD-FACT-OFF EQUAL-TIMES-TIMES-QUOTIENT-ARG2-OFF QUOTIENT-GCD-TIMES-FACT-OFF QUOTIENT-GCD-TIMES-FACT1-OFF QUOTIENT-GCD-TIMES-FACT2-OFF QUOTIENT-GCD-TIMES-FACT3-OFF QUOTIENT-GCD-TIMES-FACT4-OFF QUOTIENT-GCD-TIMES-FACT5-OFF EQUAL-TIMES-GCD-BRIDGE1-OFF NUMBERP-IF-INTEGERP-AND-NOT-NEGATIVEP-OFF1 NEGATIVEP-IF-INTEGERP-AND-NOT-NUMBERP-OFF1 REQUAL-REDUCE-REDUCE-EQUAL-OFF1 COMMUTATIVITY-OF-REQUAL-OFF REQUAL-REDUCE1-OFF REQUAL-REDUCE2-OFF REDUCE-REDUCE-OFF RPLUS-OPEN-UP-OFF1 COMMUTATIVITY-OF-RPLUS-OFF RPLUS-REQUAL-ARG1-OFF1 REQUAL-X-X-OFF RPLUS-REDUCE-ARG1-OFF RPLUS-REDUCE-ARG2-OFF REQUAL-SIMPLE-RPLUS-REDUCE-ARG1-OFF REQUAL-SIMPLE-RPLUS-REDUCE-ARG2-OFF REDUCE-NRATIONALP-OFF NUMBERP-NUMERATOR-REDUCE-OFF NEGATIVEP-INEG-OFF NUMBERP-INEG-OFF RATIONAL-INEG-NUMERATOR-REDUCE-BRIDGE-OFF REDUCE-0-OFF SIMPLE-RNEG-REDUCE-OFF RNEG-REDUCE-OFF SIMPLE-RNEG-SIMPLE-RNEG-OFF REQUAL-RNEG-RNEG-OFF RNEG-RNEG-OFF RATIONALP-MEANS-OFF MEANS-RATIONALP-OFF NRATIONAL-RPLUS-ARG1-OFF NRATIONAL-RPLUS-ARG2-OFF NRATIONAL-SIMPLE-RPLUS-ARG1-OFF NRATIONAL-SIMPLE-RPLUS-ARG2-OFF SIMPLE-RPLUS-FIX-RATIONAL-ARG1-OFF SIMPLE-RPLUS-FIX-RATIONAL-ARG2-OFF FIX-RATIONAL-OF-RATIONALP-OFF NEGATIVE-GUTS-INEG-OFF RATIONALP-SIMPLE-RPLUS-OFF FIX-RATIONAL-SIMPLE-RPLUS-OFF REQUAL-ASSOCIATIVITY-OF-SIMPLE-RPLUS-OFF EQUAL-TIMES-BRIDGE1-OFF EQUAL-TIMES-BRIDGE2-OFF EQUAL-TIMES-BRIDGE3-OFF EQUAL-TIMES-BRIDGE4-OFF TRANSITIVITY-OF-REQUAL-BRIDGE-OFF1 TRANSITIVITY-OF-REQUAL-OFF EQUAL-REQUAL-REWRITE-OFF1 REQUAL-SIMPLE-RPLUS-BRIDGE-OFF REQUAL-ASSOCIATIVITY-OF-RPLUS-OFF ASSOCIATIVITY-OF-RPLUS-OFF COMMUTATIVITY2-OF-RPLUS-OFF RPLUS-RDIFFERENCE-ARG1-OFF RPLUS-RDIFFERENCE-ARG2-OFF REDUCE-RPLUS-OFF REDUCE-RTIMES-OFF REDUCE-DIFFERENCE-OFF REDUCE-RQUOTIENT-OFF REDUCE-RMAGNITUDE-OFF REDUCE-RNEG-OFF RPLUS-REDUCE-ARG1-REWRITE-OFF RPLUS-REDUCE-ARG2-REWRITE-OFF REQUAL-RNEG-SIMPLE-RPLUS-OFF REQUAL-RPLUS-RNEG-OFF RNEG-RPLUS-OFF RDIFFERENCE-RDIFFERENCE-ARG1-OFF RDIFFERENCE-RDIFFERENCE-ARG2-OFF RPLUS-RNEG-ARG1-OFF RPLUS-RNEG-ARG2-OFF COMMUTATIVITY-OF-SIMPLE-RTIMES-OFF COMMUTATIVITY-OF-RTIMES-OFF RZEROP-OFF SIMPLE-RTIMES-RZEROP-OFF ASSOCIATIVITY-OF-SIMPLE-RTIMES-WHEN-NOT-RZEROP-OFF NUMERATOR-ZERO-RZEROP-BRIDGE-OFF ASSOCIATIVITY-OF-SIMPLE-RTIMES-OFF REQUAL-SIMPLE-RTIMES-REQUAL-ARG1-OFF REQUAL-SIMPLE-RTIMES-REQUAL-ARG2-OFF REQUAL-SIMPLE-RTIMES-REDUCE-ARG1-OFF REQUAL-SIMPLE-RTIMES-REDUCE-ARG2-OFF REQUAL-SIMPLE-RTIMES-BRIDGE-OFF REQUAL-ASSOCIATIVITY-OF-RTIMES-OFF ASSOCIATIVITY-OF-RTIMES-OFF SIMPLE-RPLUS-RZEROP-OFF NUMERATOR-TYPE-OFF RATIONALP-SIMPLE-RTIMES-OFF FIX-RATIONAL-SIMPLE-RTIMES-OFF REQUAL-SIMPLE-RTIMES-SIMPLE-RPLUS-WHEN-NOT-RZEROP-OFF REQUAL-RZEROP-SIMPLE-RPLUS-OFF COMMUTATIVITY-OF-SIMPLE-RPLUS-OFF SIMPLE-RPLUS-BRIDGE-OFF REQUAL-SIMPLE-RTIMES-SIMPLE-RPLUS-ARG1-OFF REQUAL-RTIMES-RPLUS-BRIDGE-OFF RTIMES-RPLUS-ARG1-OFF RTIMES-RPLUS-ARG2-OFF REQUAL-SIMPLE-RTIMES-SIMPLE-RNEG-OFF REQUAL-RTIMES-RNEG-OFF RTIMES-RNEG-ARG1-OFF RTIMES-RNEG-ARG2-OFF RTIMES-RDIFFERENCE-ARG1-OFF RTIMES-RDIFFERENCE-ARG2-OFF RNEG-RDIFFERENCE-OFF RDIFFERENCE-RNEG-ARG2-OFF RDIFFERENCE-RNEG-ARG2 RNEG-RDIFFERENCE RTIMES-RDIFFERENCE-ARG2 RTIMES-RDIFFERENCE-ARG1 RTIMES-RNEG-ARG2 RTIMES-RNEG-ARG1 REQUAL-RTIMES-RNEG REQUAL-SIMPLE-RTIMES-SIMPLE-RNEG RTIMES-RPLUS-ARG2 RTIMES-RPLUS-ARG1 REQUAL-RTIMES-RPLUS-BRIDGE REQUAL-SIMPLE-RTIMES-SIMPLE-RPLUS-ARG1 SIMPLE-RPLUS-BRIDGE COMMUTATIVITY-OF-SIMPLE-RPLUS REQUAL-RZEROP-SIMPLE-RPLUS REQUAL-SIMPLE-RTIMES-SIMPLE-RPLUS-WHEN-NOT-RZEROP FIX-RATIONAL-SIMPLE-RTIMES RATIONALP-SIMPLE-RTIMES NUMERATOR-TYPE SIMPLE-RPLUS-RZEROP ASSOCIATIVITY-OF-RTIMES REQUAL-ASSOCIATIVITY-OF-RTIMES REQUAL-SIMPLE-RTIMES-BRIDGE REQUAL-SIMPLE-RTIMES-REDUCE-ARG2 REQUAL-SIMPLE-RTIMES-REDUCE-ARG1 REQUAL-SIMPLE-RTIMES-REQUAL-ARG2 REQUAL-SIMPLE-RTIMES-REQUAL-ARG1 ASSOCIATIVITY-OF-SIMPLE-RTIMES NUMERATOR-ZERO-RZEROP-BRIDGE ASSOCIATIVITY-OF-SIMPLE-RTIMES-WHEN-NOT-RZEROP SIMPLE-RTIMES-RZEROP COMMUTATIVITY-OF-RTIMES COMMUTATIVITY-OF-SIMPLE-RTIMES RPLUS-RNEG-ARG2 RPLUS-RNEG-ARG1 RDIFFERENCE-RDIFFERENCE-ARG2 RDIFFERENCE-RDIFFERENCE-ARG1 RNEG-RPLUS REQUAL-RPLUS-RNEG REQUAL-RNEG-SIMPLE-RPLUS RPLUS-REDUCE-ARG2-REWRITE RPLUS-REDUCE-ARG1-REWRITE REDUCE-RNEG REDUCE-RMAGNITUDE REDUCE-RQUOTIENT REDUCE-DIFFERENCE REDUCE-RTIMES REDUCE-RPLUS RPLUS-RDIFFERENCE-ARG2 RPLUS-RDIFFERENCE-ARG1 COMMUTATIVITY2-OF-RPLUS ASSOCIATIVITY-OF-RPLUS REQUAL-ASSOCIATIVITY-OF-RPLUS REQUAL-SIMPLE-RPLUS-BRIDGE EQUAL-REQUAL-REWRITE-OFF EQUAL-REQUAL-REWRITE TRANSITIVITY-OF-REQUAL TRANSITIVITY-OF-REQUAL-BRIDGE-OFF TRANSITIVITY-OF-REQUAL-BRIDGE EQUAL-TIMES-BRIDGE4 EQUAL-TIMES-BRIDGE3 EQUAL-TIMES-BRIDGE2 EQUAL-TIMES-BRIDGE1 REQUAL-ASSOCIATIVITY-OF-SIMPLE-RPLUS FIX-RATIONAL-SIMPLE-RPLUS RATIONALP-SIMPLE-RPLUS NEGATIVE-GUTS-INEG FIX-RATIONAL-OF-RATIONALP SIMPLE-RPLUS-FIX-RATIONAL-ARG2 SIMPLE-RPLUS-FIX-RATIONAL-ARG1 NRATIONAL-SIMPLE-RPLUS-ARG2 NRATIONAL-SIMPLE-RPLUS-ARG1 NRATIONAL-RPLUS-ARG2 NRATIONAL-RPLUS-ARG1 MEANS-RATIONALP RATIONALP-MEANS RNEG-RNEG REQUAL-RNEG-RNEG SIMPLE-RNEG-SIMPLE-RNEG RNEG-REDUCE SIMPLE-RNEG-REDUCE REDUCE-0 RATIONAL-INEG-NUMERATOR-REDUCE-BRIDGE NUMBERP-INEG NEGATIVEP-INEG NUMBERP-NUMERATOR-REDUCE REDUCE-NRATIONALP REQUAL-SIMPLE-RPLUS-REDUCE-ARG2 REQUAL-SIMPLE-RPLUS-REDUCE-ARG1 RPLUS-REDUCE-ARG2 RPLUS-REDUCE-ARG1 REQUAL-X-X RPLUS-REQUAL-ARG1-OFF RPLUS-REQUAL-ARG1 COMMUTATIVITY-OF-RPLUS RPLUS-OPEN-UP-OFF RPLUS-OPEN-UP REDUCE-REDUCE REQUAL-REDUCE2 REQUAL-REDUCE1 COMMUTATIVITY-OF-REQUAL REQUAL-REDUCE-REDUCE-EQUAL-OFF REQUAL-REDUCE-REDUCE-EQUAL NEGATIVEP-IF-INTEGERP-AND-NOT-NUMBERP-OFF NUMBERP-IF-INTEGERP-AND-NOT-NEGATIVEP-OFF NEGATIVEP-IF-INTEGERP-AND-NOT-NUMBERP NUMBERP-IF-INTEGERP-AND-NOT-NEGATIVEP EQUAL-TIMES-GCD-BRIDGE1 QUOTIENT-GCD-TIMES-FACT5 QUOTIENT-GCD-TIMES-FACT4 QUOTIENT-GCD-TIMES-FACT3 QUOTIENT-GCD-TIMES-FACT2 QUOTIENT-GCD-TIMES-FACT1 QUOTIENT-GCD-TIMES-FACT EQUAL-TIMES-TIMES-QUOTIENT-ARG2 TIMES-GCD-FACT GCD-REMAINDER-TIMES-FACT1-PROOF IQUOTIENT-OFF1 IREMAINDER-OFF1 IZEROP-OFF1 FIX-INT-OFF1 INEG-OFF1 ITIMES-OFF1 IPLUS-OFF1 IDIFFERENCE-OFF1 ILESSP-OFF1 IDIFFERENCE-IPLUS-CANONICALIZER1-ON GCD-FACTORS-OFF GCD-FACTORS-GIVES-LINEAR-COMBINATION-OFF GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE-OFF DPR-HACK5-OFF DPR-HACK4-OFF DPR-HACK3-OFF DPR-HACK2-OFF DPR-HACK1-OFF REMAINDER-0-SUFFICIENCY-OFF DIVIDES-PRODUCT-REDUCTION REMAINDER-0-SUFFICIENCY DPR-HACK5 DPR-HACK4 DPR-HACK3 DPR-HACK2 DPR-HACK1 GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE IQUOTIENT-ON IREMAINDER-ON GCD-FACTORS-GIVES-LINEAR-COMBINATION GCD-FACTORS IZEROP-ON FIX-INT-ON INTEGERP-ON INEG-ON ITIMES-ON IPLUS-ON IDIFFERENCE-ON ILESSP-ON IDIFFERENCE-IPLUS-CANONICALIZER1-OFF DIVIDES-EACH-EQUALITY GCD-QUOTIENT-QUOTIENT GCD-TIMES2 GCD-TIMES1 GCD-TIMES1-INDUCT GCD-REMAINDER-FACT2 GCD-REMAINDER-FACT1 RATIONAL-GENERALIZATION FIX-RATIONAL-RMAGNITUDE FIX-RATIONAL-RQUOTIENT FIX-RATIONAL-RDIFFERENCE FIX-RATIONAL-RNEG FIX-RATIONAL-RTIMES FIX-RATIONAL-FIX-RATIONAL FIX-RATIONAL-RPLUS FIX-RATIONAL-REDUCE RATIONALP-RMAGNITUDE RATIONALP-RQUOTIENT RATIONALP-RDIFFERENCE RATIONALP-RNEG RATIONALP-RTIMES RATIONALP-FIX-RATIONAL RATIONALP-RPLUS RATIONALP-REDUCE IPLUS-IS-PLUS ITIMES-IS-TIMES EQUAL-INEG-INEG ITIMES-NEGATIVEP-ARG2 ITIMES-NEGATIVEP-ARG1 INTEGERP-IF-NUMBERP INTEGERP-IF-NEGATIVEP-NON-ZERO ITIMES-INEG-ARG2 ITIMES-INEG-ARG1 FIX-INT-ON-INTEGERS INTEGERP-MINUS REQUAL RLESSP RMAGNITUDE SIMPLE-RMAGNITUDE RQUOTIENT RINVERSE SIMPLE-RINVERSE RZEROP RTIMES SIMPLE-RTIMES RDIFFERENCE RNEG SIMPLE-RNEG RPLUS SIMPLE-RPLUS REDUCE FIX-RATIONAL RATIONALP RATIONAL-DEFNS RATIONAL CANCEL-EQUAL-TIMES-PRESERVES-INEQUALITY-BRIDGE-OFF CANCEL-EQUAL-TIMES-PRESERVES-INEQUALITY-OFF EVAL$-EQUAL-TIMES-TREE-BAGDIFF-OFF ZEROP-MAKES-EQUAL-TRUE-BRIDGE-OFF EVAL$-QUOTIENT-TIMES-TREE-BAGDIFF-OFF ZEROP-MAKES-QUOTIENT-ZERO-BRIDGE-OFF ZEROP-MAKES-LESSP-FALSE-BRIDGE-OFF EVAL$-LESSP-TIMES-TREE-BAGDIFF-OFF TIMES-TREE-OF-TIMES-FRINGE-OFF TIMES-TREE-APPEND-OFF ZEROP-MAKES-TIMES-TREE-ZERO2-OFF OR-ZEROP-TREE-IS-NOT-ZEROP-TREE-OFF ZEROP-MAKES-TIMES-TREE-ZERO-OFF EVAL$-TIMES-MEMBER-OFF EQUAL-TIMES-BRIDGE-OFF EQUAL-TIMES-ARG1-OFF STUPID-HACK-OFF LESSP-TIMES-ARG1-OFF BAGDIFF-DELETE-OFF NUMBERP-EVAL$-TIMES-TREE-OFF EVAL$-QUOTIENT2-OFF EVAL$-QUOTIENT-OFF EVAL$-IF2-OFF EVAL$-IF-OFF EVAL$-LESSP2-OFF EVAL$-LESSP-OFF EVAL$-EQUAL-OFF EVAL$-OR2-OFF EVAL$-OR-OFF EVAL$-TIMES2-OFF EVAL$-TIMES-OFF NUMBERP-EVAL$-TIMES-OFF CORRECTNESS-OF-CANCEL-EQUAL-TIMES CANCEL-EQUAL-TIMES-PRESERVES-INEQUALITY-BRIDGE CANCEL-EQUAL-TIMES-PRESERVES-INEQUALITY EVAL$-EQUAL-TIMES-TREE-BAGDIFF ZEROP-MAKES-EQUAL-TRUE-BRIDGE CANCEL-EQUAL-TIMES CORRECTNESS-OF-CANCEL-QUOTIENT-TIMES EVAL$-QUOTIENT-TIMES-TREE-BAGDIFF ZEROP-MAKES-QUOTIENT-ZERO-BRIDGE CANCEL-QUOTIENT-TIMES CORRECTNESS-OF-CANCEL-LESSP-TIMES ZEROP-MAKES-LESSP-FALSE-BRIDGE EVAL$-LESSP-TIMES-TREE-BAGDIFF CANCEL-LESSP-TIMES TIMES-TREE-OF-TIMES-FRINGE TIMES-TREE-APPEND ZEROP-MAKES-TIMES-TREE-ZERO2 OR-ZEROP-TREE-IS-NOT-ZEROP-TREE ZEROP-MAKES-TIMES-TREE-ZERO EVAL$-TIMES-MEMBER EQUAL-TIMES-BRIDGE EQUAL-TIMES-ARG1 STUPID-HACK LESSP-TIMES-ARG1 BAGDIFF-DELETE NUMBERP-EVAL$-TIMES-TREE EVAL$-IF2 EVAL$-IF EVAL$-QUOTIENT2 EVAL$-QUOTIENT EVAL$-LESSP2 EVAL$-LESSP EVAL$-EQUAL EVAL$-OR2 EVAL$-OR EVAL$-TIMES2 EVAL$-TIMES NUMBERP-EVAL$-TIMES AND-NOT-ZEROP-TREE OR-ZEROP-TREE TIMES-FRINGE TIMES-TREE INTEGERS INTEGERP-OFF FIX-INT-OFF IZEROP-OFF ILESSP-OFF ILEQ-OFF IPLUS-OFF INEG-OFF IDIFFERENCE-OFF IABS-OFF ITIMES-OFF CANCEL-IPLUS-OFF INTEGERP-EVAL$-IPLUS-OFF INTEGERP-EVAL$-IPLUS-TREE-OFF INTEGERP-EVAL$-BRIDGE-OFF EVAL$-IPLUS-TREE-APPEND-OFF IPLUS-TREE-IPLUS-FRINGE-OFF IPLUS-TREE-DELETE-OFF IPLUS-TREE-BAGDIFF-OFF NOT-INTEGERP-IMPLIES-NOT-EQUAL-IPLUS-OFF CANCEL-IDIFFERENCE-OFF IQUOTIENT-OFF IREMAINDER-OFF QUOTIENT-DIFFERENCE-LESSP-ARG2-OFF IDIV-OFF IMOD-OFF IQUO-OFF IREM-OFF FIX-INT-IREM FIX-INT-IQUO FIX-INT-IMOD FIX-INT-IDIV FIX-INT-IREMAINDER FIX-INT-IQUOTIENT IREM-FIX-INT2 IREM-FIX-INT1 IQUO-FIX-INT2 IQUO-FIX-INT1 IMOD-FIX-INT2 IMOD-FIX-INT1 IDIV-FIX-INT2 IDIV-FIX-INT1 IREMAINDER-FIX-INT2 IREMAINDER-FIX-INT1 IQUOTIENT-FIX-INT2 IQUOTIENT-FIX-INT1 INTEGERP-IREM INTEGERP-IQUO INTEGERP-IMOD INTEGERP-IDIV INTEGERP-IREMAINDER INTEGERP-IQUOTIENT IQUO-IREM-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART1 IREM IQUO IDIV-IMOD-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART1 IMOD IDIV IQUOTIENT-IREMAINDER-UNIQUENESS QUOTIENT-DIFFERENCE-LESSP-ARG2 DIVISION-THEOREM DIVISION-THEOREM-PART3 DIVISION-THEOREM-PART2 DIVISION-THEOREM-PART1 IREMAINDER IQUOTIENT QUOTIENT-REMAINDER-UNIQUENESS ITIMES-1-ARG1 EQUAL-ITIMES-MINUS-1 EQUAL-ITIMES-1 EQUAL-ITIMES-0 ITIMES-DISTRIBUTES-OVER-IDIFFERENCE ITIMES-DISTRIBUTES-OVER-IDIFFERENCE-PROOF ASSOCIATIVITY-OF-ITIMES COMMUTATIVITY2-OF-ITIMES ITIMES-DISTRIBUTES-OVER-IPLUS ITIMES-DISTRIBUTES-OVER-IPLUS-PROOF COMMUTATIVITY-OF-ITIMES ITIMES-FIX-INT2 ITIMES-FIX-INT1 ITIMES-ZERO2 ITIMES-ZERO1 CORRECTNESS-OF-CANCEL-IDIFFERENCE CANCEL-IDIFFERENCE IPLUS-IDIFFERENCE-IDIFFERENCE CORRECTNESS-OF-CANCEL-IPLUS NOT-INTEGERP-IMPLIES-NOT-EQUAL-IPLUS IPLUS-TREE-BAGDIFF IPLUS-TREE-DELETE IPLUS-TREE-IPLUS-FRINGE EVAL$-IPLUS-TREE-APPEND EVAL$-IPLUS-TREE-APPEND-INDUCTION INTEGERP-EVAL$-BRIDGE INTEGERP-EVAL$-IPLUS-TREE INTEGERP-EVAL$-IPLUS CANCEL-IPLUS IPLUS-TREE IPLUS-FRINGE EQUAL-IDIFFERENCE-0 IDIFFERENCE-CANCELLATION-1 IDIFFERENCE-0 IDIFFERENCE-FIX-INT IDIFFERENCE-IDIFFERENCE IDIFFERENCE-RIGHT-ID IDIFFERENCE-IPLUS IDIFFERENCE-IPLUS-CANONICALIZER1 IDIFFERENCE-X-X IPLUS-IDIFFERENCE-ARG2 IPLUS-IDIFFERENCE-ARG1 IPLUS-FIX-INT2 IPLUS-FIX-INT1 IPLUS-INEG2 IPLUS-INEG1 IPLUS-CANCELLATION ASSOCIATIVITY-OF-IPLUS COMMUTATIVITY-OF-IPLUS COMMUTATIVITY2-OF-IPLUS IPLUS-0 IPLUS-RIGHT-ID IPLUS-LEFT-ID INEG-FIX-INT INEG-IDIFFERENCE INEG-INEG INEG-IPLUS INEG-ID FIX-INT-ITIMES FIX-INT-IABS FIX-INT-INEG FIX-INT-IDIFFERENCE FIX-INT-IPLUS FIX-INT-FIX-INT INTEGERP-ITIMES INTEGERP-IABS INTEGERP-INEG INTEGERP-IDIFFERENCE INTEGERP-IPLUS INTEGERP-FIX-INT ITIMES IABS IDIFFERENCE INEG IPLUS ILEQ ILESSP IZEROP FIX-INT INTEGERP ARITHMETIC GCDS GCD-IDEMPOTENCE GCD-X-X COMMUTATIVITY2-OF-GCD COMMUTATIVITY2-OF-GCD-ZERO-CASE ASSOCIATIVITY-OF-GCD ASSOCIATIVITY-OF-GCD-ZERO-CASE COMMON-DIVISOR-DIVIDES-GCD GCD-IS-THE-GREATEST DISTRIBUTIVITY-OF-TIMES-OVER-GCD DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF REMAINDER-GCD GCD-PLUS-INSTANCE GCD-PLUS GCD-PLUS-PROOF GCD-PLUS-INSTANCE-TEMP GCD-PLUS-INSTANCE-TEMP-PROOF LESSP-GCD EQUAL-GCD-0 GCD-1 GCD-0 SINGLE-NUMBER-INDUCTION COMMUTATIVITY-OF-GCD GCD LOGS LOG-EXP LOG-TIMES-EXP LOG-TIMES-EXP-PROOF LOG-TIMES LOG-TIMES-PROOF LOG-QUOTIENT-EXP LOG-QUOTIENT-TIMES LOG-QUOTIENT-TIMES-PROOF LOG-QUOTIENT LEQ-LOG-LOG DOUBLE-LOG-INDUCTION LOG-1 LOG-0 EQUAL-LOG-0 LOG EXPONENTIATION EXP-DIFFERENCE EQUAL-EXP-1 EQUAL-EXP-0 EXP-EXP EXP-TIMES EXP-0-ARG2 EXP-1-ARG1 EXP-0-ARG1 EXP-PLUS EXP-ADD1 EXP-ZERO QUOTIENTS REMAINDER-EQUALS-ITS-FIRST-ARGUMENT-OFF QUOTIENT-TIMES-INSTANCE-TEMP-OFF LESSP-QUOTIENT QUOTIENT-X-X QUOTIENT-1-ARG1 QUOTIENT-1-ARG1-CASESPLIT QUOTIENT-1-ARG2 LEQ-QUOTIENT QUOTIENT-EXP QUOTIENT-QUOTIENT QUOTIENT-PLUS-TIMES-TIMES-INSTANCE QUOTIENT-PLUS-TIMES-TIMES QUOTIENT-PLUS-TIMES-TIMES-PROOF QUOTIENT-PLUS-FACT QUOTIENT-REMAINDER-INSTANCE QUOTIENT-REMAINDER QUOTIENT-REMAINDER-TIMES REMAINDER-EQUALS-ITS-FIRST-ARGUMENT QUOTIENT-DIFFERENCE3 QUOTIENT-DIFFERENCE2 QUOTIENT-LESSP-ARG1 QUOTIENT-DIFFERENCE1 QUOTIENT-TIMES-TIMES QUOTIENT-TIMES-TIMES-PROOF QUOTIENT-TIMES-INSTANCE QUOTIENT-TIMES QUOTIENT-TIMES-PROOF QUOTIENT-TIMES-INSTANCE-TEMP QUOTIENT-TIMES-INSTANCE-TEMP-PROOF QUOTIENT-PLUS QUOTIENT-PLUS-PROOF QUOTIENT-SUB1 EQUAL-QUOTIENT-0 QUOTIENT-ADD1 QUOTIENT-ZERO QUOTIENT-OF-NON-NUMBER QUOTIENT-NOOP REMAINDERS PLUS-REMAINDER-TIMES-QUOTIENT-OFF EQUAL-REMAINDER-PLUS-REMAINDER-OFF REMAINDER-TIMES-TIMES-OFF REMAINDER-DIFFERENCE3-OFF EQUAL-REMAINDER-DIFFERENCE-0-OFF LESSP-PLUS-FACT-OFF REMAINDER-EXP-EXP DOUBLE-NUMBER-INDUCTION TRANSITIVITY-OF-DIVIDES REMAINDER-X-X REMAINDER-1-ARG2 REMAINDER-1-ARG1 REMAINDER-REMAINDER REMAINDER-EXP REMAINDER-PLUS-TIMES-TIMES-INSTANCE REMAINDER-PLUS-TIMES-TIMES REMAINDER-PLUS-TIMES-TIMES-PROOF REMAINDER-PLUS-FACT LESSP-PLUS-FACT EQUAL-REMAINDER-DIFFERENCE-0 REMAINDER-DIFFERENCE3 REMAINDER-DIFFERENCE2 DOUBLE-REMAINDER-INDUCTION REMAINDER-DIFFERENCE1 REMAINDER-TIMES2-INSTANCE REMAINDER-TIMES2 REMAINDER-TIMES2-PROOF REMAINDER-TIMES-TIMES REMAINDER-TIMES-TIMES-PROOF REMAINDER-TIMES1-INSTANCE REMAINDER-TIMES1-INSTANCE-PROOF REMAINDER-TIMES1 REMAINDER-TIMES1-PROOF EQUAL-REMAINDER-PLUS-REMAINDER EQUAL-REMAINDER-PLUS-REMAINDER-PROOF EQUAL-REMAINDER-PLUS-0 EQUAL-REMAINDER-PLUS-0-PROOF REMAINDER-PLUS REMAINDER-PLUS-PROOF REMAINDER-ADD1 REMAINDER-SUB1 REMAINDER-QUOTIENT-ELIM PLUS-REMAINDER-TIMES-QUOTIENT REMAINDER-ZERO REMAINDER-OF-NON-NUMBER REMAINDER-NOOP LESSP-REMAINDER MULTIPLICATION EQUAL-SUB1-TIMES-0 LESSP-1-TIMES LESSP-PLUS-TIMES2 LESSP-PLUS-TIMES1 LESSP-PLUS-TIMES-PROOF LESSP-TIMES-CANCELLATION2 LESSP-TIMES-CANCELLATION1 LESSP-TIMES-CANCELLATION-PROOF LESSP-TIMES3 LESSP-TIMES3-PROOF2 LESSP-TIMES3-PROOF1 LESSP-TIMES2 LESSP-TIMES2-PROOF LESSP-TIMES1 LESSP-TIMES1-PROOF TIMES-1-ARG1 EQUAL-TIMES-1 EQUAL-TIMES-0 TIMES-QUOTIENT TIMES-QUOTIENT-PROOF TIMES-DISTRIBUTES-OVER-DIFFERENCE TIMES-DISTRIBUTES-OVER-DIFFERENCE-PROOF ASSOCIATIVITY-OF-TIMES COMMUTATIVITY2-OF-TIMES TIMES-DISTRIBUTES-OVER-PLUS TIMES-DISTRIBUTES-OVER-PLUS-PROOF COMMUTATIVITY-OF-TIMES TIMES-SUB1 TIMES-ADD1 TIMES-ZERO EXP ADDITION OPEN-PLUS-OFF PLUS-CANCELLATION-OFF DIFFERENCE-X-X-OFF DIFFERENCE-PLUS-OFF DIFFERENCE-PLUS-CANCELLATION1-OFF DIFFERENCE-PLUS-CANCELLATION2-OFF DIFFERENCE-CANCELLATION-0-OFF DIFFERENCE-CANCELLATION-1-OFF DIFFERENCE-1-OFF DIFFERENCE-2-OFF DIFFERENCE-ADD1-PLUS-CANCELLATION-OFF DIFFERENCE-SUB1-ARG2-OFF DIFFERENCE-DIFFERENCE-ARG1-OFF DIFFERENCE-DIFFERENCE-ARG2-OFF DIFFERENCE-DIFFERENCE-DIFFERENCE-OFF DIFFERENCE-PLUS-CANCELLATION3-OFF NUMBERP-EVAL$-PLUS-OFF NUMBERP-EVAL$-PLUS-TREE-OFF MEMBER-IMPLIES-PLUS-TREE-GREATEREQP-OFF PLUS-TREE-DELETE-OFF SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP-OFF PLUS-TREE-BAGDIFF-OFF NUMBERP-EVAL$-BRIDGE-OFF BRIDGE-TO-SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP-OFF EVAL$-PLUS-TREE-APPEND-OFF PLUS-TREE-PLUS-FRINGE-OFF MEMBER-IMPLIES-NUMBERP-OFF CADR-EVAL$-LIST-OFF EVAL$-QUOTE-OFF LISTP-EVAL$-OFF CANCEL-EQUAL-PLUS-OFF CANCEL-DIFFERENCE-PLUS-OFF LESSP-DIFFERENCE-CANCELLATION-OFF CANCEL-LESSP-PLUS-OFF CORRECTNESS-OF-CANCEL-LESSP-PLUS CANCEL-LESSP-PLUS LESSP-DIFFERENCE LESSP-DIFFERENCE-CANCELLATION DIFF-X-X DIFF-SUB1-ARG2 DIFF-SUB1-ARG2-CASESPLIT DIFF-ADD1-ARG2 DIFF-ADD1-ARG2-CASESPLIT DIFF-DIFF-DIFF DIFF-DIFF-DIFF-CASESPLIT DIFF-DIFF-ARG2 DIFF-DIFF-ARG2-CASESPLIT DIFF-DIFF-ARG1 CORRECTNESS-OF-CANCEL-DIFFERENCE-PLUS CANCEL-DIFFERENCE-PLUS CORRECTNESS-OF-CANCEL-EQUAL-PLUS CANCEL-EQUAL-PLUS LISTP-EVAL$ EVAL$-QUOTE CADR-EVAL$-LIST MEMBER-IMPLIES-NUMBERP PLUS-TREE-PLUS-FRINGE EVAL$-PLUS-TREE-APPEND BRIDGE-TO-SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP NUMBERP-EVAL$-BRIDGE PLUS-TREE-BAGDIFF SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP PLUS-TREE-DELETE MEMBER-IMPLIES-PLUS-TREE-GREATEREQP NUMBERP-EVAL$-PLUS-TREE NUMBERP-EVAL$-PLUS PLUS-TREE PLUS-FRINGE DIFFERENCE-PLUS-CANCELLATION3 DIFFERENCE-DIFFERENCE-DIFFERENCE DIFFERENCE-DIFFERENCE-ARG2 DIFFERENCE-DIFFERENCE-ARG1 DIFFERENCE-SUB1-ARG2 DIFFERENCE-ADD1-PLUS-CANCELLATION DIFFERENCE-2 DIFFERENCE-1 DIFFERENCE-CANCELLATION-1 DIFFERENCE-CANCELLATION-0 DIFFERENCE-PLUS-CANCELLATION2 DIFFERENCE-PLUS-CANCELLATION1 DIFFERENCE-PLUS EQUAL-DIFFERENCE-0 DIFFERENCE-X-X DIFFERENCE-LEQ-ARG1 DIFFERENCE-ELIM PLUS-DIFFERENCE-DIFFERENCE PLUS-DIFFERENCE-DIFFERENCE-CASESPLIT PLUS-DIFFERENCE-ARG2 PLUS-DIFFERENCE-ARG2-CASESPLIT PLUS-DIFFERENCE-ARG1 PLUS-DIFFERENCE-ARG1-CASESPLIT PLUS-CANCELLATION EQUAL-PLUS-1 EQUAL-PLUS-0 ASSOCIATIVITY-OF-PLUS COMMUTATIVITY-OF-PLUS COMMUTATIVITY2-OF-PLUS PLUS-ADD1 PLUS-RIGHT-ID2 PLUS-STOPPER OPEN-PLUS SETS-AND-BAGS SUBBAGP-BAGINT2 SUBBAGP-BAGINT1 SUBBAGP-CDR2 SUBBAGP-CDR1 SUBBAGP-DELETE SETP-PERMUTATION SETP-PERMUTATION-INDUCTION-STEP SETP-PERMUTATION-BASE-CASE SETP-PERMUTATION-INDUCTION SETP-DELETE TRANSITIVITY-OF-PERMUTATION TRANSITIVITY-OF-PERMUTATION-INDUCTION-STEP TRANSITIVITY-OF-PERMUTATION-BASE-CASE TRANSITIVITY-OF-PERMUTATION-INDUCTION PERMUTATION-DELETE-DELETE PERMUTATION-REFLEXIVITY COMMUTATIVITY-OF-PERMUTATION PERMUTATION-RIGHT-CONS PERMUTATION-RIGHT-CONS1 NOT-PERMUTATION MEMBER-BAGINT MEMBER-BAGDIFF PERMUTATION-IMPLIES-MEMBERSHIP-EQUIVALENCE MEMBER-DELETE MEMBER-DELETE-IMPLIES-MEMBERSHIP MEMBER-CONS MEMBER-NON-LIST OCCURRENCES-BAGINT OCCURRENCES-BAGDIFF OCCURRENCES-DELETE OCCURRENCES-CONS OCCURRENCES-IN-A-SET EQUAL-OCCURRENCES-ZERO DELETE-DELETE DELETE-NON-MEMBER LISTP-DELETE SUBBAGP SETP PERMUTATION OCCURRENCES BAGINT BAGDIFF DELETE GROUND-ZERO))) (SETQ LIB-ATOMS-WITH-PROPS (QUOTE (R2 CANCEL-RPLUS-OFF CORRECTNESS-OF-CANCEL-RPLUS-OFF CORRECTNESS-OF-CANCEL-RPLUS *1*CANCEL-RPLUS CANCEL-RPLUS RPLUS-RZEROP-BRIDGE-OFF RPLUS-RZEROP-BRIDGE2-OFF RPLUS-RZEROP-OFF EVAL$-RPLUS-OFF EVAL$-REDUCE-OFF MEMBER-APPEND-OFF DELETE-APPEND-OFF MEMBER-SUBBAGP-OFF OCCURRENCES-DELETE2-OFF OCCURRENCES-APPEND-OFF SUBBAGP-APPEND-OFF SUBBAGP-DELETE-SAME-OFF SUBBAGP-DELETE-SAME-MEANS-OFF SUBBAGP-DELETE-CAR-OFF SUBBAGP-DELETE-CAR2-OFF SUBBAGP-PERMUTATION-OFF PERMUTATION-A-B-OFF NOT-SUBBAGP-NOT-PERMUTATION-OFF SUBBAGP-NECC-OFF SUBBAGP-TRANSITIVE-OFF NOT-MEMBER-MAKE-NEGS-FACT-OFF MAKE-NEGS-DELETE-OFF MAKE-NEGS-BAGDIFF-OFF APPEND-BAGDIFF-ARG1-OFF APPEND-BAGDIFF-ARG2-OFF BAGDIFF-BAGDIFF-OFF MEMBER-RNEG-MAKE-NEGS-OFF SUBBAGP-MAKE-NEGS-OFF RDIFFERENCE-REDUCE-OFF REQUAL-SIMPLE-RPLUS-X-SIMPLE-RNEG-X-OFF REQUAL-RPLUS-X-SIMPLE-RNEG-X-OFF RPLUS-X-RNEG-X-OFF RDIFFERENCE-X-X-OFF RDIFFERENCE-RPLUS-HACK-OFF RDIFFERENCE-RPLUS-HACK2-OFF RPLUS-RDIFFERENCE-HACK-OFF EQUAL-DIFFERENCE-HACK1-OFF EQUAL-DIFFERENCE-HACK2-OFF EQUAL-DIFFERENCE-REWRITE-OFF EQUAL-DIFFERENCE-REWRITE2-OFF EQUAL-TIMES-BRIDGE5-OFF EQUAL-PLUS-DIFFERENCE-REWRITE-OFF LESSP-TIMES-BRIDGE1-OFF EQUAL-DIFFERENCE-OFF REQUAL-SIMPLE-RPLUS-X-X-REWRITE-OFF EQUAL-RPLUS-X-X-REWRITE-OFF EQUAL-RPLUS-RDIFFERENCE-HACK-OFF MEMBER-CAR-X-X-OFF MEMBER-BAGDIFF-APPEND-OFF PERMUTATION-TRANSITIVE-OFF BAGDIFF-X-X-OFF BAGDIFF-APPEND-ARG1-OFF BAGDIFF-CONS-Z-Z-OFF BAGDIFF-NOT-LISTP-OFF BAGDIFF-CAR-IN-OFF LAST-CDR-DELETE-OFF MEMBER-SUBBAGP2-OFF MEMBER-SUBBAGP-DELETE-OFF SUBBAGP-BAGDIFF-OFF PERMUTATION-BAGDIFF-OFF PERMUTATION-APPEND-ARG1-ARG2-BRIDGE-OFF SUBBAGP-TRANSITIVE-BRIDGE-HELPER-OFF SUBBAGP-TRANSITIVE-BRIDGE-OFF EQUAL-PERMUTATION-OFF PERMUTATION-BAGDIFF-APPEND-HELPER-OFF PERMUTATION-BAGDIFF-APPEND-OFF SUBBAGP-APPEND-SIMPLIFY1-OFF SUBBAGP-PERMUTATION-EQUIV-OFF SUBBAGP-APPEND-SIMPLIFY2-OFF SUBBAGP-APPEND-BRIDGE-OFF SUBBAGP-APPEND-BRIDGE2-OFF SUBBAGP-X-X-OFF RNEGS-NOT-CAR-SPLIT-BY-PARITY-OFF PERMUTATION-APPEND-SPLIT-BY-PARITY-BRIDGE-OFF MEMBER-CDR-SPLIT-BY-PARITY-OFF ALL-RNEGS-MAKE-NEGS-BAGINT-FACT-OFF ALL-RNEGS-MAKE-NEGS-BAGINT-OFF BAGINT-ALL-RNEGS-CAR-SPLIT-BY-PARITY-OFF BAGINT-MAKE-NEGS-SPLIT-BY-PARITY-OFF REDUCE-EVAL$-RPLUS-TREE-OFF RPLUS-EVAL$-RPLUS-TREE-OFF EVAL$-RPLUS-TREE-DELETE-OFF PERMUTATION-DOES-NOT-EFFECT-RPLUS-OFF EVAL$-RPLUS-TREE-ZERO-OFF CANCEL-ZERO-FACT-OFF CANCEL-ZERO-FACT-BRIDGE-OFF RNEGS-CANCEL-LIST-OFF CANCELLING-FROM-RPLUS-OFF EVAL$-RPLUS-TREE-RPLUS-FRINGE-OFF COMMUTATIVITY2-OF-RTIMES BAGINT-MAKE-NEGS-SPLIT-BY-PARITY BAGINT-ALL-RNEGS-CAR-SPLIT-BY-PARITY ALL-RNEGS-MAKE-NEGS-BAGINT ALL-RNEGS-MAKE-NEGS-BAGINT-FACT *1*ALL-RNEGS ALL-RNEGS MEMBER-CDR-SPLIT-BY-PARITY PERMUTATION-APPEND-SPLIT-BY-PARITY-BRIDGE RNEGS-NOT-CAR-SPLIT-BY-PARITY SUBBAGP-X-X EVAL$-RPLUS-TREE-RPLUS-FRINGE CANCELLING-FROM-RPLUS SUBBAGP-APPEND-BRIDGE2 SUBBAGP-APPEND-BRIDGE SUBBAGP-APPEND-SIMPLIFY2 SUBBAGP-PERMUTATION-EQUIV SUBBAGP-APPEND-SIMPLIFY1 RNEGS-CANCEL-LIST CANCEL-ZERO-FACT-BRIDGE PERMUTATION-BAGDIFF-APPEND PERMUTATION-BAGDIFF-APPEND-HELPER EQUAL-PERMUTATION SUBBAGP-TRANSITIVE-BRIDGE SUBBAGP-TRANSITIVE-BRIDGE-HELPER PERMUTATION-APPEND-ARG1-ARG2-BRIDGE PERMUTATION-BAGDIFF SUBBAGP-BAGDIFF MEMBER-SUBBAGP-DELETE MEMBER-SUBBAGP2 LAST-CDR-DELETE BAGDIFF-CAR-IN BAGDIFF-NOT-LISTP BAGDIFF-CONS-Z-Z BAGDIFF-APPEND-ARG1 BAGDIFF-X-X *1*LAST-CDR LAST-CDR PERMUTATION-TRANSITIVE MEMBER-BAGDIFF-APPEND MEMBER-CAR-X-X CANCEL-ZERO-FACT EVAL$-RPLUS-TREE-ZERO PERMUTATION-DOES-NOT-EFFECT-RPLUS EVAL$-RPLUS-TREE-DELETE EQUAL-RPLUS-RDIFFERENCE-HACK EQUAL-RPLUS-X-X-REWRITE REQUAL-SIMPLE-RPLUS-X-X-REWRITE EQUAL-DIFFERENCE LESSP-TIMES-BRIDGE1 EQUAL-PLUS-DIFFERENCE-REWRITE EQUAL-TIMES-BRIDGE5 EQUAL-DIFFERENCE-REWRITE2 EQUAL-DIFFERENCE-REWRITE EQUAL-DIFFERENCE-HACK2 EQUAL-DIFFERENCE-HACK1 RPLUS-RDIFFERENCE-HACK RDIFFERENCE-RPLUS-HACK2 RDIFFERENCE-RPLUS-HACK RDIFFERENCE-X-X RPLUS-X-RNEG-X REQUAL-RPLUS-X-SIMPLE-RNEG-X REQUAL-SIMPLE-RPLUS-X-SIMPLE-RNEG-X RDIFFERENCE-REDUCE SUBBAGP-MAKE-NEGS MEMBER-RNEG-MAKE-NEGS BAGDIFF-BAGDIFF APPEND-BAGDIFF-ARG2 APPEND-BAGDIFF-ARG1 MAKE-NEGS-BAGDIFF MAKE-NEGS-DELETE NOT-MEMBER-MAKE-NEGS-FACT SUBBAGP-TRANSITIVE SUBBAGP-NECC PERMUTATION-AS-SUBBAGP-OFF PERMUTATION-AS-SUBBAGP-HELPER-OFF PERMUTATION-AS-SUBBAGP PERMUTATION-AS-SUBBAGP-HELPER NOT-SUBBAGP-NOT-PERMUTATION PERMUTATION-A-B SUBBAGP-PERMUTATION SUBBAGP-DELETE-CAR2 SUBBAGP-DELETE-CAR SUBBAGP-DELETE-SAME-MEANS SUBBAGP-DELETE-SAME SUBBAGP-WIT-LEMMA-OFF MEMBER-OCCUR-OFF SUBBAGP-APPEND OCCURRENCES-APPEND SUBBAGP-WIT-LEMMA OCCURRENCES-DELETE2 MEMBER-OCCUR *1*BADGUY BADGUY MEMBER-SUBBAGP DELETE-APPEND MEMBER-APPEND RPLUS-EVAL$-RPLUS-TREE REDUCE-EVAL$-RPLUS-TREE EVAL$-REDUCE EVAL$-RPLUS RPLUS-RZEROP RPLUS-RZEROP-BRIDGE2 RPLUS-RZEROP-BRIDGE *1*MAKE-NEGS MAKE-NEGS *1*SPLIT-BY-PARITY SPLIT-BY-PARITY *1*RPLUS-FRINGE RPLUS-FRINGE *1*RPLUS-TREE RPLUS-TREE R1 RATIONALP-OFF FIX-RATIONAL-OFF REDUCE-OFF SIMPLE-RPLUS-OFF RPLUS-OFF SIMPLE-RNEG-OFF RNEG-OFF RDIFFERENCE-OFF SIMPLE-RTIMES-OFF RTIMES-OFF RQUOTIENT-OFF SIMPLE-RMAGNITUDE-OFF RMAGNITUDE-OFF RLESSP-OFF REQUAL-OFF INTEGERP-MINUS-OFF FIX-INT-ON-INTEGERS-OFF ITIMES-INEG-ARG1-OFF ITIMES-INEG-ARG2-OFF INTEGERP-IF-NEGATIVEP-NON-ZERO-OFF INTEGERP-IF-NUMBERP-OFF ITIMES-NEGATIVEP-ARG1-OFF ITIMES-NEGATIVEP-ARG2-OFF EQUAL-INEG-INEG-OFF ITIMES-IS-TIMES-OFF IPLUS-IS-PLUS-OFF RATIONALP-REDUCE-OFF RATIONALP-RPLUS-OFF RATIONALP-FIX-RATIONAL-OFF RATIONALP-RTIMES-OFF RATIONALP-RNEG-OFF RATIONALP-RDIFFERENCE-OFF RATIONALP-RQUOTIENT-OFF RATIONALP-RMAGNITUDE-OFF FIX-RATIONAL-REDUCE-OFF FIX-RATIONAL-RPLUS-OFF FIX-RATIONAL-FIX-RATIONAL-OFF FIX-RATIONAL-RTIMES-OFF FIX-RATIONAL-RNEG-OFF FIX-RATIONAL-RDIFFERENCE-OFF FIX-RATIONAL-RQUOTIENT-OFF FIX-RATIONAL-RMAGNITUDE-OFF RATIONAL-GENERALIZATION-OFF GCD-REMAINDER-FACT1-OFF GCD-REMAINDER-FACT2-OFF GCD-TIMES1-INDUCT-OFF GCD-TIMES1-OFF GCD-TIMES2-OFF GCD-QUOTIENT-QUOTIENT-OFF DIVIDES-EACH-EQUALITY-OFF GCD-FACTORS-OFF1 GCD-FACTORS-GIVES-LINEAR-COMBINATION-OFF1 GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE-OFF1 DPR-HACK1-OFF1 DPR-HACK2-OFF1 DPR-HACK3-OFF1 DPR-HACK4-OFF1 DPR-HACK5-OFF1 REMAINDER-0-SUFFICIENCY-OFF1 DIVIDES-PRODUCT-REDUCTION-OFF GCD-REMAINDER-TIMES-FACT1-PROOF-OFF TIMES-GCD-FACT-OFF EQUAL-TIMES-TIMES-QUOTIENT-ARG2-OFF QUOTIENT-GCD-TIMES-FACT-OFF QUOTIENT-GCD-TIMES-FACT1-OFF QUOTIENT-GCD-TIMES-FACT2-OFF QUOTIENT-GCD-TIMES-FACT3-OFF QUOTIENT-GCD-TIMES-FACT4-OFF QUOTIENT-GCD-TIMES-FACT5-OFF EQUAL-TIMES-GCD-BRIDGE1-OFF NUMBERP-IF-INTEGERP-AND-NOT-NEGATIVEP-OFF1 NEGATIVEP-IF-INTEGERP-AND-NOT-NUMBERP-OFF1 REQUAL-REDUCE-REDUCE-EQUAL-OFF1 COMMUTATIVITY-OF-REQUAL-OFF REQUAL-REDUCE1-OFF REQUAL-REDUCE2-OFF REDUCE-REDUCE-OFF RPLUS-OPEN-UP-OFF1 COMMUTATIVITY-OF-RPLUS-OFF RPLUS-REQUAL-ARG1-OFF1 REQUAL-X-X-OFF RPLUS-REDUCE-ARG1-OFF RPLUS-REDUCE-ARG2-OFF REQUAL-SIMPLE-RPLUS-REDUCE-ARG1-OFF REQUAL-SIMPLE-RPLUS-REDUCE-ARG2-OFF REDUCE-NRATIONALP-OFF NUMBERP-NUMERATOR-REDUCE-OFF NEGATIVEP-INEG-OFF NUMBERP-INEG-OFF RATIONAL-INEG-NUMERATOR-REDUCE-BRIDGE-OFF REDUCE-0-OFF SIMPLE-RNEG-REDUCE-OFF RNEG-REDUCE-OFF SIMPLE-RNEG-SIMPLE-RNEG-OFF REQUAL-RNEG-RNEG-OFF RNEG-RNEG-OFF RATIONALP-MEANS-OFF MEANS-RATIONALP-OFF NRATIONAL-RPLUS-ARG1-OFF NRATIONAL-RPLUS-ARG2-OFF NRATIONAL-SIMPLE-RPLUS-ARG1-OFF NRATIONAL-SIMPLE-RPLUS-ARG2-OFF SIMPLE-RPLUS-FIX-RATIONAL-ARG1-OFF SIMPLE-RPLUS-FIX-RATIONAL-ARG2-OFF FIX-RATIONAL-OF-RATIONALP-OFF NEGATIVE-GUTS-INEG-OFF RATIONALP-SIMPLE-RPLUS-OFF FIX-RATIONAL-SIMPLE-RPLUS-OFF REQUAL-ASSOCIATIVITY-OF-SIMPLE-RPLUS-OFF EQUAL-TIMES-BRIDGE1-OFF EQUAL-TIMES-BRIDGE2-OFF EQUAL-TIMES-BRIDGE3-OFF EQUAL-TIMES-BRIDGE4-OFF TRANSITIVITY-OF-REQUAL-BRIDGE-OFF1 TRANSITIVITY-OF-REQUAL-OFF EQUAL-REQUAL-REWRITE-OFF1 REQUAL-SIMPLE-RPLUS-BRIDGE-OFF REQUAL-ASSOCIATIVITY-OF-RPLUS-OFF ASSOCIATIVITY-OF-RPLUS-OFF COMMUTATIVITY2-OF-RPLUS-OFF RPLUS-RDIFFERENCE-ARG1-OFF RPLUS-RDIFFERENCE-ARG2-OFF REDUCE-RPLUS-OFF REDUCE-RTIMES-OFF REDUCE-DIFFERENCE-OFF REDUCE-RQUOTIENT-OFF REDUCE-RMAGNITUDE-OFF REDUCE-RNEG-OFF RPLUS-REDUCE-ARG1-REWRITE-OFF RPLUS-REDUCE-ARG2-REWRITE-OFF REQUAL-RNEG-SIMPLE-RPLUS-OFF REQUAL-RPLUS-RNEG-OFF RNEG-RPLUS-OFF RDIFFERENCE-RDIFFERENCE-ARG1-OFF RDIFFERENCE-RDIFFERENCE-ARG2-OFF RPLUS-RNEG-ARG1-OFF RPLUS-RNEG-ARG2-OFF COMMUTATIVITY-OF-SIMPLE-RTIMES-OFF COMMUTATIVITY-OF-RTIMES-OFF RZEROP-OFF SIMPLE-RTIMES-RZEROP-OFF ASSOCIATIVITY-OF-SIMPLE-RTIMES-WHEN-NOT-RZEROP-OFF NUMERATOR-ZERO-RZEROP-BRIDGE-OFF ASSOCIATIVITY-OF-SIMPLE-RTIMES-OFF REQUAL-SIMPLE-RTIMES-REQUAL-ARG1-OFF REQUAL-SIMPLE-RTIMES-REQUAL-ARG2-OFF REQUAL-SIMPLE-RTIMES-REDUCE-ARG1-OFF REQUAL-SIMPLE-RTIMES-REDUCE-ARG2-OFF REQUAL-SIMPLE-RTIMES-BRIDGE-OFF REQUAL-ASSOCIATIVITY-OF-RTIMES-OFF ASSOCIATIVITY-OF-RTIMES-OFF SIMPLE-RPLUS-RZEROP-OFF NUMERATOR-TYPE-OFF RATIONALP-SIMPLE-RTIMES-OFF FIX-RATIONAL-SIMPLE-RTIMES-OFF REQUAL-SIMPLE-RTIMES-SIMPLE-RPLUS-WHEN-NOT-RZEROP-OFF REQUAL-RZEROP-SIMPLE-RPLUS-OFF COMMUTATIVITY-OF-SIMPLE-RPLUS-OFF SIMPLE-RPLUS-BRIDGE-OFF REQUAL-SIMPLE-RTIMES-SIMPLE-RPLUS-ARG1-OFF REQUAL-RTIMES-RPLUS-BRIDGE-OFF RTIMES-RPLUS-ARG1-OFF RTIMES-RPLUS-ARG2-OFF REQUAL-SIMPLE-RTIMES-SIMPLE-RNEG-OFF REQUAL-RTIMES-RNEG-OFF RTIMES-RNEG-ARG1-OFF RTIMES-RNEG-ARG2-OFF RTIMES-RDIFFERENCE-ARG1-OFF RTIMES-RDIFFERENCE-ARG2-OFF RNEG-RDIFFERENCE-OFF RDIFFERENCE-RNEG-ARG2-OFF RDIFFERENCE-RNEG-ARG2 RNEG-RDIFFERENCE RTIMES-RDIFFERENCE-ARG2 RTIMES-RDIFFERENCE-ARG1 RTIMES-RNEG-ARG2 RTIMES-RNEG-ARG1 REQUAL-RTIMES-RNEG REQUAL-SIMPLE-RTIMES-SIMPLE-RNEG RTIMES-RPLUS-ARG2 RTIMES-RPLUS-ARG1 REQUAL-RTIMES-RPLUS-BRIDGE REQUAL-SIMPLE-RTIMES-SIMPLE-RPLUS-ARG1 SIMPLE-RPLUS-BRIDGE COMMUTATIVITY-OF-SIMPLE-RPLUS REQUAL-RZEROP-SIMPLE-RPLUS REQUAL-SIMPLE-RTIMES-SIMPLE-RPLUS-WHEN-NOT-RZEROP FIX-RATIONAL-SIMPLE-RTIMES RATIONALP-SIMPLE-RTIMES NUMERATOR-TYPE SIMPLE-RPLUS-RZEROP ASSOCIATIVITY-OF-RTIMES REQUAL-ASSOCIATIVITY-OF-RTIMES REQUAL-SIMPLE-RTIMES-BRIDGE REQUAL-SIMPLE-RTIMES-REDUCE-ARG2 REQUAL-SIMPLE-RTIMES-REDUCE-ARG1 REQUAL-SIMPLE-RTIMES-REQUAL-ARG2 REQUAL-SIMPLE-RTIMES-REQUAL-ARG1 ASSOCIATIVITY-OF-SIMPLE-RTIMES NUMERATOR-ZERO-RZEROP-BRIDGE ASSOCIATIVITY-OF-SIMPLE-RTIMES-WHEN-NOT-RZEROP SIMPLE-RTIMES-RZEROP COMMUTATIVITY-OF-RTIMES COMMUTATIVITY-OF-SIMPLE-RTIMES RPLUS-RNEG-ARG2 RPLUS-RNEG-ARG1 RDIFFERENCE-RDIFFERENCE-ARG2 RDIFFERENCE-RDIFFERENCE-ARG1 RNEG-RPLUS REQUAL-RPLUS-RNEG REQUAL-RNEG-SIMPLE-RPLUS RPLUS-REDUCE-ARG2-REWRITE RPLUS-REDUCE-ARG1-REWRITE REDUCE-RNEG REDUCE-RMAGNITUDE REDUCE-RQUOTIENT REDUCE-DIFFERENCE REDUCE-RTIMES REDUCE-RPLUS RPLUS-RDIFFERENCE-ARG2 RPLUS-RDIFFERENCE-ARG1 COMMUTATIVITY2-OF-RPLUS ASSOCIATIVITY-OF-RPLUS REQUAL-ASSOCIATIVITY-OF-RPLUS REQUAL-SIMPLE-RPLUS-BRIDGE EQUAL-REQUAL-REWRITE-OFF EQUAL-REQUAL-REWRITE TRANSITIVITY-OF-REQUAL TRANSITIVITY-OF-REQUAL-BRIDGE-OFF TRANSITIVITY-OF-REQUAL-BRIDGE EQUAL-TIMES-BRIDGE4 EQUAL-TIMES-BRIDGE3 EQUAL-TIMES-BRIDGE2 EQUAL-TIMES-BRIDGE1 REQUAL-ASSOCIATIVITY-OF-SIMPLE-RPLUS FIX-RATIONAL-SIMPLE-RPLUS RATIONALP-SIMPLE-RPLUS NEGATIVE-GUTS-INEG FIX-RATIONAL-OF-RATIONALP SIMPLE-RPLUS-FIX-RATIONAL-ARG2 SIMPLE-RPLUS-FIX-RATIONAL-ARG1 NRATIONAL-SIMPLE-RPLUS-ARG2 NRATIONAL-SIMPLE-RPLUS-ARG1 NRATIONAL-RPLUS-ARG2 NRATIONAL-RPLUS-ARG1 MEANS-RATIONALP RATIONALP-MEANS RNEG-RNEG REQUAL-RNEG-RNEG SIMPLE-RNEG-SIMPLE-RNEG RNEG-REDUCE SIMPLE-RNEG-REDUCE REDUCE-0 RATIONAL-INEG-NUMERATOR-REDUCE-BRIDGE NUMBERP-INEG NEGATIVEP-INEG NUMBERP-NUMERATOR-REDUCE REDUCE-NRATIONALP REQUAL-SIMPLE-RPLUS-REDUCE-ARG2 REQUAL-SIMPLE-RPLUS-REDUCE-ARG1 RPLUS-REDUCE-ARG2 RPLUS-REDUCE-ARG1 REQUAL-X-X RPLUS-REQUAL-ARG1-OFF RPLUS-REQUAL-ARG1 COMMUTATIVITY-OF-RPLUS RPLUS-OPEN-UP-OFF RPLUS-OPEN-UP REDUCE-REDUCE REQUAL-REDUCE2 REQUAL-REDUCE1 COMMUTATIVITY-OF-REQUAL REQUAL-REDUCE-REDUCE-EQUAL-OFF REQUAL-REDUCE-REDUCE-EQUAL NEGATIVEP-IF-INTEGERP-AND-NOT-NUMBERP-OFF NUMBERP-IF-INTEGERP-AND-NOT-NEGATIVEP-OFF NEGATIVEP-IF-INTEGERP-AND-NOT-NUMBERP NUMBERP-IF-INTEGERP-AND-NOT-NEGATIVEP EQUAL-TIMES-GCD-BRIDGE1 QUOTIENT-GCD-TIMES-FACT5 QUOTIENT-GCD-TIMES-FACT4 QUOTIENT-GCD-TIMES-FACT3 QUOTIENT-GCD-TIMES-FACT2 QUOTIENT-GCD-TIMES-FACT1 QUOTIENT-GCD-TIMES-FACT EQUAL-TIMES-TIMES-QUOTIENT-ARG2 TIMES-GCD-FACT GCD-REMAINDER-TIMES-FACT1-PROOF IQUOTIENT-OFF1 IREMAINDER-OFF1 IZEROP-OFF1 FIX-INT-OFF1 INEG-OFF1 ITIMES-OFF1 IPLUS-OFF1 IDIFFERENCE-OFF1 ILESSP-OFF1 IDIFFERENCE-IPLUS-CANONICALIZER1-ON GCD-FACTORS-OFF GCD-FACTORS-GIVES-LINEAR-COMBINATION-OFF GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE-OFF DPR-HACK5-OFF DPR-HACK4-OFF DPR-HACK3-OFF DPR-HACK2-OFF DPR-HACK1-OFF REMAINDER-0-SUFFICIENCY-OFF DIVIDES-PRODUCT-REDUCTION REMAINDER-0-SUFFICIENCY DPR-HACK5 DPR-HACK4 DPR-HACK3 DPR-HACK2 DPR-HACK1 GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE IQUOTIENT-ON IREMAINDER-ON GCD-FACTORS-GIVES-LINEAR-COMBINATION *1*GCD-FACTORS GCD-FACTORS IZEROP-ON FIX-INT-ON INTEGERP-ON INEG-ON ITIMES-ON IPLUS-ON IDIFFERENCE-ON ILESSP-ON IDIFFERENCE-IPLUS-CANONICALIZER1-OFF DIVIDES-EACH-EQUALITY GCD-QUOTIENT-QUOTIENT GCD-TIMES2 GCD-TIMES1 *1*GCD-TIMES1-INDUCT GCD-TIMES1-INDUCT GCD-REMAINDER-FACT2 GCD-REMAINDER-FACT1 RATIONAL-GENERALIZATION FIX-RATIONAL-RMAGNITUDE FIX-RATIONAL-RQUOTIENT FIX-RATIONAL-RDIFFERENCE FIX-RATIONAL-RNEG FIX-RATIONAL-RTIMES FIX-RATIONAL-FIX-RATIONAL FIX-RATIONAL-RPLUS FIX-RATIONAL-REDUCE RATIONALP-RMAGNITUDE RATIONALP-RQUOTIENT RATIONALP-RDIFFERENCE RATIONALP-RNEG RATIONALP-RTIMES RATIONALP-FIX-RATIONAL RATIONALP-RPLUS RATIONALP-REDUCE IPLUS-IS-PLUS ITIMES-IS-TIMES EQUAL-INEG-INEG ITIMES-NEGATIVEP-ARG2 ITIMES-NEGATIVEP-ARG1 INTEGERP-IF-NUMBERP INTEGERP-IF-NEGATIVEP-NON-ZERO ITIMES-INEG-ARG2 ITIMES-INEG-ARG1 FIX-INT-ON-INTEGERS INTEGERP-MINUS *1*REQUAL REQUAL *1*RLESSP RLESSP *1*RMAGNITUDE RMAGNITUDE *1*SIMPLE-RMAGNITUDE SIMPLE-RMAGNITUDE *1*RQUOTIENT RQUOTIENT *1*RINVERSE RINVERSE *1*SIMPLE-RINVERSE SIMPLE-RINVERSE *1*RZEROP RZEROP *1*RTIMES RTIMES *1*SIMPLE-RTIMES SIMPLE-RTIMES *1*RDIFFERENCE RDIFFERENCE *1*RNEG RNEG *1*SIMPLE-RNEG SIMPLE-RNEG *1*RPLUS RPLUS *1*SIMPLE-RPLUS SIMPLE-RPLUS *1*REDUCE REDUCE *1*FIX-RATIONAL FIX-RATIONAL *1*RATIONALP RATIONALP RATIONAL-DEFNS COUNT-RATIONAL NUMERATOR-DENOMINATOR-ELIM RATIONAL-NUMERATOR-DENOMINATOR RATIONAL-EQUAL DENOMINATOR-LESSEQP DENOMINATOR-LESSP DENOMINATOR-TYPE-RESTRICTION DENOMINATOR-NRATIONAL-FORMP DENOMINATOR-RATIONAL NUMERATOR-LESSEQP NUMERATOR-LESSP NUMERATOR-TYPE-RESTRICTION NUMERATOR-NRATIONAL-FORMP NUMERATOR-RATIONAL *1*RATIONAL *1*DENOMINATOR DENOMINATOR *1*NUMERATOR NUMERATOR *1*RATIONAL-FORMP RATIONAL-FORMP RATIONAL CANCEL-EQUAL-TIMES-PRESERVES-INEQUALITY-BRIDGE-OFF CANCEL-EQUAL-TIMES-PRESERVES-INEQUALITY-OFF EVAL$-EQUAL-TIMES-TREE-BAGDIFF-OFF ZEROP-MAKES-EQUAL-TRUE-BRIDGE-OFF EVAL$-QUOTIENT-TIMES-TREE-BAGDIFF-OFF ZEROP-MAKES-QUOTIENT-ZERO-BRIDGE-OFF ZEROP-MAKES-LESSP-FALSE-BRIDGE-OFF EVAL$-LESSP-TIMES-TREE-BAGDIFF-OFF TIMES-TREE-OF-TIMES-FRINGE-OFF TIMES-TREE-APPEND-OFF ZEROP-MAKES-TIMES-TREE-ZERO2-OFF OR-ZEROP-TREE-IS-NOT-ZEROP-TREE-OFF ZEROP-MAKES-TIMES-TREE-ZERO-OFF EVAL$-TIMES-MEMBER-OFF EQUAL-TIMES-BRIDGE-OFF EQUAL-TIMES-ARG1-OFF STUPID-HACK-OFF LESSP-TIMES-ARG1-OFF BAGDIFF-DELETE-OFF NUMBERP-EVAL$-TIMES-TREE-OFF EVAL$-QUOTIENT2-OFF EVAL$-QUOTIENT-OFF EVAL$-IF2-OFF EVAL$-IF-OFF EVAL$-LESSP2-OFF EVAL$-LESSP-OFF EVAL$-EQUAL-OFF EVAL$-OR2-OFF EVAL$-OR-OFF EVAL$-TIMES2-OFF EVAL$-TIMES-OFF NUMBERP-EVAL$-TIMES-OFF CORRECTNESS-OF-CANCEL-EQUAL-TIMES CANCEL-EQUAL-TIMES-PRESERVES-INEQUALITY-BRIDGE CANCEL-EQUAL-TIMES-PRESERVES-INEQUALITY EVAL$-EQUAL-TIMES-TREE-BAGDIFF ZEROP-MAKES-EQUAL-TRUE-BRIDGE *1*CANCEL-EQUAL-TIMES CANCEL-EQUAL-TIMES CORRECTNESS-OF-CANCEL-QUOTIENT-TIMES EVAL$-QUOTIENT-TIMES-TREE-BAGDIFF ZEROP-MAKES-QUOTIENT-ZERO-BRIDGE *1*CANCEL-QUOTIENT-TIMES CANCEL-QUOTIENT-TIMES CORRECTNESS-OF-CANCEL-LESSP-TIMES ZEROP-MAKES-LESSP-FALSE-BRIDGE EVAL$-LESSP-TIMES-TREE-BAGDIFF *1*CANCEL-LESSP-TIMES CANCEL-LESSP-TIMES TIMES-TREE-OF-TIMES-FRINGE TIMES-TREE-APPEND ZEROP-MAKES-TIMES-TREE-ZERO2 OR-ZEROP-TREE-IS-NOT-ZEROP-TREE ZEROP-MAKES-TIMES-TREE-ZERO EVAL$-TIMES-MEMBER EQUAL-TIMES-BRIDGE EQUAL-TIMES-ARG1 STUPID-HACK LESSP-TIMES-ARG1 BAGDIFF-DELETE NUMBERP-EVAL$-TIMES-TREE EVAL$-IF2 EVAL$-IF EVAL$-QUOTIENT2 EVAL$-QUOTIENT EVAL$-LESSP2 EVAL$-LESSP EVAL$-EQUAL EVAL$-OR2 EVAL$-OR EVAL$-TIMES2 EVAL$-TIMES NUMBERP-EVAL$-TIMES *1*AND-NOT-ZEROP-TREE AND-NOT-ZEROP-TREE *1*OR-ZEROP-TREE OR-ZEROP-TREE *1*TIMES-FRINGE TIMES-FRINGE *1*TIMES-TREE TIMES-TREE INTEGERS INTEGERP-OFF FIX-INT-OFF IZEROP-OFF ILESSP-OFF ILEQ-OFF IPLUS-OFF INEG-OFF IDIFFERENCE-OFF IABS-OFF ITIMES-OFF CANCEL-IPLUS-OFF INTEGERP-EVAL$-IPLUS-OFF INTEGERP-EVAL$-IPLUS-TREE-OFF INTEGERP-EVAL$-BRIDGE-OFF EVAL$-IPLUS-TREE-APPEND-OFF IPLUS-TREE-IPLUS-FRINGE-OFF IPLUS-TREE-DELETE-OFF IPLUS-TREE-BAGDIFF-OFF NOT-INTEGERP-IMPLIES-NOT-EQUAL-IPLUS-OFF CANCEL-IDIFFERENCE-OFF IQUOTIENT-OFF IREMAINDER-OFF QUOTIENT-DIFFERENCE-LESSP-ARG2-OFF IDIV-OFF IMOD-OFF IQUO-OFF IREM-OFF FIX-INT-IREM FIX-INT-IQUO FIX-INT-IMOD FIX-INT-IDIV FIX-INT-IREMAINDER FIX-INT-IQUOTIENT IREM-FIX-INT2 IREM-FIX-INT1 IQUO-FIX-INT2 IQUO-FIX-INT1 IMOD-FIX-INT2 IMOD-FIX-INT1 IDIV-FIX-INT2 IDIV-FIX-INT1 IREMAINDER-FIX-INT2 IREMAINDER-FIX-INT1 IQUOTIENT-FIX-INT2 IQUOTIENT-FIX-INT1 INTEGERP-IREM INTEGERP-IQUO INTEGERP-IMOD INTEGERP-IDIV INTEGERP-IREMAINDER INTEGERP-IQUOTIENT IQUO-IREM-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART1 *1*IREM IREM *1*IQUO IQUO IDIV-IMOD-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART1 *1*IMOD IMOD *1*IDIV IDIV IQUOTIENT-IREMAINDER-UNIQUENESS QUOTIENT-DIFFERENCE-LESSP-ARG2 DIVISION-THEOREM DIVISION-THEOREM-PART3 DIVISION-THEOREM-PART2 DIVISION-THEOREM-PART1 *1*IREMAINDER IREMAINDER *1*IQUOTIENT IQUOTIENT QUOTIENT-REMAINDER-UNIQUENESS ITIMES-1-ARG1 EQUAL-ITIMES-MINUS-1 EQUAL-ITIMES-1 EQUAL-ITIMES-0 ITIMES-DISTRIBUTES-OVER-IDIFFERENCE ITIMES-DISTRIBUTES-OVER-IDIFFERENCE-PROOF ASSOCIATIVITY-OF-ITIMES COMMUTATIVITY2-OF-ITIMES ITIMES-DISTRIBUTES-OVER-IPLUS ITIMES-DISTRIBUTES-OVER-IPLUS-PROOF COMMUTATIVITY-OF-ITIMES ITIMES-FIX-INT2 ITIMES-FIX-INT1 ITIMES-ZERO2 ITIMES-ZERO1 CORRECTNESS-OF-CANCEL-IDIFFERENCE *1*CANCEL-IDIFFERENCE CANCEL-IDIFFERENCE IPLUS-IDIFFERENCE-IDIFFERENCE CORRECTNESS-OF-CANCEL-IPLUS NOT-INTEGERP-IMPLIES-NOT-EQUAL-IPLUS IPLUS-TREE-BAGDIFF IPLUS-TREE-DELETE IPLUS-TREE-IPLUS-FRINGE EVAL$-IPLUS-TREE-APPEND *1*EVAL$-IPLUS-TREE-APPEND-INDUCTION EVAL$-IPLUS-TREE-APPEND-INDUCTION INTEGERP-EVAL$-BRIDGE INTEGERP-EVAL$-IPLUS-TREE INTEGERP-EVAL$-IPLUS *1*CANCEL-IPLUS CANCEL-IPLUS *1*IPLUS-TREE IPLUS-TREE *1*IPLUS-FRINGE IPLUS-FRINGE EQUAL-IDIFFERENCE-0 IDIFFERENCE-CANCELLATION-1 IDIFFERENCE-0 IDIFFERENCE-FIX-INT IDIFFERENCE-IDIFFERENCE IDIFFERENCE-RIGHT-ID IDIFFERENCE-IPLUS IDIFFERENCE-IPLUS-CANONICALIZER1 IDIFFERENCE-X-X IPLUS-IDIFFERENCE-ARG2 IPLUS-IDIFFERENCE-ARG1 IPLUS-FIX-INT2 IPLUS-FIX-INT1 IPLUS-INEG2 IPLUS-INEG1 IPLUS-CANCELLATION ASSOCIATIVITY-OF-IPLUS COMMUTATIVITY-OF-IPLUS COMMUTATIVITY2-OF-IPLUS IPLUS-0 IPLUS-RIGHT-ID IPLUS-LEFT-ID INEG-FIX-INT INEG-IDIFFERENCE INEG-INEG INEG-IPLUS INEG-ID FIX-INT-ITIMES FIX-INT-IABS FIX-INT-INEG FIX-INT-IDIFFERENCE FIX-INT-IPLUS FIX-INT-FIX-INT INTEGERP-ITIMES INTEGERP-IABS INTEGERP-INEG INTEGERP-IDIFFERENCE INTEGERP-IPLUS INTEGERP-FIX-INT *1*ITIMES ITIMES *1*IABS IABS *1*IDIFFERENCE IDIFFERENCE *1*INEG INEG *1*IPLUS IPLUS *1*ILEQ ILEQ *1*ILESSP ILESSP *1*IZEROP IZEROP *1*FIX-INT FIX-INT *1*INTEGERP INTEGERP ARITHMETIC GCDS GCD-IDEMPOTENCE GCD-X-X COMMUTATIVITY2-OF-GCD COMMUTATIVITY2-OF-GCD-ZERO-CASE ASSOCIATIVITY-OF-GCD ASSOCIATIVITY-OF-GCD-ZERO-CASE COMMON-DIVISOR-DIVIDES-GCD GCD-IS-THE-GREATEST DISTRIBUTIVITY-OF-TIMES-OVER-GCD DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF REMAINDER-GCD GCD-PLUS-INSTANCE GCD-PLUS GCD-PLUS-PROOF GCD-PLUS-INSTANCE-TEMP GCD-PLUS-INSTANCE-TEMP-PROOF LESSP-GCD EQUAL-GCD-0 GCD-1 GCD-0 *1*SINGLE-NUMBER-INDUCTION SINGLE-NUMBER-INDUCTION COMMUTATIVITY-OF-GCD *1*GCD GCD LOGS LOG-EXP LOG-TIMES-EXP LOG-TIMES-EXP-PROOF LOG-TIMES LOG-TIMES-PROOF LOG-QUOTIENT-EXP LOG-QUOTIENT-TIMES LOG-QUOTIENT-TIMES-PROOF LOG-QUOTIENT LEQ-LOG-LOG *1*DOUBLE-LOG-INDUCTION DOUBLE-LOG-INDUCTION LOG-1 LOG-0 EQUAL-LOG-0 *1*LOG LOG EXPONENTIATION EXP-DIFFERENCE EQUAL-EXP-1 EQUAL-EXP-0 EXP-EXP EXP-TIMES EXP-0-ARG2 EXP-1-ARG1 EXP-0-ARG1 EXP-PLUS EXP-ADD1 EXP-ZERO QUOTIENTS REMAINDER-EQUALS-ITS-FIRST-ARGUMENT-OFF QUOTIENT-TIMES-INSTANCE-TEMP-OFF LESSP-QUOTIENT QUOTIENT-X-X QUOTIENT-1-ARG1 QUOTIENT-1-ARG1-CASESPLIT QUOTIENT-1-ARG2 LEQ-QUOTIENT QUOTIENT-EXP QUOTIENT-QUOTIENT QUOTIENT-PLUS-TIMES-TIMES-INSTANCE QUOTIENT-PLUS-TIMES-TIMES QUOTIENT-PLUS-TIMES-TIMES-PROOF QUOTIENT-PLUS-FACT QUOTIENT-REMAINDER-INSTANCE QUOTIENT-REMAINDER QUOTIENT-REMAINDER-TIMES REMAINDER-EQUALS-ITS-FIRST-ARGUMENT QUOTIENT-DIFFERENCE3 QUOTIENT-DIFFERENCE2 QUOTIENT-LESSP-ARG1 QUOTIENT-DIFFERENCE1 QUOTIENT-TIMES-TIMES QUOTIENT-TIMES-TIMES-PROOF QUOTIENT-TIMES-INSTANCE QUOTIENT-TIMES QUOTIENT-TIMES-PROOF QUOTIENT-TIMES-INSTANCE-TEMP QUOTIENT-TIMES-INSTANCE-TEMP-PROOF QUOTIENT-PLUS QUOTIENT-PLUS-PROOF QUOTIENT-SUB1 EQUAL-QUOTIENT-0 QUOTIENT-ADD1 QUOTIENT-ZERO QUOTIENT-OF-NON-NUMBER QUOTIENT-NOOP REMAINDERS PLUS-REMAINDER-TIMES-QUOTIENT-OFF EQUAL-REMAINDER-PLUS-REMAINDER-OFF REMAINDER-TIMES-TIMES-OFF REMAINDER-DIFFERENCE3-OFF EQUAL-REMAINDER-DIFFERENCE-0-OFF LESSP-PLUS-FACT-OFF REMAINDER-EXP-EXP *1*DOUBLE-NUMBER-INDUCTION DOUBLE-NUMBER-INDUCTION TRANSITIVITY-OF-DIVIDES REMAINDER-X-X REMAINDER-1-ARG2 REMAINDER-1-ARG1 REMAINDER-REMAINDER REMAINDER-EXP REMAINDER-PLUS-TIMES-TIMES-INSTANCE REMAINDER-PLUS-TIMES-TIMES REMAINDER-PLUS-TIMES-TIMES-PROOF REMAINDER-PLUS-FACT LESSP-PLUS-FACT EQUAL-REMAINDER-DIFFERENCE-0 REMAINDER-DIFFERENCE3 REMAINDER-DIFFERENCE2 *1*DOUBLE-REMAINDER-INDUCTION DOUBLE-REMAINDER-INDUCTION REMAINDER-DIFFERENCE1 REMAINDER-TIMES2-INSTANCE REMAINDER-TIMES2 REMAINDER-TIMES2-PROOF REMAINDER-TIMES-TIMES REMAINDER-TIMES-TIMES-PROOF REMAINDER-TIMES1-INSTANCE REMAINDER-TIMES1-INSTANCE-PROOF REMAINDER-TIMES1 REMAINDER-TIMES1-PROOF EQUAL-REMAINDER-PLUS-REMAINDER EQUAL-REMAINDER-PLUS-REMAINDER-PROOF EQUAL-REMAINDER-PLUS-0 EQUAL-REMAINDER-PLUS-0-PROOF REMAINDER-PLUS REMAINDER-PLUS-PROOF REMAINDER-ADD1 REMAINDER-SUB1 REMAINDER-QUOTIENT-ELIM PLUS-REMAINDER-TIMES-QUOTIENT REMAINDER-ZERO REMAINDER-OF-NON-NUMBER REMAINDER-NOOP LESSP-REMAINDER MULTIPLICATION EQUAL-SUB1-TIMES-0 LESSP-1-TIMES LESSP-PLUS-TIMES2 LESSP-PLUS-TIMES1 LESSP-PLUS-TIMES-PROOF LESSP-TIMES-CANCELLATION2 LESSP-TIMES-CANCELLATION1 LESSP-TIMES-CANCELLATION-PROOF LESSP-TIMES3 LESSP-TIMES3-PROOF2 LESSP-TIMES3-PROOF1 LESSP-TIMES2 LESSP-TIMES2-PROOF LESSP-TIMES1 LESSP-TIMES1-PROOF TIMES-1-ARG1 EQUAL-TIMES-1 EQUAL-TIMES-0 TIMES-QUOTIENT TIMES-QUOTIENT-PROOF TIMES-DISTRIBUTES-OVER-DIFFERENCE TIMES-DISTRIBUTES-OVER-DIFFERENCE-PROOF ASSOCIATIVITY-OF-TIMES COMMUTATIVITY2-OF-TIMES TIMES-DISTRIBUTES-OVER-PLUS TIMES-DISTRIBUTES-OVER-PLUS-PROOF COMMUTATIVITY-OF-TIMES TIMES-SUB1 TIMES-ADD1 TIMES-ZERO *1*EXP EXP ADDITION OPEN-PLUS-OFF PLUS-CANCELLATION-OFF DIFFERENCE-X-X-OFF DIFFERENCE-PLUS-OFF DIFFERENCE-PLUS-CANCELLATION1-OFF DIFFERENCE-PLUS-CANCELLATION2-OFF DIFFERENCE-CANCELLATION-0-OFF DIFFERENCE-CANCELLATION-1-OFF DIFFERENCE-1-OFF DIFFERENCE-2-OFF DIFFERENCE-ADD1-PLUS-CANCELLATION-OFF DIFFERENCE-SUB1-ARG2-OFF DIFFERENCE-DIFFERENCE-ARG1-OFF DIFFERENCE-DIFFERENCE-ARG2-OFF DIFFERENCE-DIFFERENCE-DIFFERENCE-OFF DIFFERENCE-PLUS-CANCELLATION3-OFF NUMBERP-EVAL$-PLUS-OFF NUMBERP-EVAL$-PLUS-TREE-OFF MEMBER-IMPLIES-PLUS-TREE-GREATEREQP-OFF PLUS-TREE-DELETE-OFF SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP-OFF PLUS-TREE-BAGDIFF-OFF NUMBERP-EVAL$-BRIDGE-OFF BRIDGE-TO-SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP-OFF EVAL$-PLUS-TREE-APPEND-OFF PLUS-TREE-PLUS-FRINGE-OFF MEMBER-IMPLIES-NUMBERP-OFF CADR-EVAL$-LIST-OFF EVAL$-QUOTE-OFF LISTP-EVAL$-OFF CANCEL-EQUAL-PLUS-OFF CANCEL-DIFFERENCE-PLUS-OFF LESSP-DIFFERENCE-CANCELLATION-OFF CANCEL-LESSP-PLUS-OFF CORRECTNESS-OF-CANCEL-LESSP-PLUS *1*CANCEL-LESSP-PLUS CANCEL-LESSP-PLUS LESSP-DIFFERENCE LESSP-DIFFERENCE-CANCELLATION DIFF-X-X DIFF-SUB1-ARG2 DIFF-SUB1-ARG2-CASESPLIT DIFF-ADD1-ARG2 DIFF-ADD1-ARG2-CASESPLIT DIFF-DIFF-DIFF DIFF-DIFF-DIFF-CASESPLIT DIFF-DIFF-ARG2 DIFF-DIFF-ARG2-CASESPLIT DIFF-DIFF-ARG1 CORRECTNESS-OF-CANCEL-DIFFERENCE-PLUS *1*CANCEL-DIFFERENCE-PLUS CANCEL-DIFFERENCE-PLUS CORRECTNESS-OF-CANCEL-EQUAL-PLUS *1*CANCEL-EQUAL-PLUS CANCEL-EQUAL-PLUS LISTP-EVAL$ EVAL$-QUOTE CADR-EVAL$-LIST MEMBER-IMPLIES-NUMBERP PLUS-TREE-PLUS-FRINGE EVAL$-PLUS-TREE-APPEND BRIDGE-TO-SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP NUMBERP-EVAL$-BRIDGE PLUS-TREE-BAGDIFF SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP PLUS-TREE-DELETE MEMBER-IMPLIES-PLUS-TREE-GREATEREQP NUMBERP-EVAL$-PLUS-TREE NUMBERP-EVAL$-PLUS *1*PLUS-TREE PLUS-TREE *1*PLUS-FRINGE PLUS-FRINGE DIFFERENCE-PLUS-CANCELLATION3 DIFFERENCE-DIFFERENCE-DIFFERENCE DIFFERENCE-DIFFERENCE-ARG2 DIFFERENCE-DIFFERENCE-ARG1 DIFFERENCE-SUB1-ARG2 DIFFERENCE-ADD1-PLUS-CANCELLATION DIFFERENCE-2 DIFFERENCE-1 DIFFERENCE-CANCELLATION-1 DIFFERENCE-CANCELLATION-0 DIFFERENCE-PLUS-CANCELLATION2 DIFFERENCE-PLUS-CANCELLATION1 DIFFERENCE-PLUS EQUAL-DIFFERENCE-0 DIFFERENCE-X-X DIFFERENCE-LEQ-ARG1 DIFFERENCE-ELIM PLUS-DIFFERENCE-DIFFERENCE PLUS-DIFFERENCE-DIFFERENCE-CASESPLIT PLUS-DIFFERENCE-ARG2 PLUS-DIFFERENCE-ARG2-CASESPLIT PLUS-DIFFERENCE-ARG1 PLUS-DIFFERENCE-ARG1-CASESPLIT PLUS-CANCELLATION EQUAL-PLUS-1 EQUAL-PLUS-0 ASSOCIATIVITY-OF-PLUS COMMUTATIVITY-OF-PLUS COMMUTATIVITY2-OF-PLUS PLUS-ADD1 PLUS-RIGHT-ID2 PLUS-STOPPER OPEN-PLUS SETS-AND-BAGS SUBBAGP-BAGINT2 SUBBAGP-BAGINT1 SUBBAGP-CDR2 SUBBAGP-CDR1 SUBBAGP-DELETE SETP-PERMUTATION SETP-PERMUTATION-INDUCTION-STEP SETP-PERMUTATION-BASE-CASE *1*SETP-PERMUTATION-INDUCTION SETP-PERMUTATION-INDUCTION SETP-DELETE TRANSITIVITY-OF-PERMUTATION TRANSITIVITY-OF-PERMUTATION-INDUCTION-STEP TRANSITIVITY-OF-PERMUTATION-BASE-CASE *1*TRANSITIVITY-OF-PERMUTATION-INDUCTION TRANSITIVITY-OF-PERMUTATION-INDUCTION PERMUTATION-DELETE-DELETE PERMUTATION-REFLEXIVITY COMMUTATIVITY-OF-PERMUTATION PERMUTATION-RIGHT-CONS PERMUTATION-RIGHT-CONS1 NOT-PERMUTATION MEMBER-BAGINT MEMBER-BAGDIFF PERMUTATION-IMPLIES-MEMBERSHIP-EQUIVALENCE MEMBER-DELETE MEMBER-DELETE-IMPLIES-MEMBERSHIP MEMBER-CONS MEMBER-NON-LIST OCCURRENCES-BAGINT OCCURRENCES-BAGDIFF OCCURRENCES-DELETE OCCURRENCES-CONS OCCURRENCES-IN-A-SET EQUAL-OCCURRENCES-ZERO DELETE-DELETE DELETE-NON-MEMBER LISTP-DELETE *1*SUBBAGP SUBBAGP *1*SETP SETP *1*PERMUTATION PERMUTATION *1*OCCURRENCES OCCURRENCES *1*BAGINT BAGINT *1*BAGDIFF BAGDIFF *1*DELETE DELETE *1*IDENTITY IDENTITY REWRITE-EVAL$ REWRITE-CAR-V&C$ REWRITE-V&C-APPLY$ REWRITE-V&C$ REWRITE-APPLY-SUBR REWRITE-APPLY$ REWRITE-CAR-V&C-APPLY$ *1*FOR FOR *1*QUANTIFIER-OPERATION QUANTIFIER-OPERATION *1*UNION UNION NUMBERP-MAX *1*MAX MAX *1*APPEND APPEND *1*ADD-TO-SET ADD-TO-SET *1*QUANTIFIER-INITIAL-VALUE QUANTIFIER-INITIAL-VALUE NOT-SUBRP-APPLY-SUBR SUBRP-BODY SUBRP-FORMALS NOT-LITATOM-BODY NOT-LITATOM-FORMALS NOT-LITATOM-SUBRP *1*EVAL$ EVAL$ *1*APPLY$ APPLY$ *1*V&C-APPLY$ V&C-APPLY$ *1*V&C$ V&C$ *1*SUM-CDRS SUM-CDRS *1*STRIP-CARS STRIP-CARS *1*FIX-COST FIX-COST *1*BODY BODY *1*FORMALS FORMALS *1*APPLY-SUBR APPLY-SUBR SUBRP-BOOLEAN *1*SUBRP SUBRP *1*PAIRLIST PAIRLIST *1*ASSOC ASSOC *1*ORDINALP ORDINALP *1*ORD-LESSP ORD-LESSP *1*IFF IFF *1*MEMBER MEMBER *1*REMAINDER REMAINDER *1*QUOTIENT QUOTIENT *1*TIMES TIMES *1*DIFFERENCE 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 *1*NEGATIVE-GUTS NEGATIVE-GUTS *1*NEGATIVEP NEGATIVEP *1*MINUS MINUS *1*NLISTP 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 *1*CDR CDR *1*CAR CAR *1*LISTP LISTP *1*CONS CONS COUNT-PACK UNPACK-ELIM PACK-UNPACK PACK-EQUAL UNPACK-LESSEQP UNPACK-LESSP UNPACK-NLITATOM UNPACK-PACK *1*UNPACK UNPACK *1*LITATOM LITATOM *1*PACK PACK COUNT-NOT-LESSP COUNT-NUMBERP *1*PLUS PLUS *1*FIX FIX *1*ZEROP ZEROP *1*GEQ GEQ *1*LEQ LEQ *1*GREATERP GREATERP *1*LESSP LESSP COUNT-ADD1 SUB1-ELIM ADD1-SUB1 ADD1-EQUAL SUB1-LESSEQP SUB1-LESSP SUB1-TYPE-RESTRICTION SUB1-NNUMBERP SUB1-ADD1 *1*ZERO ZERO *1*SUB1 SUB1 *1*NUMBERP NUMBERP *1*ADD1 ADD1 *1*IMPLIES IMPLIES *1*OR OR *1*AND AND *1*NOT NOT *1*TRUEP TRUEP *1*TRUE TRUE *1*FALSEP FALSEP *1*FALSE FALSE *1*COUNT COUNT QUOTE *1*EQUAL EQUAL *1*IF-ERROR IF GROUND-ZERO))) (SETQ LIB-ATOMS-WITH-DEFS (QUOTE (*1*CANCEL-RPLUS *1*ALL-RNEGS *1*LAST-CDR *1*BADGUY *1*MAKE-NEGS *1*SPLIT-BY-PARITY *1*RPLUS-FRINGE *1*RPLUS-TREE *1*GCD-FACTORS *1*GCD-TIMES1-INDUCT *1*REQUAL *1*RLESSP *1*RMAGNITUDE *1*SIMPLE-RMAGNITUDE *1*RQUOTIENT *1*RINVERSE *1*SIMPLE-RINVERSE *1*RZEROP *1*RTIMES *1*SIMPLE-RTIMES *1*RDIFFERENCE *1*RNEG *1*SIMPLE-RNEG *1*RPLUS *1*SIMPLE-RPLUS *1*REDUCE *1*FIX-RATIONAL *1*RATIONALP *1*RATIONAL *1*DENOMINATOR *1*NUMERATOR *1*RATIONAL-FORMP *1*CANCEL-EQUAL-TIMES *1*CANCEL-QUOTIENT-TIMES *1*CANCEL-LESSP-TIMES *1*AND-NOT-ZEROP-TREE *1*OR-ZEROP-TREE *1*TIMES-FRINGE *1*TIMES-TREE *1*IREM *1*IQUO *1*IMOD *1*IDIV *1*IREMAINDER *1*IQUOTIENT *1*CANCEL-IDIFFERENCE *1*EVAL$-IPLUS-TREE-APPEND-INDUCTION *1*CANCEL-IPLUS *1*IPLUS-TREE *1*IPLUS-FRINGE *1*ITIMES *1*IABS *1*IDIFFERENCE *1*INEG *1*IPLUS *1*ILEQ *1*ILESSP *1*IZEROP *1*FIX-INT *1*INTEGERP *1*SINGLE-NUMBER-INDUCTION *1*GCD *1*DOUBLE-LOG-INDUCTION *1*LOG *1*DOUBLE-NUMBER-INDUCTION *1*DOUBLE-REMAINDER-INDUCTION *1*EXP *1*CANCEL-LESSP-PLUS *1*CANCEL-DIFFERENCE-PLUS *1*CANCEL-EQUAL-PLUS *1*PLUS-TREE *1*PLUS-FRINGE *1*SETP-PERMUTATION-INDUCTION *1*TRANSITIVITY-OF-PERMUTATION-INDUCTION *1*SUBBAGP *1*SETP *1*PERMUTATION *1*OCCURRENCES *1*BAGINT *1*BAGDIFF *1*DELETE *1*IDENTITY *1*FOR *1*QUANTIFIER-OPERATION *1*UNION *1*MAX *1*APPEND *1*ADD-TO-SET *1*QUANTIFIER-INITIAL-VALUE *1*EVAL$ *1*V&C-APPLY$ *1*V&C$ *1*SUM-CDRS *1*STRIP-CARS 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R2) (IMMEDIATE-DEPENDENTS0 FIX-RATIONAL-RMAGNITUDE . R2) (IMMEDIATE-DEPENDENTS0 FIX-RATIONAL-RQUOTIENT . R2) (IMMEDIATE-DEPENDENTS0 FIX-RATIONAL-RDIFFERENCE . R2) (IMMEDIATE-DEPENDENTS0 FIX-RATIONAL-RNEG . R2) (IMMEDIATE-DEPENDENTS0 FIX-RATIONAL-RTIMES . R2) (IMMEDIATE-DEPENDENTS0 FIX-RATIONAL-FIX-RATIONAL . R2) (IMMEDIATE-DEPENDENTS0 FIX-RATIONAL-RPLUS . R2) (IMMEDIATE-DEPENDENTS0 FIX-RATIONAL-REDUCE . R2) (IMMEDIATE-DEPENDENTS0 RATIONALP-RMAGNITUDE . R2) (IMMEDIATE-DEPENDENTS0 RATIONALP-RQUOTIENT . R2) (IMMEDIATE-DEPENDENTS0 RATIONALP-RDIFFERENCE . R2) (IMMEDIATE-DEPENDENTS0 RATIONALP-RNEG . R2) (IMMEDIATE-DEPENDENTS0 RATIONALP-RTIMES . R2) (IMMEDIATE-DEPENDENTS0 RATIONALP-FIX-RATIONAL . R2) (IMMEDIATE-DEPENDENTS0 RATIONALP-RPLUS . R2) (IMMEDIATE-DEPENDENTS0 RATIONALP-REDUCE . R2) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-RTIMES . R2) (IMMEDIATE-DEPENDENTS0 RDIFFERENCE . R2) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-RPLUS . 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T))))) (PUT1-LST (QUOTE CORRECTNESS-OF-CANCEL-RPLUS) (QUOTE (IDATE 1000404112850 IMMEDIATE-DEPENDENTS0 (R2 CORRECTNESS-OF-CANCEL-RPLUS-OFF) EVENT (PROVE-LEMMA CORRECTNESS-OF-CANCEL-RPLUS ((META RPLUS)) (EQUAL (EVAL$ (QUOTE *1*TRUE) X A) (EVAL$ (QUOTE *1*TRUE) (CANCEL-RPLUS X) A)) ((INSTRUCTIONS (DIVE 2 2) X-DUMB TOP S-PROP SPLIT (DIVE 2) (REWRITE CANCELLING-FROM-RPLUS) (REWRITE PERMUTATION-DOES-NOT-EFFECT-RPLUS (($Y (RPLUS-FRINGE X)))) (REWRITE EVAL$-RPLUS-TREE-RPLUS-FRINGE) TOP S (REWRITE PERMUTATION-APPEND-SPLIT-BY-PARITY-BRIDGE) (REWRITE SUBBAGP-BAGINT1) (REWRITE SUBBAGP-BAGINT2) (GENERALIZE (((RPLUS-FRINGE X) Y))) DROP (DIVE 1) (REWRITE BAGINT-MAKE-NEGS-SPLIT-BY-PARITY) TOP S))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 BAGINT-MAKE-NEGS-SPLIT-BY-PARITY . CORRECTNESS-OF-CANCEL-RPLUS) (IMMEDIATE-DEPENDENTS0 SUBBAGP-BAGINT2 . CORRECTNESS-OF-CANCEL-RPLUS) (IMMEDIATE-DEPENDENTS0 SUBBAGP-BAGINT1 . 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T))))) (PUT1-LST (QUOTE SUBBAGP-NECC-OFF) (QUOTE (IDATE 1000404112850 EVENT (TOGGLE SUBBAGP-NECC-OFF SUBBAGP-NECC T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SUBBAGP-NECC . SUBBAGP-NECC-OFF) (DISABLED-LEMMAS NIL SUBBAGP-NECC SUBBAGP-NECC-OFF . T))))) (PUT1-LST (QUOTE SUBBAGP-TRANSITIVE-OFF) (QUOTE (IDATE 1000404112850 EVENT (TOGGLE SUBBAGP-TRANSITIVE-OFF SUBBAGP-TRANSITIVE T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SUBBAGP-TRANSITIVE . SUBBAGP-TRANSITIVE-OFF) (DISABLED-LEMMAS NIL SUBBAGP-TRANSITIVE SUBBAGP-TRANSITIVE-OFF . T))))) (PUT1-LST (QUOTE NOT-MEMBER-MAKE-NEGS-FACT-OFF) (QUOTE (IDATE 1000404112850 EVENT (TOGGLE NOT-MEMBER-MAKE-NEGS-FACT-OFF NOT-MEMBER-MAKE-NEGS-FACT T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 NOT-MEMBER-MAKE-NEGS-FACT . NOT-MEMBER-MAKE-NEGS-FACT-OFF) (DISABLED-LEMMAS NIL NOT-MEMBER-MAKE-NEGS-FACT NOT-MEMBER-MAKE-NEGS-FACT-OFF . 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T))))) (PUT1-LST (QUOTE APPEND-BAGDIFF-ARG2-OFF) (QUOTE (IDATE 1000404112850 EVENT (TOGGLE APPEND-BAGDIFF-ARG2-OFF APPEND-BAGDIFF-ARG2 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 APPEND-BAGDIFF-ARG2 . APPEND-BAGDIFF-ARG2-OFF) (DISABLED-LEMMAS NIL APPEND-BAGDIFF-ARG2 APPEND-BAGDIFF-ARG2-OFF . T))))) (PUT1-LST (QUOTE BAGDIFF-BAGDIFF-OFF) (QUOTE (IDATE 1000404112850 EVENT (TOGGLE BAGDIFF-BAGDIFF-OFF BAGDIFF-BAGDIFF T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 BAGDIFF-BAGDIFF . BAGDIFF-BAGDIFF-OFF) (DISABLED-LEMMAS NIL BAGDIFF-BAGDIFF BAGDIFF-BAGDIFF-OFF . T))))) (PUT1-LST (QUOTE MEMBER-RNEG-MAKE-NEGS-OFF) (QUOTE (IDATE 1000404112850 EVENT (TOGGLE MEMBER-RNEG-MAKE-NEGS-OFF MEMBER-RNEG-MAKE-NEGS T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 MEMBER-RNEG-MAKE-NEGS . MEMBER-RNEG-MAKE-NEGS-OFF) (DISABLED-LEMMAS NIL MEMBER-RNEG-MAKE-NEGS MEMBER-RNEG-MAKE-NEGS-OFF . T))))) (PUT1-LST (QUOTE SUBBAGP-MAKE-NEGS-OFF) (QUOTE (IDATE 1000404112850 EVENT (TOGGLE SUBBAGP-MAKE-NEGS-OFF SUBBAGP-MAKE-NEGS T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SUBBAGP-MAKE-NEGS . SUBBAGP-MAKE-NEGS-OFF) (DISABLED-LEMMAS NIL SUBBAGP-MAKE-NEGS SUBBAGP-MAKE-NEGS-OFF . T))))) (PUT1-LST (QUOTE RDIFFERENCE-REDUCE-OFF) (QUOTE (IDATE 1000404112850 EVENT (TOGGLE RDIFFERENCE-REDUCE-OFF RDIFFERENCE-REDUCE T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RDIFFERENCE-REDUCE . RDIFFERENCE-REDUCE-OFF) (DISABLED-LEMMAS NIL RDIFFERENCE-REDUCE RDIFFERENCE-REDUCE-OFF . T))))) (PUT1-LST (QUOTE REQUAL-SIMPLE-RPLUS-X-SIMPLE-RNEG-X-OFF) (QUOTE (IDATE 1000404112850 EVENT (TOGGLE REQUAL-SIMPLE-RPLUS-X-SIMPLE-RNEG-X-OFF REQUAL-SIMPLE-RPLUS-X-SIMPLE-RNEG-X T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REQUAL-SIMPLE-RPLUS-X-SIMPLE-RNEG-X . REQUAL-SIMPLE-RPLUS-X-SIMPLE-RNEG-X-OFF) (DISABLED-LEMMAS NIL REQUAL-SIMPLE-RPLUS-X-SIMPLE-RNEG-X REQUAL-SIMPLE-RPLUS-X-SIMPLE-RNEG-X-OFF . T))))) (PUT1-LST (QUOTE REQUAL-RPLUS-X-SIMPLE-RNEG-X-OFF) (QUOTE (IDATE 1000404112850 EVENT (TOGGLE REQUAL-RPLUS-X-SIMPLE-RNEG-X-OFF REQUAL-RPLUS-X-SIMPLE-RNEG-X T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REQUAL-RPLUS-X-SIMPLE-RNEG-X . REQUAL-RPLUS-X-SIMPLE-RNEG-X-OFF) (DISABLED-LEMMAS NIL REQUAL-RPLUS-X-SIMPLE-RNEG-X REQUAL-RPLUS-X-SIMPLE-RNEG-X-OFF . T))))) (PUT1-LST (QUOTE RPLUS-X-RNEG-X-OFF) (QUOTE (IDATE 1000404112850 EVENT (TOGGLE RPLUS-X-RNEG-X-OFF RPLUS-X-RNEG-X T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RPLUS-X-RNEG-X . RPLUS-X-RNEG-X-OFF) (DISABLED-LEMMAS NIL RPLUS-X-RNEG-X RPLUS-X-RNEG-X-OFF . T))))) (PUT1-LST (QUOTE RDIFFERENCE-X-X-OFF) (QUOTE (IDATE 1000404112850 EVENT (TOGGLE RDIFFERENCE-X-X-OFF RDIFFERENCE-X-X T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RDIFFERENCE-X-X . RDIFFERENCE-X-X-OFF) (DISABLED-LEMMAS NIL RDIFFERENCE-X-X RDIFFERENCE-X-X-OFF . T))))) (PUT1-LST (QUOTE RDIFFERENCE-RPLUS-HACK-OFF) (QUOTE (IDATE 1000404112850 EVENT (TOGGLE RDIFFERENCE-RPLUS-HACK-OFF RDIFFERENCE-RPLUS-HACK T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RDIFFERENCE-RPLUS-HACK . RDIFFERENCE-RPLUS-HACK-OFF) (DISABLED-LEMMAS NIL RDIFFERENCE-RPLUS-HACK RDIFFERENCE-RPLUS-HACK-OFF . T))))) (PUT1-LST (QUOTE RDIFFERENCE-RPLUS-HACK2-OFF) (QUOTE (IDATE 1000404112850 EVENT (TOGGLE RDIFFERENCE-RPLUS-HACK2-OFF RDIFFERENCE-RPLUS-HACK2 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RDIFFERENCE-RPLUS-HACK2 . RDIFFERENCE-RPLUS-HACK2-OFF) (DISABLED-LEMMAS NIL RDIFFERENCE-RPLUS-HACK2 RDIFFERENCE-RPLUS-HACK2-OFF . T))))) (PUT1-LST (QUOTE RPLUS-RDIFFERENCE-HACK-OFF) (QUOTE (IDATE 1000404112850 EVENT (TOGGLE RPLUS-RDIFFERENCE-HACK-OFF RPLUS-RDIFFERENCE-HACK T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RPLUS-RDIFFERENCE-HACK . RPLUS-RDIFFERENCE-HACK-OFF) (DISABLED-LEMMAS NIL RPLUS-RDIFFERENCE-HACK RPLUS-RDIFFERENCE-HACK-OFF . T))))) (PUT1-LST (QUOTE EQUAL-DIFFERENCE-HACK1-OFF) (QUOTE (IDATE 1000404112850 EVENT (TOGGLE EQUAL-DIFFERENCE-HACK1-OFF EQUAL-DIFFERENCE-HACK1 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE-HACK1 . EQUAL-DIFFERENCE-HACK1-OFF) (DISABLED-LEMMAS NIL EQUAL-DIFFERENCE-HACK1 EQUAL-DIFFERENCE-HACK1-OFF . T))))) (PUT1-LST (QUOTE EQUAL-DIFFERENCE-HACK2-OFF) (QUOTE (IDATE 1000404112850 EVENT (TOGGLE EQUAL-DIFFERENCE-HACK2-OFF EQUAL-DIFFERENCE-HACK2 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE-HACK2 . EQUAL-DIFFERENCE-HACK2-OFF) (DISABLED-LEMMAS NIL EQUAL-DIFFERENCE-HACK2 EQUAL-DIFFERENCE-HACK2-OFF . T))))) (PUT1-LST (QUOTE EQUAL-DIFFERENCE-REWRITE-OFF) (QUOTE (IDATE 1000404112850 EVENT (TOGGLE EQUAL-DIFFERENCE-REWRITE-OFF EQUAL-DIFFERENCE-REWRITE T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE-REWRITE . EQUAL-DIFFERENCE-REWRITE-OFF) (DISABLED-LEMMAS NIL EQUAL-DIFFERENCE-REWRITE EQUAL-DIFFERENCE-REWRITE-OFF . T))))) (PUT1-LST (QUOTE EQUAL-DIFFERENCE-REWRITE2-OFF) (QUOTE (IDATE 1000404112850 EVENT (TOGGLE EQUAL-DIFFERENCE-REWRITE2-OFF EQUAL-DIFFERENCE-REWRITE2 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE-REWRITE2 . EQUAL-DIFFERENCE-REWRITE2-OFF) (DISABLED-LEMMAS NIL EQUAL-DIFFERENCE-REWRITE2 EQUAL-DIFFERENCE-REWRITE2-OFF . T))))) (PUT1-LST (QUOTE EQUAL-TIMES-BRIDGE5-OFF) (QUOTE (IDATE 1000404112850 EVENT (TOGGLE EQUAL-TIMES-BRIDGE5-OFF EQUAL-TIMES-BRIDGE5 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-BRIDGE5 . EQUAL-TIMES-BRIDGE5-OFF) (DISABLED-LEMMAS NIL EQUAL-TIMES-BRIDGE5 EQUAL-TIMES-BRIDGE5-OFF . T))))) (PUT1-LST (QUOTE EQUAL-PLUS-DIFFERENCE-REWRITE-OFF) (QUOTE (IDATE 1000404112850 EVENT (TOGGLE EQUAL-PLUS-DIFFERENCE-REWRITE-OFF EQUAL-PLUS-DIFFERENCE-REWRITE T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQUAL-PLUS-DIFFERENCE-REWRITE . EQUAL-PLUS-DIFFERENCE-REWRITE-OFF) (DISABLED-LEMMAS NIL EQUAL-PLUS-DIFFERENCE-REWRITE EQUAL-PLUS-DIFFERENCE-REWRITE-OFF . T))))) (PUT1-LST (QUOTE LESSP-TIMES-BRIDGE1-OFF) (QUOTE (IDATE 1000404112850 EVENT (TOGGLE LESSP-TIMES-BRIDGE1-OFF LESSP-TIMES-BRIDGE1 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LESSP-TIMES-BRIDGE1 . LESSP-TIMES-BRIDGE1-OFF) (DISABLED-LEMMAS NIL LESSP-TIMES-BRIDGE1 LESSP-TIMES-BRIDGE1-OFF . T))))) (PUT1-LST (QUOTE EQUAL-DIFFERENCE-OFF) (QUOTE (IDATE 1000404112850 EVENT (TOGGLE EQUAL-DIFFERENCE-OFF EQUAL-DIFFERENCE T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE . EQUAL-DIFFERENCE-OFF) (DISABLED-LEMMAS NIL EQUAL-DIFFERENCE EQUAL-DIFFERENCE-OFF . T))))) (PUT1-LST (QUOTE REQUAL-SIMPLE-RPLUS-X-X-REWRITE-OFF) (QUOTE (IDATE 1000404112850 EVENT (TOGGLE REQUAL-SIMPLE-RPLUS-X-X-REWRITE-OFF REQUAL-SIMPLE-RPLUS-X-X-REWRITE T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REQUAL-SIMPLE-RPLUS-X-X-REWRITE . REQUAL-SIMPLE-RPLUS-X-X-REWRITE-OFF) (DISABLED-LEMMAS NIL REQUAL-SIMPLE-RPLUS-X-X-REWRITE REQUAL-SIMPLE-RPLUS-X-X-REWRITE-OFF . 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EVAL$-RPLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 RDIFFERENCE-REDUCE . EVAL$-RPLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 MEMBER-NON-LIST . EVAL$-RPLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE-NON-MEMBER . EVAL$-RPLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 R1 . EVAL$-RPLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 RDIFFERENCE . EVAL$-RPLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE . EVAL$-RPLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 RPLUS-TREE . EVAL$-RPLUS-TREE-DELETE) (LEMMAS EVAL$ . EVAL$-RPLUS-TREE-DELETE))))) (PUT1-LST (QUOTE EQUAL-RPLUS-RDIFFERENCE-HACK) (QUOTE (IDATE 1000404112840 IMMEDIATE-DEPENDENTS0 (EQUAL-RPLUS-RDIFFERENCE-HACK-OFF EVAL$-RPLUS-TREE-DELETE) EVENT (PROVE-LEMMA EQUAL-RPLUS-RDIFFERENCE-HACK (REWRITE) (EQUAL (EQUAL (RPLUS X Y) (RDIFFERENCE (RPLUS X Z) V)) (EQUAL (REDUCE Y) (RDIFFERENCE Z V))) ((ENABLE RDIFFERENCE ASSOCIATIVITY-OF-RPLUS REDUCE-RPLUS))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REDUCE-RPLUS . EQUAL-RPLUS-RDIFFERENCE-HACK) (IMMEDIATE-DEPENDENTS0 EQUAL-RPLUS-X-X-REWRITE . EQUAL-RPLUS-RDIFFERENCE-HACK) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-RPLUS . EQUAL-RPLUS-RDIFFERENCE-HACK) (IMMEDIATE-DEPENDENTS0 REDUCE . EQUAL-RPLUS-RDIFFERENCE-HACK) (IMMEDIATE-DEPENDENTS0 RDIFFERENCE . EQUAL-RPLUS-RDIFFERENCE-HACK) (IMMEDIATE-DEPENDENTS0 RPLUS . EQUAL-RPLUS-RDIFFERENCE-HACK) (LEMMAS EQUAL . EQUAL-RPLUS-RDIFFERENCE-HACK))))) (PUT1-LST (QUOTE EQUAL-RPLUS-X-X-REWRITE) (QUOTE (IDATE 1000404112840 IMMEDIATE-DEPENDENTS0 (EQUAL-RPLUS-X-X-REWRITE-OFF EVAL$-RPLUS-TREE-RPLUS-FRINGE EQUAL-RPLUS-RDIFFERENCE-HACK) EVENT (PROVE-LEMMA EQUAL-RPLUS-X-X-REWRITE (REWRITE) (EQUAL (EQUAL (RPLUS X Y) (RPLUS X Z)) (EQUAL (REDUCE Y) (REDUCE Z))) ((USE (REQUAL-SIMPLE-RPLUS-X-X-REWRITE)) (ENABLE REQUAL-REDUCE-REDUCE-EQUAL RPLUS) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REQUAL-REDUCE-REDUCE-EQUAL . EQUAL-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 REQUAL-SIMPLE-RPLUS-X-X-REWRITE . EQUAL-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 REDUCE . EQUAL-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 RPLUS . EQUAL-RPLUS-X-X-REWRITE) (LEMMAS EQUAL . EQUAL-RPLUS-X-X-REWRITE))))) (PUT1-LST (QUOTE REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (QUOTE (IDATE 1000404112840 IMMEDIATE-DEPENDENTS0 (REQUAL-SIMPLE-RPLUS-X-X-REWRITE-OFF EQUAL-RPLUS-X-X-REWRITE) EVENT (PROVE-LEMMA REQUAL-SIMPLE-RPLUS-X-X-REWRITE (REWRITE) (EQUAL (REQUAL (SIMPLE-RPLUS X Y) (SIMPLE-RPLUS X Z)) (REQUAL Y Z)) ((ENABLE SIMPLE-RPLUS FIX-RATIONAL IPLUS ITIMES FIX-INT-ON-INTEGERS INTEGERP-MINUS REQUAL EQUAL-TIMES-BRIDGE1 EQUAL-TIMES-BRIDGE2 EQUAL-TIMES-BRIDGE3 EQUAL-TIMES-BRIDGE4) (ENABLE-THEORY R1))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REQUAL-X-X . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 INTEGERP-FIX-INT . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 RATIONAL . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES-BRIDGE1 . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 INTEGERP-ITIMES . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-IPLUS . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 ITIMES-1-ARG1 . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 IZEROP . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 ITIMES-ZERO1 . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 IPLUS-0 . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 TIMES-1-ARG1 . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 FIX-INT-ON-INTEGERS . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES2 . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 PLUS-STOPPER . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 FIX-INT . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 EQUAL-PLUS-DIFFERENCE-REWRITE . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE-REWRITE2 . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 INTEGERP-MINUS . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-BRIDGE4 . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 INTEGERP . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 RATIONAL-GENERALIZATION . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE-REWRITE . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 ITIMES-FIX-INT2 . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-LESSP-TIMES . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 IPLUS-FIX-INT2 . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 IPLUS . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-EQUAL-PLUS . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-EQUAL-TIMES . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 ITIMES-DISTRIBUTES-OVER-IPLUS . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-TIMES . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-TIMES . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 FIX-RATIONAL-OF-RATIONALP . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES1 . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 INTEGERP-IPLUS . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 MEANS-RATIONALP . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 IPLUS-FIX-INT1 . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-REQUAL . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 ITIMES . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-IPLUS . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-ITIMES . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 FIX-RATIONAL . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 RATIONALP-MEANS . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 R1 . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 SIMPLE-RPLUS . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (IMMEDIATE-DEPENDENTS0 REQUAL . REQUAL-SIMPLE-RPLUS-X-X-REWRITE) (LEMMAS REQUAL . REQUAL-SIMPLE-RPLUS-X-X-REWRITE))))) (PUT1-LST (QUOTE EQUAL-DIFFERENCE) (QUOTE (IDATE 1000404112800 IMMEDIATE-DEPENDENTS0 (EQUAL-DIFFERENCE-OFF REQUAL-SIMPLE-RPLUS-X-X-REWRITE) EVENT (PROVE-LEMMA EQUAL-DIFFERENCE (REWRITE) (AND (EQUAL (EQUAL A (DIFFERENCE A B)) (AND (NUMBERP A) (OR (ZEROP A) (ZEROP B)))) (EQUAL (EQUAL (DIFFERENCE A B) A) (AND (NUMBERP A) (OR (ZEROP A) (ZEROP B)))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIFFERENCE-LEQ-ARG1 . EQUAL-DIFFERENCE) (LEMMAS EQUAL . EQUAL-DIFFERENCE) (LEMMAS EQUAL . EQUAL-DIFFERENCE))))) (PUT1-LST (QUOTE LESSP-TIMES-BRIDGE1) (QUOTE (IDATE 1000404112800 IMMEDIATE-DEPENDENTS0 (LESSP-TIMES-BRIDGE1-OFF REQUAL-SIMPLE-RPLUS-X-X-REWRITE) EVENT (PROVE-LEMMA LESSP-TIMES-BRIDGE1 (REWRITE) (IMPLIES (AND (LESSP (TIMES C V) (TIMES X1 Z1)) (AND (EQUAL (TIMES W X1) (TIMES C D)) (AND (NOT (ZEROP C)) (NOT (ZEROP D))))) (LESSP (TIMES V W) (TIMES D Z1))) ((INSTRUCTIONS PROMOTE (= (LESSP (TIMES (TIMES C D) (TIMES V W)) (TIMES (TIMES C D) (TIMES D Z1)))) (DIVE 2 1) = TOP PROVE))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . LESSP-TIMES-BRIDGE1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-TIMES . LESSP-TIMES-BRIDGE1) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-LESSP-TIMES . LESSP-TIMES-BRIDGE1) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-TIMES . LESSP-TIMES-BRIDGE1) (LINEAR-LEMMAS TIMES . LESSP-TIMES-BRIDGE1) (LINEAR-LEMMAS TIMES . LESSP-TIMES-BRIDGE1))))) (PUT1-LST (QUOTE EQUAL-PLUS-DIFFERENCE-REWRITE) (QUOTE (IDATE 1000404112759 IMMEDIATE-DEPENDENTS0 (EQUAL-PLUS-DIFFERENCE-REWRITE-OFF REQUAL-SIMPLE-RPLUS-X-X-REWRITE) EVENT (PROVE-LEMMA EQUAL-PLUS-DIFFERENCE-REWRITE (REWRITE) (IMPLIES (EQUAL (FIX A) (FIX C)) (AND (EQUAL (EQUAL (PLUS A B) (DIFFERENCE C D)) (AND (ZEROP B) (OR (ZEROP A) (ZEROP D)))) (AND (EQUAL (EQUAL (PLUS B A) (DIFFERENCE C D)) (AND (ZEROP B) (OR (ZEROP A) (ZEROP D)))) (AND (EQUAL (EQUAL (DIFFERENCE C D) (PLUS A B)) (AND (ZEROP B) (OR (ZEROP A) (ZEROP D)))) (EQUAL (EQUAL (DIFFERENCE C D) (PLUS B A)) (AND (ZEROP B) (OR (ZEROP A) (ZEROP D))))))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQUAL-PLUS-0 . EQUAL-PLUS-DIFFERENCE-REWRITE) (IMMEDIATE-DEPENDENTS0 PLUS-RIGHT-ID2 . EQUAL-PLUS-DIFFERENCE-REWRITE) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . EQUAL-PLUS-DIFFERENCE-REWRITE) (IMMEDIATE-DEPENDENTS0 PLUS-STOPPER . EQUAL-PLUS-DIFFERENCE-REWRITE) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-LEQ-ARG1 . EQUAL-PLUS-DIFFERENCE-REWRITE) (LEMMAS EQUAL . EQUAL-PLUS-DIFFERENCE-REWRITE) (LEMMAS EQUAL . EQUAL-PLUS-DIFFERENCE-REWRITE) (LEMMAS EQUAL . EQUAL-PLUS-DIFFERENCE-REWRITE) (LEMMAS EQUAL . EQUAL-PLUS-DIFFERENCE-REWRITE))))) (PUT1-LST (QUOTE EQUAL-TIMES-BRIDGE5) (QUOTE (IDATE 1000404112759 IMMEDIATE-DEPENDENTS0 (EQUAL-TIMES-BRIDGE5-OFF) EVENT (PROVE-LEMMA EQUAL-TIMES-BRIDGE5 (REWRITE) (IMPLIES (AND (EQUAL (TIMES B A) (TIMES C D)) (AND (EQUAL (TIMES X A) (TIMES C Y)) (NOT (ZEROP A)))) (EQUAL (EQUAL (TIMES B Y) (TIMES X D)) (QUOTE *1*TRUE))) ((ENABLE EQUAL-TIMES-BRIDGE1))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . EQUAL-TIMES-BRIDGE5) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-BRIDGE1 . EQUAL-TIMES-BRIDGE5) (LEMMAS EQUAL . EQUAL-TIMES-BRIDGE5))))) (PUT1-LST (QUOTE EQUAL-DIFFERENCE-REWRITE2) (QUOTE (IDATE 1000404112759 IMMEDIATE-DEPENDENTS0 (EQUAL-DIFFERENCE-REWRITE2-OFF REQUAL-SIMPLE-RPLUS-X-X-REWRITE) EVENT (PROVE-LEMMA EQUAL-DIFFERENCE-REWRITE2 (REWRITE) (IMPLIES (EQUAL (FIX A) (FIX C)) (EQUAL (EQUAL (DIFFERENCE A B) (DIFFERENCE C D)) (OR (AND (NOT (LESSP B A)) (NOT (LESSP D C))) (EQUAL (FIX B) (FIX D)))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE-0 . EQUAL-DIFFERENCE-REWRITE2) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-LEQ-ARG1 . EQUAL-DIFFERENCE-REWRITE2) (LEMMAS EQUAL . EQUAL-DIFFERENCE-REWRITE2))))) (PUT1-LST (QUOTE EQUAL-DIFFERENCE-REWRITE) (QUOTE (IDATE 1000404112759 IMMEDIATE-DEPENDENTS0 (EQUAL-DIFFERENCE-REWRITE-OFF REQUAL-SIMPLE-RPLUS-X-X-REWRITE) EVENT (PROVE-LEMMA EQUAL-DIFFERENCE-REWRITE (REWRITE) (IMPLIES (EQUAL (FIX B) (FIX D)) (EQUAL (EQUAL (DIFFERENCE A B) (DIFFERENCE C D)) (OR (AND (NOT (LESSP B A)) (NOT (LESSP B C))) (EQUAL A C))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PLUS-STOPPER . EQUAL-DIFFERENCE-REWRITE) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . EQUAL-DIFFERENCE-REWRITE) (IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE-0 . EQUAL-DIFFERENCE-REWRITE) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-ELIM . EQUAL-DIFFERENCE-REWRITE) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-LEQ-ARG1 . EQUAL-DIFFERENCE-REWRITE) (LEMMAS EQUAL . EQUAL-DIFFERENCE-REWRITE))))) (PUT1-LST (QUOTE EQUAL-DIFFERENCE-HACK2) (QUOTE (IDATE 1000404112758 IMMEDIATE-DEPENDENTS0 (EQUAL-DIFFERENCE-HACK2-OFF PERMUTATION-DOES-NOT-EFFECT-RPLUS) EVENT (PROVE-LEMMA EQUAL-DIFFERENCE-HACK2 (REWRITE) (IMPLIES (EQUAL (REDUCE A) (RDIFFERENCE B C)) (EQUAL (RPLUS C A) (REDUCE B))) ((INSTRUCTIONS PROMOTE (DIVE 1) (= * (RPLUS C (REDUCE A)) ((ENABLE RPLUS-REDUCE-ARG2-REWRITE))) (DIVE 2) = TOP PROVE))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RPLUS-RDIFFERENCE-HACK . EQUAL-DIFFERENCE-HACK2) (IMMEDIATE-DEPENDENTS0 RPLUS-REDUCE-ARG2-REWRITE . EQUAL-DIFFERENCE-HACK2) (IMMEDIATE-DEPENDENTS0 RPLUS . EQUAL-DIFFERENCE-HACK2) (IMMEDIATE-DEPENDENTS0 RDIFFERENCE . EQUAL-DIFFERENCE-HACK2) (IMMEDIATE-DEPENDENTS0 REDUCE . EQUAL-DIFFERENCE-HACK2) (LEMMAS RPLUS . EQUAL-DIFFERENCE-HACK2))))) (PUT1-LST (QUOTE EQUAL-DIFFERENCE-HACK1) (QUOTE (IDATE 1000404112758 IMMEDIATE-DEPENDENTS0 (EQUAL-DIFFERENCE-HACK1-OFF PERMUTATION-DOES-NOT-EFFECT-RPLUS) EVENT (PROVE-LEMMA EQUAL-DIFFERENCE-HACK1 (REWRITE) (IMPLIES (EQUAL A (RDIFFERENCE B C)) (EQUAL (RPLUS C A) (REDUCE B))) ((ENABLE-THEORY R1))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RPLUS-RDIFFERENCE-HACK . EQUAL-DIFFERENCE-HACK1) (IMMEDIATE-DEPENDENTS0 R1 . EQUAL-DIFFERENCE-HACK1) (IMMEDIATE-DEPENDENTS0 REDUCE . EQUAL-DIFFERENCE-HACK1) (IMMEDIATE-DEPENDENTS0 RPLUS . EQUAL-DIFFERENCE-HACK1) (IMMEDIATE-DEPENDENTS0 RDIFFERENCE . EQUAL-DIFFERENCE-HACK1) (LEMMAS RPLUS . EQUAL-DIFFERENCE-HACK1))))) (PUT1-LST (QUOTE RPLUS-RDIFFERENCE-HACK) (QUOTE (IDATE 1000404112758 IMMEDIATE-DEPENDENTS0 (RPLUS-RDIFFERENCE-HACK-OFF RNEGS-CANCEL-LIST EVAL$-RPLUS-TREE-ZERO EQUAL-DIFFERENCE-HACK2 EQUAL-DIFFERENCE-HACK1) EVENT (PROVE-LEMMA RPLUS-RDIFFERENCE-HACK (REWRITE) (AND (EQUAL (RPLUS A (RDIFFERENCE B A)) (REDUCE B)) (EQUAL (RPLUS (RDIFFERENCE B A) A) (REDUCE B))) ((ENABLE-THEORY R1))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RDIFFERENCE-RPLUS-HACK2 . RPLUS-RDIFFERENCE-HACK) (IMMEDIATE-DEPENDENTS0 RPLUS-RDIFFERENCE-ARG1 . RPLUS-RDIFFERENCE-HACK) (IMMEDIATE-DEPENDENTS0 RDIFFERENCE-RPLUS-HACK . RPLUS-RDIFFERENCE-HACK) (IMMEDIATE-DEPENDENTS0 RPLUS-RDIFFERENCE-ARG2 . RPLUS-RDIFFERENCE-HACK) (IMMEDIATE-DEPENDENTS0 R1 . RPLUS-RDIFFERENCE-HACK) (IMMEDIATE-DEPENDENTS0 REDUCE . RPLUS-RDIFFERENCE-HACK) (IMMEDIATE-DEPENDENTS0 RDIFFERENCE . RPLUS-RDIFFERENCE-HACK) (IMMEDIATE-DEPENDENTS0 RPLUS . RPLUS-RDIFFERENCE-HACK) (LEMMAS RPLUS . RPLUS-RDIFFERENCE-HACK) (LEMMAS RPLUS . RPLUS-RDIFFERENCE-HACK))))) (PUT1-LST (QUOTE RDIFFERENCE-RPLUS-HACK2) (QUOTE (IDATE 1000404112758 IMMEDIATE-DEPENDENTS0 (RDIFFERENCE-RPLUS-HACK2-OFF EVAL$-RPLUS-TREE-DELETE RPLUS-RDIFFERENCE-HACK) EVENT (PROVE-LEMMA RDIFFERENCE-RPLUS-HACK2 (REWRITE) (EQUAL (RDIFFERENCE (RPLUS B A) A) (REDUCE B)) ((ENABLE RDIFFERENCE-RPLUS-HACK COMMUTATIVITY-OF-RPLUS) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-RPLUS . RDIFFERENCE-RPLUS-HACK2) (IMMEDIATE-DEPENDENTS0 RDIFFERENCE-RPLUS-HACK . RDIFFERENCE-RPLUS-HACK2) (IMMEDIATE-DEPENDENTS0 REDUCE . RDIFFERENCE-RPLUS-HACK2) (IMMEDIATE-DEPENDENTS0 RPLUS . RDIFFERENCE-RPLUS-HACK2) (IMMEDIATE-DEPENDENTS0 RDIFFERENCE . RDIFFERENCE-RPLUS-HACK2) (LEMMAS RDIFFERENCE . 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RPLUS-RZEROP) (IMMEDIATE-DEPENDENTS0 REDUCE . RPLUS-RZEROP) (IMMEDIATE-DEPENDENTS0 RPLUS . RPLUS-RZEROP) (IMMEDIATE-DEPENDENTS0 RZEROP . RPLUS-RZEROP) (LEMMAS RPLUS . RPLUS-RZEROP) (LEMMAS RPLUS . RPLUS-RZEROP))))) (PUT1-LST (QUOTE RPLUS-RZEROP-BRIDGE2) (QUOTE (IDATE 1000404112752 IMMEDIATE-DEPENDENTS0 (RPLUS-RZEROP-BRIDGE2-OFF RPLUS-RZEROP) EVENT (PROVE-LEMMA RPLUS-RZEROP-BRIDGE2 (REWRITE) (IMPLIES (NOT (ZEROP V)) (EQUAL (REDUCE (RATIONAL (MINUS (TIMES D V)) (TIMES V W))) (REDUCE (RATIONAL (MINUS D) W)))) ((ENABLE REDUCE RATIONALP) (ENABLE-THEORY R1))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-QUOTIENT-TIMES . RPLUS-RZEROP-BRIDGE2) (IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-TIMES-OVER-GCD . RPLUS-RZEROP-BRIDGE2) (IMMEDIATE-DEPENDENTS0 RATIONALP . RPLUS-RZEROP-BRIDGE2) (IMMEDIATE-DEPENDENTS0 RATIONAL . RPLUS-RZEROP-BRIDGE2) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . RPLUS-RZEROP-BRIDGE2) (IMMEDIATE-DEPENDENTS0 INTEGERP . 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R1) (IMMEDIATE-DEPENDENTS0 RATIONALP-RNEG . R1) (IMMEDIATE-DEPENDENTS0 RATIONALP-RTIMES . R1) (IMMEDIATE-DEPENDENTS0 RATIONALP-FIX-RATIONAL . R1) (IMMEDIATE-DEPENDENTS0 RATIONALP-RPLUS . R1) (IMMEDIATE-DEPENDENTS0 RATIONALP-REDUCE . R1))))) (PUT1-LST (QUOTE RATIONALP-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE RATIONALP-OFF RATIONALP T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RATIONALP . RATIONALP-OFF) (DISABLED-LEMMAS NIL RATIONALP RATIONALP-OFF . T))))) (PUT1-LST (QUOTE FIX-RATIONAL-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE FIX-RATIONAL-OFF FIX-RATIONAL T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 FIX-RATIONAL . FIX-RATIONAL-OFF) (DISABLED-LEMMAS NIL FIX-RATIONAL FIX-RATIONAL-OFF . T))))) (PUT1-LST (QUOTE REDUCE-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE REDUCE-OFF REDUCE T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REDUCE . REDUCE-OFF) (DISABLED-LEMMAS NIL REDUCE REDUCE-OFF . T))))) (PUT1-LST (QUOTE SIMPLE-RPLUS-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE SIMPLE-RPLUS-OFF SIMPLE-RPLUS T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SIMPLE-RPLUS . SIMPLE-RPLUS-OFF) (DISABLED-LEMMAS NIL SIMPLE-RPLUS SIMPLE-RPLUS-OFF . T))))) (PUT1-LST (QUOTE RPLUS-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE RPLUS-OFF RPLUS T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RPLUS . RPLUS-OFF) (DISABLED-LEMMAS NIL RPLUS RPLUS-OFF . T))))) (PUT1-LST (QUOTE SIMPLE-RNEG-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE SIMPLE-RNEG-OFF SIMPLE-RNEG T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SIMPLE-RNEG . SIMPLE-RNEG-OFF) (DISABLED-LEMMAS NIL SIMPLE-RNEG SIMPLE-RNEG-OFF . T))))) (PUT1-LST (QUOTE RNEG-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE RNEG-OFF RNEG T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RNEG . RNEG-OFF) (DISABLED-LEMMAS NIL RNEG RNEG-OFF . T))))) (PUT1-LST (QUOTE RDIFFERENCE-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE RDIFFERENCE-OFF RDIFFERENCE T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RDIFFERENCE . RDIFFERENCE-OFF) (DISABLED-LEMMAS NIL RDIFFERENCE RDIFFERENCE-OFF . T))))) (PUT1-LST (QUOTE SIMPLE-RTIMES-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE SIMPLE-RTIMES-OFF SIMPLE-RTIMES T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SIMPLE-RTIMES . SIMPLE-RTIMES-OFF) (DISABLED-LEMMAS NIL SIMPLE-RTIMES SIMPLE-RTIMES-OFF . T))))) (PUT1-LST (QUOTE RTIMES-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE RTIMES-OFF RTIMES T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RTIMES . RTIMES-OFF) (DISABLED-LEMMAS NIL RTIMES RTIMES-OFF . T))))) (PUT1-LST (QUOTE RQUOTIENT-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE RQUOTIENT-OFF RQUOTIENT T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RQUOTIENT . RQUOTIENT-OFF) (DISABLED-LEMMAS NIL RQUOTIENT RQUOTIENT-OFF . T))))) (PUT1-LST (QUOTE SIMPLE-RMAGNITUDE-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE SIMPLE-RMAGNITUDE-OFF SIMPLE-RMAGNITUDE T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SIMPLE-RMAGNITUDE . SIMPLE-RMAGNITUDE-OFF) (DISABLED-LEMMAS NIL SIMPLE-RMAGNITUDE SIMPLE-RMAGNITUDE-OFF . T))))) (PUT1-LST (QUOTE RMAGNITUDE-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE RMAGNITUDE-OFF RMAGNITUDE T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RMAGNITUDE . RMAGNITUDE-OFF) (DISABLED-LEMMAS NIL RMAGNITUDE RMAGNITUDE-OFF . T))))) (PUT1-LST (QUOTE RLESSP-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE RLESSP-OFF RLESSP T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RLESSP . RLESSP-OFF) (DISABLED-LEMMAS NIL RLESSP RLESSP-OFF . T))))) (PUT1-LST (QUOTE REQUAL-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE REQUAL-OFF REQUAL T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REQUAL . REQUAL-OFF) (DISABLED-LEMMAS NIL REQUAL REQUAL-OFF . T))))) (PUT1-LST (QUOTE INTEGERP-MINUS-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE INTEGERP-MINUS-OFF INTEGERP-MINUS T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 INTEGERP-MINUS . INTEGERP-MINUS-OFF) (DISABLED-LEMMAS NIL INTEGERP-MINUS INTEGERP-MINUS-OFF . T))))) (PUT1-LST (QUOTE FIX-INT-ON-INTEGERS-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE FIX-INT-ON-INTEGERS-OFF FIX-INT-ON-INTEGERS T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 FIX-INT-ON-INTEGERS . FIX-INT-ON-INTEGERS-OFF) (DISABLED-LEMMAS NIL FIX-INT-ON-INTEGERS FIX-INT-ON-INTEGERS-OFF . T))))) (PUT1-LST (QUOTE ITIMES-INEG-ARG1-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE ITIMES-INEG-ARG1-OFF ITIMES-INEG-ARG1 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ITIMES-INEG-ARG1 . ITIMES-INEG-ARG1-OFF) (DISABLED-LEMMAS NIL ITIMES-INEG-ARG1 ITIMES-INEG-ARG1-OFF . T))))) (PUT1-LST (QUOTE ITIMES-INEG-ARG2-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE ITIMES-INEG-ARG2-OFF ITIMES-INEG-ARG2 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ITIMES-INEG-ARG2 . ITIMES-INEG-ARG2-OFF) (DISABLED-LEMMAS NIL ITIMES-INEG-ARG2 ITIMES-INEG-ARG2-OFF . T))))) (PUT1-LST (QUOTE INTEGERP-IF-NEGATIVEP-NON-ZERO-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE INTEGERP-IF-NEGATIVEP-NON-ZERO-OFF INTEGERP-IF-NEGATIVEP-NON-ZERO T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 INTEGERP-IF-NEGATIVEP-NON-ZERO . INTEGERP-IF-NEGATIVEP-NON-ZERO-OFF) (DISABLED-LEMMAS NIL INTEGERP-IF-NEGATIVEP-NON-ZERO INTEGERP-IF-NEGATIVEP-NON-ZERO-OFF . T))))) (PUT1-LST (QUOTE INTEGERP-IF-NUMBERP-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE INTEGERP-IF-NUMBERP-OFF INTEGERP-IF-NUMBERP T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 INTEGERP-IF-NUMBERP . INTEGERP-IF-NUMBERP-OFF) (DISABLED-LEMMAS NIL INTEGERP-IF-NUMBERP INTEGERP-IF-NUMBERP-OFF . T))))) (PUT1-LST (QUOTE ITIMES-NEGATIVEP-ARG1-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE ITIMES-NEGATIVEP-ARG1-OFF ITIMES-NEGATIVEP-ARG1 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ITIMES-NEGATIVEP-ARG1 . ITIMES-NEGATIVEP-ARG1-OFF) (DISABLED-LEMMAS NIL ITIMES-NEGATIVEP-ARG1 ITIMES-NEGATIVEP-ARG1-OFF . T))))) (PUT1-LST (QUOTE ITIMES-NEGATIVEP-ARG2-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE ITIMES-NEGATIVEP-ARG2-OFF ITIMES-NEGATIVEP-ARG2 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ITIMES-NEGATIVEP-ARG2 . ITIMES-NEGATIVEP-ARG2-OFF) (DISABLED-LEMMAS NIL ITIMES-NEGATIVEP-ARG2 ITIMES-NEGATIVEP-ARG2-OFF . T))))) (PUT1-LST (QUOTE EQUAL-INEG-INEG-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE EQUAL-INEG-INEG-OFF EQUAL-INEG-INEG T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQUAL-INEG-INEG . EQUAL-INEG-INEG-OFF) (DISABLED-LEMMAS NIL EQUAL-INEG-INEG EQUAL-INEG-INEG-OFF . T))))) (PUT1-LST (QUOTE ITIMES-IS-TIMES-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE ITIMES-IS-TIMES-OFF ITIMES-IS-TIMES T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ITIMES-IS-TIMES . ITIMES-IS-TIMES-OFF) (DISABLED-LEMMAS NIL ITIMES-IS-TIMES ITIMES-IS-TIMES-OFF . T))))) (PUT1-LST (QUOTE IPLUS-IS-PLUS-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE IPLUS-IS-PLUS-OFF IPLUS-IS-PLUS T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 IPLUS-IS-PLUS . IPLUS-IS-PLUS-OFF) (DISABLED-LEMMAS NIL IPLUS-IS-PLUS IPLUS-IS-PLUS-OFF . T))))) (PUT1-LST (QUOTE RATIONALP-REDUCE-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE RATIONALP-REDUCE-OFF RATIONALP-REDUCE T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RATIONALP-REDUCE . RATIONALP-REDUCE-OFF) (DISABLED-LEMMAS NIL RATIONALP-REDUCE RATIONALP-REDUCE-OFF . T))))) (PUT1-LST (QUOTE RATIONALP-RPLUS-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE RATIONALP-RPLUS-OFF RATIONALP-RPLUS T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RATIONALP-RPLUS . RATIONALP-RPLUS-OFF) (DISABLED-LEMMAS NIL RATIONALP-RPLUS RATIONALP-RPLUS-OFF . T))))) (PUT1-LST (QUOTE RATIONALP-FIX-RATIONAL-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE RATIONALP-FIX-RATIONAL-OFF RATIONALP-FIX-RATIONAL T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RATIONALP-FIX-RATIONAL . RATIONALP-FIX-RATIONAL-OFF) (DISABLED-LEMMAS NIL RATIONALP-FIX-RATIONAL RATIONALP-FIX-RATIONAL-OFF . T))))) (PUT1-LST (QUOTE RATIONALP-RTIMES-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE RATIONALP-RTIMES-OFF RATIONALP-RTIMES T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RATIONALP-RTIMES . RATIONALP-RTIMES-OFF) (DISABLED-LEMMAS NIL RATIONALP-RTIMES RATIONALP-RTIMES-OFF . T))))) (PUT1-LST (QUOTE RATIONALP-RNEG-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE RATIONALP-RNEG-OFF RATIONALP-RNEG T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RATIONALP-RNEG . RATIONALP-RNEG-OFF) (DISABLED-LEMMAS NIL RATIONALP-RNEG RATIONALP-RNEG-OFF . T))))) (PUT1-LST (QUOTE RATIONALP-RDIFFERENCE-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE RATIONALP-RDIFFERENCE-OFF RATIONALP-RDIFFERENCE T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RATIONALP-RDIFFERENCE . RATIONALP-RDIFFERENCE-OFF) (DISABLED-LEMMAS NIL RATIONALP-RDIFFERENCE RATIONALP-RDIFFERENCE-OFF . T))))) (PUT1-LST (QUOTE RATIONALP-RQUOTIENT-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE RATIONALP-RQUOTIENT-OFF RATIONALP-RQUOTIENT T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RATIONALP-RQUOTIENT . RATIONALP-RQUOTIENT-OFF) (DISABLED-LEMMAS NIL RATIONALP-RQUOTIENT RATIONALP-RQUOTIENT-OFF . T))))) (PUT1-LST (QUOTE RATIONALP-RMAGNITUDE-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE RATIONALP-RMAGNITUDE-OFF RATIONALP-RMAGNITUDE T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RATIONALP-RMAGNITUDE . RATIONALP-RMAGNITUDE-OFF) (DISABLED-LEMMAS NIL RATIONALP-RMAGNITUDE RATIONALP-RMAGNITUDE-OFF . T))))) (PUT1-LST (QUOTE FIX-RATIONAL-REDUCE-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE FIX-RATIONAL-REDUCE-OFF FIX-RATIONAL-REDUCE T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 FIX-RATIONAL-REDUCE . FIX-RATIONAL-REDUCE-OFF) (DISABLED-LEMMAS NIL FIX-RATIONAL-REDUCE FIX-RATIONAL-REDUCE-OFF . T))))) (PUT1-LST (QUOTE FIX-RATIONAL-RPLUS-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE FIX-RATIONAL-RPLUS-OFF FIX-RATIONAL-RPLUS T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 FIX-RATIONAL-RPLUS . FIX-RATIONAL-RPLUS-OFF) (DISABLED-LEMMAS NIL FIX-RATIONAL-RPLUS FIX-RATIONAL-RPLUS-OFF . T))))) (PUT1-LST (QUOTE FIX-RATIONAL-FIX-RATIONAL-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE FIX-RATIONAL-FIX-RATIONAL-OFF FIX-RATIONAL-FIX-RATIONAL T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 FIX-RATIONAL-FIX-RATIONAL . FIX-RATIONAL-FIX-RATIONAL-OFF) (DISABLED-LEMMAS NIL FIX-RATIONAL-FIX-RATIONAL FIX-RATIONAL-FIX-RATIONAL-OFF . T))))) (PUT1-LST (QUOTE FIX-RATIONAL-RTIMES-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE FIX-RATIONAL-RTIMES-OFF FIX-RATIONAL-RTIMES T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 FIX-RATIONAL-RTIMES . FIX-RATIONAL-RTIMES-OFF) (DISABLED-LEMMAS NIL FIX-RATIONAL-RTIMES FIX-RATIONAL-RTIMES-OFF . T))))) (PUT1-LST (QUOTE FIX-RATIONAL-RNEG-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE FIX-RATIONAL-RNEG-OFF FIX-RATIONAL-RNEG T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 FIX-RATIONAL-RNEG . FIX-RATIONAL-RNEG-OFF) (DISABLED-LEMMAS NIL FIX-RATIONAL-RNEG FIX-RATIONAL-RNEG-OFF . T))))) (PUT1-LST (QUOTE FIX-RATIONAL-RDIFFERENCE-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE FIX-RATIONAL-RDIFFERENCE-OFF FIX-RATIONAL-RDIFFERENCE T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 FIX-RATIONAL-RDIFFERENCE . FIX-RATIONAL-RDIFFERENCE-OFF) (DISABLED-LEMMAS NIL FIX-RATIONAL-RDIFFERENCE FIX-RATIONAL-RDIFFERENCE-OFF . T))))) (PUT1-LST (QUOTE FIX-RATIONAL-RQUOTIENT-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE FIX-RATIONAL-RQUOTIENT-OFF FIX-RATIONAL-RQUOTIENT T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 FIX-RATIONAL-RQUOTIENT . FIX-RATIONAL-RQUOTIENT-OFF) (DISABLED-LEMMAS NIL FIX-RATIONAL-RQUOTIENT FIX-RATIONAL-RQUOTIENT-OFF . T))))) (PUT1-LST (QUOTE FIX-RATIONAL-RMAGNITUDE-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE FIX-RATIONAL-RMAGNITUDE-OFF FIX-RATIONAL-RMAGNITUDE T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 FIX-RATIONAL-RMAGNITUDE . FIX-RATIONAL-RMAGNITUDE-OFF) (DISABLED-LEMMAS NIL FIX-RATIONAL-RMAGNITUDE FIX-RATIONAL-RMAGNITUDE-OFF . T))))) (PUT1-LST (QUOTE RATIONAL-GENERALIZATION-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE RATIONAL-GENERALIZATION-OFF RATIONAL-GENERALIZATION T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RATIONAL-GENERALIZATION . RATIONAL-GENERALIZATION-OFF) (DISABLED-LEMMAS NIL RATIONAL-GENERALIZATION RATIONAL-GENERALIZATION-OFF . T))))) (PUT1-LST (QUOTE GCD-REMAINDER-FACT1-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE GCD-REMAINDER-FACT1-OFF GCD-REMAINDER-FACT1 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 GCD-REMAINDER-FACT1 . GCD-REMAINDER-FACT1-OFF) (DISABLED-LEMMAS NIL GCD-REMAINDER-FACT1 GCD-REMAINDER-FACT1-OFF . T))))) (PUT1-LST (QUOTE GCD-REMAINDER-FACT2-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE GCD-REMAINDER-FACT2-OFF GCD-REMAINDER-FACT2 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 GCD-REMAINDER-FACT2 . GCD-REMAINDER-FACT2-OFF) (DISABLED-LEMMAS NIL GCD-REMAINDER-FACT2 GCD-REMAINDER-FACT2-OFF . T))))) (PUT1-LST (QUOTE GCD-TIMES1-INDUCT-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE GCD-TIMES1-INDUCT-OFF GCD-TIMES1-INDUCT T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 GCD-TIMES1-INDUCT . GCD-TIMES1-INDUCT-OFF) (DISABLED-LEMMAS NIL GCD-TIMES1-INDUCT GCD-TIMES1-INDUCT-OFF . T))))) (PUT1-LST (QUOTE GCD-TIMES1-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE GCD-TIMES1-OFF GCD-TIMES1 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 GCD-TIMES1 . GCD-TIMES1-OFF) (DISABLED-LEMMAS NIL GCD-TIMES1 GCD-TIMES1-OFF . T))))) (PUT1-LST (QUOTE GCD-TIMES2-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE GCD-TIMES2-OFF GCD-TIMES2 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 GCD-TIMES2 . GCD-TIMES2-OFF) (DISABLED-LEMMAS NIL GCD-TIMES2 GCD-TIMES2-OFF . T))))) (PUT1-LST (QUOTE GCD-QUOTIENT-QUOTIENT-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE GCD-QUOTIENT-QUOTIENT-OFF GCD-QUOTIENT-QUOTIENT T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 GCD-QUOTIENT-QUOTIENT . GCD-QUOTIENT-QUOTIENT-OFF) (DISABLED-LEMMAS NIL GCD-QUOTIENT-QUOTIENT GCD-QUOTIENT-QUOTIENT-OFF . T))))) (PUT1-LST (QUOTE DIVIDES-EACH-EQUALITY-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE DIVIDES-EACH-EQUALITY-OFF DIVIDES-EACH-EQUALITY T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIVIDES-EACH-EQUALITY . DIVIDES-EACH-EQUALITY-OFF) (DISABLED-LEMMAS NIL DIVIDES-EACH-EQUALITY DIVIDES-EACH-EQUALITY-OFF . T))))) (PUT1-LST (QUOTE GCD-FACTORS-OFF1) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE GCD-FACTORS-OFF1 GCD-FACTORS T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 GCD-FACTORS . GCD-FACTORS-OFF1) (DISABLED-LEMMAS NIL GCD-FACTORS GCD-FACTORS-OFF1 . T))))) (PUT1-LST (QUOTE GCD-FACTORS-GIVES-LINEAR-COMBINATION-OFF1) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE GCD-FACTORS-GIVES-LINEAR-COMBINATION-OFF1 GCD-FACTORS-GIVES-LINEAR-COMBINATION T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 GCD-FACTORS-GIVES-LINEAR-COMBINATION . GCD-FACTORS-GIVES-LINEAR-COMBINATION-OFF1) (DISABLED-LEMMAS NIL GCD-FACTORS-GIVES-LINEAR-COMBINATION GCD-FACTORS-GIVES-LINEAR-COMBINATION-OFF1 . T))))) (PUT1-LST (QUOTE GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE-OFF1) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE-OFF1 GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE . GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE-OFF1) (DISABLED-LEMMAS NIL GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE-OFF1 . T))))) (PUT1-LST (QUOTE DPR-HACK1-OFF1) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE DPR-HACK1-OFF1 DPR-HACK1 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DPR-HACK1 . DPR-HACK1-OFF1) (DISABLED-LEMMAS NIL DPR-HACK1 DPR-HACK1-OFF1 . T))))) (PUT1-LST (QUOTE DPR-HACK2-OFF1) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE DPR-HACK2-OFF1 DPR-HACK2 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DPR-HACK2 . DPR-HACK2-OFF1) (DISABLED-LEMMAS NIL DPR-HACK2 DPR-HACK2-OFF1 . T))))) (PUT1-LST (QUOTE DPR-HACK3-OFF1) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE DPR-HACK3-OFF1 DPR-HACK3 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DPR-HACK3 . DPR-HACK3-OFF1) (DISABLED-LEMMAS NIL DPR-HACK3 DPR-HACK3-OFF1 . T))))) (PUT1-LST (QUOTE DPR-HACK4-OFF1) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE DPR-HACK4-OFF1 DPR-HACK4 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DPR-HACK4 . DPR-HACK4-OFF1) (DISABLED-LEMMAS NIL DPR-HACK4 DPR-HACK4-OFF1 . T))))) (PUT1-LST (QUOTE DPR-HACK5-OFF1) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE DPR-HACK5-OFF1 DPR-HACK5 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DPR-HACK5 . DPR-HACK5-OFF1) (DISABLED-LEMMAS NIL DPR-HACK5 DPR-HACK5-OFF1 . T))))) (PUT1-LST (QUOTE REMAINDER-0-SUFFICIENCY-OFF1) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE REMAINDER-0-SUFFICIENCY-OFF1 REMAINDER-0-SUFFICIENCY T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REMAINDER-0-SUFFICIENCY . 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T))))) (PUT1-LST (QUOTE REQUAL-RNEG-RNEG-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE REQUAL-RNEG-RNEG-OFF REQUAL-RNEG-RNEG T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REQUAL-RNEG-RNEG . REQUAL-RNEG-RNEG-OFF) (DISABLED-LEMMAS NIL REQUAL-RNEG-RNEG REQUAL-RNEG-RNEG-OFF . T))))) (PUT1-LST (QUOTE RNEG-RNEG-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE RNEG-RNEG-OFF RNEG-RNEG T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RNEG-RNEG . RNEG-RNEG-OFF) (DISABLED-LEMMAS NIL RNEG-RNEG RNEG-RNEG-OFF . T))))) (PUT1-LST (QUOTE RATIONALP-MEANS-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE RATIONALP-MEANS-OFF RATIONALP-MEANS T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RATIONALP-MEANS . RATIONALP-MEANS-OFF) (DISABLED-LEMMAS NIL RATIONALP-MEANS RATIONALP-MEANS-OFF . T))))) (PUT1-LST (QUOTE MEANS-RATIONALP-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE MEANS-RATIONALP-OFF MEANS-RATIONALP T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 MEANS-RATIONALP . 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T))))) (PUT1-LST (QUOTE SIMPLE-RPLUS-FIX-RATIONAL-ARG2-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE SIMPLE-RPLUS-FIX-RATIONAL-ARG2-OFF SIMPLE-RPLUS-FIX-RATIONAL-ARG2 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SIMPLE-RPLUS-FIX-RATIONAL-ARG2 . SIMPLE-RPLUS-FIX-RATIONAL-ARG2-OFF) (DISABLED-LEMMAS NIL SIMPLE-RPLUS-FIX-RATIONAL-ARG2 SIMPLE-RPLUS-FIX-RATIONAL-ARG2-OFF . T))))) (PUT1-LST (QUOTE FIX-RATIONAL-OF-RATIONALP-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE FIX-RATIONAL-OF-RATIONALP-OFF FIX-RATIONAL-OF-RATIONALP T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 FIX-RATIONAL-OF-RATIONALP . FIX-RATIONAL-OF-RATIONALP-OFF) (DISABLED-LEMMAS NIL FIX-RATIONAL-OF-RATIONALP FIX-RATIONAL-OF-RATIONALP-OFF . T))))) (PUT1-LST (QUOTE NEGATIVE-GUTS-INEG-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE NEGATIVE-GUTS-INEG-OFF NEGATIVE-GUTS-INEG T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 NEGATIVE-GUTS-INEG . NEGATIVE-GUTS-INEG-OFF) (DISABLED-LEMMAS NIL NEGATIVE-GUTS-INEG NEGATIVE-GUTS-INEG-OFF . 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T))))) (PUT1-LST (QUOTE RZEROP-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE RZEROP-OFF RZEROP T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RZEROP . RZEROP-OFF) (DISABLED-LEMMAS NIL RZEROP RZEROP-OFF . T))))) (PUT1-LST (QUOTE SIMPLE-RTIMES-RZEROP-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE SIMPLE-RTIMES-RZEROP-OFF SIMPLE-RTIMES-RZEROP T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SIMPLE-RTIMES-RZEROP . SIMPLE-RTIMES-RZEROP-OFF) (DISABLED-LEMMAS NIL SIMPLE-RTIMES-RZEROP SIMPLE-RTIMES-RZEROP-OFF . T))))) (PUT1-LST (QUOTE ASSOCIATIVITY-OF-SIMPLE-RTIMES-WHEN-NOT-RZEROP-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE ASSOCIATIVITY-OF-SIMPLE-RTIMES-WHEN-NOT-RZEROP-OFF ASSOCIATIVITY-OF-SIMPLE-RTIMES-WHEN-NOT-RZEROP T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-SIMPLE-RTIMES-WHEN-NOT-RZEROP . ASSOCIATIVITY-OF-SIMPLE-RTIMES-WHEN-NOT-RZEROP-OFF) (DISABLED-LEMMAS NIL ASSOCIATIVITY-OF-SIMPLE-RTIMES-WHEN-NOT-RZEROP ASSOCIATIVITY-OF-SIMPLE-RTIMES-WHEN-NOT-RZEROP-OFF . T))))) (PUT1-LST (QUOTE NUMERATOR-ZERO-RZEROP-BRIDGE-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE NUMERATOR-ZERO-RZEROP-BRIDGE-OFF NUMERATOR-ZERO-RZEROP-BRIDGE T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 NUMERATOR-ZERO-RZEROP-BRIDGE . NUMERATOR-ZERO-RZEROP-BRIDGE-OFF) (DISABLED-LEMMAS NIL NUMERATOR-ZERO-RZEROP-BRIDGE NUMERATOR-ZERO-RZEROP-BRIDGE-OFF . T))))) (PUT1-LST (QUOTE ASSOCIATIVITY-OF-SIMPLE-RTIMES-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE ASSOCIATIVITY-OF-SIMPLE-RTIMES-OFF ASSOCIATIVITY-OF-SIMPLE-RTIMES T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-SIMPLE-RTIMES . ASSOCIATIVITY-OF-SIMPLE-RTIMES-OFF) (DISABLED-LEMMAS NIL ASSOCIATIVITY-OF-SIMPLE-RTIMES ASSOCIATIVITY-OF-SIMPLE-RTIMES-OFF . T))))) (PUT1-LST (QUOTE REQUAL-SIMPLE-RTIMES-REQUAL-ARG1-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE REQUAL-SIMPLE-RTIMES-REQUAL-ARG1-OFF REQUAL-SIMPLE-RTIMES-REQUAL-ARG1 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REQUAL-SIMPLE-RTIMES-REQUAL-ARG1 . 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T))))) (PUT1-LST (QUOTE RTIMES-RDIFFERENCE-ARG1-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE RTIMES-RDIFFERENCE-ARG1-OFF RTIMES-RDIFFERENCE-ARG1 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RTIMES-RDIFFERENCE-ARG1 . RTIMES-RDIFFERENCE-ARG1-OFF) (DISABLED-LEMMAS NIL RTIMES-RDIFFERENCE-ARG1 RTIMES-RDIFFERENCE-ARG1-OFF . T))))) (PUT1-LST (QUOTE RTIMES-RDIFFERENCE-ARG2-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE RTIMES-RDIFFERENCE-ARG2-OFF RTIMES-RDIFFERENCE-ARG2 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RTIMES-RDIFFERENCE-ARG2 . RTIMES-RDIFFERENCE-ARG2-OFF) (DISABLED-LEMMAS NIL RTIMES-RDIFFERENCE-ARG2 RTIMES-RDIFFERENCE-ARG2-OFF . T))))) (PUT1-LST (QUOTE RNEG-RDIFFERENCE-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE RNEG-RDIFFERENCE-OFF RNEG-RDIFFERENCE T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RNEG-RDIFFERENCE . RNEG-RDIFFERENCE-OFF) (DISABLED-LEMMAS NIL RNEG-RDIFFERENCE RNEG-RDIFFERENCE-OFF . T))))) (PUT1-LST (QUOTE RDIFFERENCE-RNEG-ARG2-OFF) (QUOTE (IDATE 1000404112751 EVENT (TOGGLE RDIFFERENCE-RNEG-ARG2-OFF RDIFFERENCE-RNEG-ARG2 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RDIFFERENCE-RNEG-ARG2 . RDIFFERENCE-RNEG-ARG2-OFF) (DISABLED-LEMMAS NIL RDIFFERENCE-RNEG-ARG2 RDIFFERENCE-RNEG-ARG2-OFF . T))))) (PUT1-LST (QUOTE RDIFFERENCE-RNEG-ARG2) (QUOTE (IDATE 1000404112751 IMMEDIATE-DEPENDENTS0 (R1 RDIFFERENCE-RNEG-ARG2-OFF) EVENT (PROVE-LEMMA RDIFFERENCE-RNEG-ARG2 (REWRITE) (EQUAL (RDIFFERENCE X (RNEG Y)) (RPLUS X Y)) ((DISABLE RPLUS RNEG))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RPLUS-REDUCE-ARG2-REWRITE . RDIFFERENCE-RNEG-ARG2) (IMMEDIATE-DEPENDENTS0 RNEG-RNEG . RDIFFERENCE-RNEG-ARG2) (IMMEDIATE-DEPENDENTS0 RPLUS . RDIFFERENCE-RNEG-ARG2) (IMMEDIATE-DEPENDENTS0 RNEG . RDIFFERENCE-RNEG-ARG2) (IMMEDIATE-DEPENDENTS0 RDIFFERENCE . RDIFFERENCE-RNEG-ARG2) (LEMMAS RDIFFERENCE . 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QUOTIENT-GCD-TIMES-FACT5) (LEMMAS EQUAL . QUOTIENT-GCD-TIMES-FACT5))))) (PUT1-LST (QUOTE QUOTIENT-GCD-TIMES-FACT4) (QUOTE (IDATE 1000404112608 IMMEDIATE-DEPENDENTS0 (QUOTIENT-GCD-TIMES-FACT4-OFF REQUAL-REDUCE-REDUCE-EQUAL) EVENT (PROVE-LEMMA QUOTIENT-GCD-TIMES-FACT4 (REWRITE) (IMPLIES (AND (EQUAL (TIMES V Z) (TIMES W X)) (AND (LESSP (QUOTE 0) W) (LESSP (QUOTE 0) Z))) (EQUAL (EQUAL (QUOTIENT V (GCD W V)) (QUOTIENT X (GCD Z X))) (QUOTE *1*TRUE))) ((ENABLE QUOTIENT-GCD-TIMES-FACT COMMUTATIVITY-OF-GCD) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-GCD . QUOTIENT-GCD-TIMES-FACT4) (IMMEDIATE-DEPENDENTS0 QUOTIENT-GCD-TIMES-FACT . QUOTIENT-GCD-TIMES-FACT4) (IMMEDIATE-DEPENDENTS0 GCD . QUOTIENT-GCD-TIMES-FACT4) (LEMMAS EQUAL . 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QUOTIENT-GCD-TIMES-FACT) (IMMEDIATE-DEPENDENTS0 TIMES-GCD-FACT . QUOTIENT-GCD-TIMES-FACT) (IMMEDIATE-DEPENDENTS0 EQUAL-GCD-0 . QUOTIENT-GCD-TIMES-FACT) (IMMEDIATE-DEPENDENTS0 LESSP-GCD . QUOTIENT-GCD-TIMES-FACT) (IMMEDIATE-DEPENDENTS0 EQUAL-QUOTIENT-0 . QUOTIENT-GCD-TIMES-FACT) (IMMEDIATE-DEPENDENTS0 REMAINDER-GCD . QUOTIENT-GCD-TIMES-FACT) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-TIMES-QUOTIENT-ARG2 . QUOTIENT-GCD-TIMES-FACT) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO . QUOTIENT-GCD-TIMES-FACT) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . QUOTIENT-GCD-TIMES-FACT) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . QUOTIENT-GCD-TIMES-FACT) (IMMEDIATE-DEPENDENTS0 GCD-0 . QUOTIENT-GCD-TIMES-FACT) (IMMEDIATE-DEPENDENTS0 QUOTIENT-LESSP-ARG1 . QUOTIENT-GCD-TIMES-FACT) (IMMEDIATE-DEPENDENTS0 GCD . QUOTIENT-GCD-TIMES-FACT) (LEMMAS QUOTIENT . 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EQUAL-TIMES-TIMES-QUOTIENT-ARG2) (IMMEDIATE-DEPENDENTS0 REMAINDER-NOOP . EQUAL-TIMES-TIMES-QUOTIENT-ARG2) (IMMEDIATE-DEPENDENTS0 REMAINDER-ZERO . EQUAL-TIMES-TIMES-QUOTIENT-ARG2) (IMMEDIATE-DEPENDENTS0 REMAINDER-OF-NON-NUMBER . EQUAL-TIMES-TIMES-QUOTIENT-ARG2) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO . EQUAL-TIMES-TIMES-QUOTIENT-ARG2) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . EQUAL-TIMES-TIMES-QUOTIENT-ARG2) (IMMEDIATE-DEPENDENTS0 QUOTIENT-OF-NON-NUMBER . EQUAL-TIMES-TIMES-QUOTIENT-ARG2) (IMMEDIATE-DEPENDENTS0 EQUAL-QUOTIENT-0 . EQUAL-TIMES-TIMES-QUOTIENT-ARG2) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER . EQUAL-TIMES-TIMES-QUOTIENT-ARG2) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . EQUAL-TIMES-TIMES-QUOTIENT-ARG2) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . EQUAL-TIMES-TIMES-QUOTIENT-ARG2) (LEMMAS EQUAL . EQUAL-TIMES-TIMES-QUOTIENT-ARG2) (LEMMAS EQUAL . EQUAL-TIMES-TIMES-QUOTIENT-ARG2) (LEMMAS EQUAL . 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TIMES-GCD-FACT) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . TIMES-GCD-FACT) (IMMEDIATE-DEPENDENTS0 GCD-REMAINDER-TIMES-FACT1-PROOF . TIMES-GCD-FACT) (IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES1-INSTANCE . TIMES-GCD-FACT) (IMMEDIATE-DEPENDENTS0 GCD-0 . TIMES-GCD-FACT) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-GCD . TIMES-GCD-FACT) (IMMEDIATE-DEPENDENTS0 GCD-1 . TIMES-GCD-FACT) (IMMEDIATE-DEPENDENTS0 TIMES-1-ARG1 . TIMES-GCD-FACT) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . TIMES-GCD-FACT) (IMMEDIATE-DEPENDENTS0 GCD . TIMES-GCD-FACT) (LEMMAS EQUAL . 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GCD-REMAINDER-TIMES-FACT1-PROOF) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO . GCD-REMAINDER-TIMES-FACT1-PROOF) (IMMEDIATE-DEPENDENTS0 REMAINDER-OF-NON-NUMBER . GCD-REMAINDER-TIMES-FACT1-PROOF) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . GCD-REMAINDER-TIMES-FACT1-PROOF) (IMMEDIATE-DEPENDENTS0 DIVIDES-PRODUCT-REDUCTION . GCD-REMAINDER-TIMES-FACT1-PROOF) (IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES1 . GCD-REMAINDER-TIMES-FACT1-PROOF) (IMMEDIATE-DEPENDENTS0 GCD . GCD-REMAINDER-TIMES-FACT1-PROOF) (LEMMAS EQUAL . GCD-REMAINDER-TIMES-FACT1-PROOF))))) (PUT1-LST (QUOTE IQUOTIENT-OFF1) (QUOTE (IDATE 1000404112603 EVENT (TOGGLE IQUOTIENT-OFF1 IQUOTIENT T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 IQUOTIENT . IQUOTIENT-OFF1) (DISABLED-LEMMAS NIL IQUOTIENT IQUOTIENT-OFF1 . T))))) (PUT1-LST (QUOTE IREMAINDER-OFF1) (QUOTE (IDATE 1000404112603 EVENT (TOGGLE IREMAINDER-OFF1 IREMAINDER T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 IREMAINDER . IREMAINDER-OFF1) (DISABLED-LEMMAS NIL IREMAINDER IREMAINDER-OFF1 . T))))) (PUT1-LST (QUOTE IZEROP-OFF1) (QUOTE (IDATE 1000404112603 EVENT (TOGGLE IZEROP-OFF1 IZEROP T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 IZEROP . IZEROP-OFF1) (DISABLED-LEMMAS NIL IZEROP IZEROP-OFF1 . T))))) (PUT1-LST (QUOTE FIX-INT-OFF1) (QUOTE (IDATE 1000404112603 EVENT (TOGGLE FIX-INT-OFF1 FIX-INT T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 FIX-INT . FIX-INT-OFF1) (DISABLED-LEMMAS NIL FIX-INT FIX-INT-OFF1 . T))))) (PUT1-LST (QUOTE INEG-OFF1) (QUOTE (IDATE 1000404112603 EVENT (TOGGLE INEG-OFF1 INEG T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 INEG . INEG-OFF1) (DISABLED-LEMMAS NIL INEG INEG-OFF1 . T))))) (PUT1-LST (QUOTE ITIMES-OFF1) (QUOTE (IDATE 1000404112603 EVENT (TOGGLE ITIMES-OFF1 ITIMES T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ITIMES . ITIMES-OFF1) (DISABLED-LEMMAS NIL ITIMES ITIMES-OFF1 . T))))) (PUT1-LST (QUOTE IPLUS-OFF1) (QUOTE (IDATE 1000404112603 EVENT (TOGGLE IPLUS-OFF1 IPLUS T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 IPLUS . 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T))))) (PUT1-LST (QUOTE GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE-OFF) (QUOTE (IDATE 1000404112603 EVENT (TOGGLE GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE-OFF GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE . GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE-OFF) (DISABLED-LEMMAS NIL GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE-OFF . T))))) (PUT1-LST (QUOTE DPR-HACK5-OFF) (QUOTE (IDATE 1000404112603 EVENT (TOGGLE DPR-HACK5-OFF DPR-HACK5 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DPR-HACK5 . DPR-HACK5-OFF) (DISABLED-LEMMAS NIL DPR-HACK5 DPR-HACK5-OFF . T))))) (PUT1-LST (QUOTE DPR-HACK4-OFF) (QUOTE (IDATE 1000404112603 EVENT (TOGGLE DPR-HACK4-OFF DPR-HACK4 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DPR-HACK4 . DPR-HACK4-OFF) (DISABLED-LEMMAS NIL DPR-HACK4 DPR-HACK4-OFF . T))))) (PUT1-LST (QUOTE DPR-HACK3-OFF) (QUOTE (IDATE 1000404112603 EVENT (TOGGLE DPR-HACK3-OFF DPR-HACK3 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DPR-HACK3 . DPR-HACK3-OFF) (DISABLED-LEMMAS NIL DPR-HACK3 DPR-HACK3-OFF . T))))) (PUT1-LST (QUOTE DPR-HACK2-OFF) (QUOTE (IDATE 1000404112603 EVENT (TOGGLE DPR-HACK2-OFF DPR-HACK2 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DPR-HACK2 . DPR-HACK2-OFF) (DISABLED-LEMMAS NIL DPR-HACK2 DPR-HACK2-OFF . T))))) (PUT1-LST (QUOTE DPR-HACK1-OFF) (QUOTE (IDATE 1000404112603 EVENT (TOGGLE DPR-HACK1-OFF DPR-HACK1 T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DPR-HACK1 . DPR-HACK1-OFF) (DISABLED-LEMMAS NIL DPR-HACK1 DPR-HACK1-OFF . T))))) (PUT1-LST (QUOTE REMAINDER-0-SUFFICIENCY-OFF) (QUOTE (IDATE 1000404112603 EVENT (TOGGLE REMAINDER-0-SUFFICIENCY-OFF REMAINDER-0-SUFFICIENCY T) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REMAINDER-0-SUFFICIENCY . REMAINDER-0-SUFFICIENCY-OFF) (DISABLED-LEMMAS NIL REMAINDER-0-SUFFICIENCY REMAINDER-0-SUFFICIENCY-OFF . T))))) (PUT1-LST (QUOTE DIVIDES-PRODUCT-REDUCTION) (QUOTE (IDATE 1000404112603 IMMEDIATE-DEPENDENTS0 (DIVIDES-PRODUCT-REDUCTION-OFF TIMES-GCD-FACT GCD-REMAINDER-TIMES-FACT1-PROOF) EVENT (PROVE-LEMMA DIVIDES-PRODUCT-REDUCTION (REWRITE) (IMPLIES (AND (NUMBERP X) (AND (NUMBERP Y) (AND (NUMBERP C) (AND (EQUAL (GCD X Y) (QUOTE 1)) (EQUAL (REMAINDER (TIMES C Y) X) (QUOTE 0)))))) (EQUAL (REMAINDER C X) (QUOTE 0))) ((INSTRUCTIONS PROMOTE (REWRITE REMAINDER-0-SUFFICIENCY (($P (IPLUS (ITIMES C (CAR (GCD-FACTORS X Y))) (ITIMES (CDR (GCD-FACTORS X Y)) (IQUOTIENT (ITIMES C Y) X)))))) (DIVE 1) (REWRITE DPR-HACK5) TOP (CONTRADICT 4) (DIVE 1 1) (REWRITE GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE) TOP PROVE (DROP 4) PROVE))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-QUOTIENT . DIVIDES-PRODUCT-REDUCTION) (IMMEDIATE-DEPENDENTS0 DIFF-X-X . DIVIDES-PRODUCT-REDUCTION) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-LESSP-TIMES . DIVIDES-PRODUCT-REDUCTION) (IMMEDIATE-DEPENDENTS0 IPLUS . DIVIDES-PRODUCT-REDUCTION) (IMMEDIATE-DEPENDENTS0 REMAINDER-NOOP . DIVIDES-PRODUCT-REDUCTION) (IMMEDIATE-DEPENDENTS0 REMAINDER-ZERO . DIVIDES-PRODUCT-REDUCTION) (IMMEDIATE-DEPENDENTS0 EQUAL-QUOTIENT-0 . DIVIDES-PRODUCT-REDUCTION) (IMMEDIATE-DEPENDENTS0 PLUS-STOPPER . DIVIDES-PRODUCT-REDUCTION) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . DIVIDES-PRODUCT-REDUCTION) (IMMEDIATE-DEPENDENTS0 IPLUS-IS-PLUS . DIVIDES-PRODUCT-REDUCTION) (IMMEDIATE-DEPENDENTS0 IDIFFERENCE . DIVIDES-PRODUCT-REDUCTION) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . DIVIDES-PRODUCT-REDUCTION) (IMMEDIATE-DEPENDENTS0 INEG . DIVIDES-PRODUCT-REDUCTION) (IMMEDIATE-DEPENDENTS0 IQUOTIENT . DIVIDES-PRODUCT-REDUCTION) (IMMEDIATE-DEPENDENTS0 IZEROP . DIVIDES-PRODUCT-REDUCTION) (IMMEDIATE-DEPENDENTS0 FIX-INT-ON-INTEGERS . DIVIDES-PRODUCT-REDUCTION) (IMMEDIATE-DEPENDENTS0 INTEGERP-IF-NUMBERP . DIVIDES-PRODUCT-REDUCTION) (IMMEDIATE-DEPENDENTS0 IREMAINDER . DIVIDES-PRODUCT-REDUCTION) (IMMEDIATE-DEPENDENTS0 TIMES-1-ARG1 . DIVIDES-PRODUCT-REDUCTION) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . DIVIDES-PRODUCT-REDUCTION) (IMMEDIATE-DEPENDENTS0 ITIMES-IS-TIMES . DIVIDES-PRODUCT-REDUCTION) (IMMEDIATE-DEPENDENTS0 GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE . DIVIDES-PRODUCT-REDUCTION) (IMMEDIATE-DEPENDENTS0 DPR-HACK5 . DIVIDES-PRODUCT-REDUCTION) (IMMEDIATE-DEPENDENTS0 REMAINDER-0-SUFFICIENCY . DIVIDES-PRODUCT-REDUCTION) (IMMEDIATE-DEPENDENTS0 GCD . DIVIDES-PRODUCT-REDUCTION) (LEMMAS REMAINDER . DIVIDES-PRODUCT-REDUCTION))))) (PUT1-LST (QUOTE REMAINDER-0-SUFFICIENCY) (QUOTE (IDATE 1000404112602 IMMEDIATE-DEPENDENTS0 (REMAINDER-0-SUFFICIENCY-OFF1 REMAINDER-0-SUFFICIENCY-OFF DIVIDES-PRODUCT-REDUCTION) EVENT (PROVE-LEMMA REMAINDER-0-SUFFICIENCY (REWRITE) (IMPLIES (AND (NUMBERP X) (AND (NUMBERP C) (EQUAL (ITIMES X P) C))) (EQUAL (EQUAL (REMAINDER C X) (QUOTE 0)) (QUOTE *1*TRUE)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 FIX-INT . REMAINDER-0-SUFFICIENCY) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . REMAINDER-0-SUFFICIENCY) (IMMEDIATE-DEPENDENTS0 INTEGERP-MINUS . REMAINDER-0-SUFFICIENCY) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . REMAINDER-0-SUFFICIENCY) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-ITIMES . REMAINDER-0-SUFFICIENCY) (IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES1-INSTANCE . REMAINDER-0-SUFFICIENCY) (IMMEDIATE-DEPENDENTS0 IZEROP . REMAINDER-0-SUFFICIENCY) (IMMEDIATE-DEPENDENTS0 ITIMES-ZERO1 . REMAINDER-0-SUFFICIENCY) (IMMEDIATE-DEPENDENTS0 ITIMES . REMAINDER-0-SUFFICIENCY) (LEMMAS EQUAL . REMAINDER-0-SUFFICIENCY))))) (PUT1-LST (QUOTE DPR-HACK5) (QUOTE (IDATE 1000404112602 IMMEDIATE-DEPENDENTS0 (DPR-HACK5-OFF1 DPR-HACK5-OFF DIVIDES-PRODUCT-REDUCTION) EVENT (PROVE-LEMMA DPR-HACK5 (REWRITE) (IMPLIES (AND (NUMBERP X) (AND (NUMBERP Y) (AND (NUMBERP C) (EQUAL (IREMAINDER (ITIMES C Y) X) (QUOTE 0))))) (EQUAL (ITIMES X (IPLUS (ITIMES C A) (ITIMES B (IQUOTIENT (ITIMES C Y) X)))) (ITIMES C (IPLUS (ITIMES A X) (ITIMES B Y))))) ((ENABLE DPR-HACK1 DPR-HACK2 DPR-HACK3 DPR-HACK4) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DPR-HACK2 . DPR-HACK5) (IMMEDIATE-DEPENDENTS0 DPR-HACK1 . DPR-HACK5) (IMMEDIATE-DEPENDENTS0 DPR-HACK4 . DPR-HACK5) (IMMEDIATE-DEPENDENTS0 DPR-HACK3 . DPR-HACK5) (IMMEDIATE-DEPENDENTS0 IQUOTIENT . DPR-HACK5) (IMMEDIATE-DEPENDENTS0 IPLUS . DPR-HACK5) (IMMEDIATE-DEPENDENTS0 ITIMES . DPR-HACK5) (IMMEDIATE-DEPENDENTS0 IREMAINDER . DPR-HACK5) (LEMMAS ITIMES . DPR-HACK5))))) (PUT1-LST (QUOTE DPR-HACK4) (QUOTE (IDATE 1000404112602 IMMEDIATE-DEPENDENTS0 (DPR-HACK4-OFF1 DPR-HACK4-OFF DPR-HACK5) EVENT (PROVE-LEMMA DPR-HACK4 (REWRITE) (EQUAL (IPLUS (ITIMES C (ITIMES A X)) (ITIMES C (ITIMES B Y))) (ITIMES C (IPLUS (ITIMES A X) (ITIMES B Y)))) ((ENABLE-THEORY INTEGERS GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-ITIMES . DPR-HACK4) (IMMEDIATE-DEPENDENTS0 ITIMES-DISTRIBUTES-OVER-IPLUS . DPR-HACK4) (IMMEDIATE-DEPENDENTS0 INTEGERS . DPR-HACK4) (IMMEDIATE-DEPENDENTS0 ITIMES . DPR-HACK4) (IMMEDIATE-DEPENDENTS0 IPLUS . DPR-HACK4) (LEMMAS IPLUS . DPR-HACK4))))) (PUT1-LST (QUOTE DPR-HACK3) (QUOTE (IDATE 1000404112602 IMMEDIATE-DEPENDENTS0 (DPR-HACK3-OFF1 DPR-HACK3-OFF DPR-HACK5) EVENT (PROVE-LEMMA DPR-HACK3 (REWRITE) (EQUAL (IPLUS (ITIMES C (ITIMES A X)) (ITIMES B (ITIMES C Y))) (IPLUS (ITIMES C (ITIMES A X)) (ITIMES C (ITIMES B Y)))) ((ENABLE-THEORY INTEGERS GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-ITIMES . DPR-HACK3) (IMMEDIATE-DEPENDENTS0 FIX-INT-ITIMES . DPR-HACK3) (IMMEDIATE-DEPENDENTS0 IPLUS-CANCELLATION . DPR-HACK3) (IMMEDIATE-DEPENDENTS0 INTEGERS . DPR-HACK3) (IMMEDIATE-DEPENDENTS0 ITIMES . DPR-HACK3) (IMMEDIATE-DEPENDENTS0 IPLUS . DPR-HACK3) (LEMMAS IPLUS . DPR-HACK3))))) (PUT1-LST (QUOTE DPR-HACK2) (QUOTE (IDATE 1000404112602 IMMEDIATE-DEPENDENTS0 (DPR-HACK2-OFF1 DPR-HACK2-OFF DPR-HACK5) EVENT (PROVE-LEMMA DPR-HACK2 (REWRITE) (IMPLIES (AND (NUMBERP X) (AND (NUMBERP Y) (AND (NUMBERP C) (EQUAL (IREMAINDER (ITIMES C Y) X) (QUOTE 0))))) (EQUAL (ITIMES (IQUOTIENT (ITIMES C Y) X) X) (ITIMES C Y)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 IPLUS . DPR-HACK2) (IMMEDIATE-DEPENDENTS0 EQUAL-QUOTIENT-0 . DPR-HACK2) (IMMEDIATE-DEPENDENTS0 PLUS-STOPPER . DPR-HACK2) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . DPR-HACK2) (IMMEDIATE-DEPENDENTS0 IPLUS-IS-PLUS . DPR-HACK2) (IMMEDIATE-DEPENDENTS0 ITIMES-IS-TIMES . DPR-HACK2) (IMMEDIATE-DEPENDENTS0 IDIFFERENCE . DPR-HACK2) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . DPR-HACK2) (IMMEDIATE-DEPENDENTS0 INEG . DPR-HACK2) (IMMEDIATE-DEPENDENTS0 IZEROP . DPR-HACK2) (IMMEDIATE-DEPENDENTS0 FIX-INT-ON-INTEGERS . DPR-HACK2) (IMMEDIATE-DEPENDENTS0 INTEGERP-IF-NUMBERP . DPR-HACK2) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . DPR-HACK2) (IMMEDIATE-DEPENDENTS0 IQUOTIENT . DPR-HACK2) (IMMEDIATE-DEPENDENTS0 ITIMES . DPR-HACK2) (IMMEDIATE-DEPENDENTS0 IREMAINDER . DPR-HACK2) (LEMMAS ITIMES . DPR-HACK2))))) (PUT1-LST (QUOTE DPR-HACK1) (QUOTE (IDATE 1000404112601 IMMEDIATE-DEPENDENTS0 (DPR-HACK1-OFF1 DPR-HACK1-OFF DPR-HACK5) EVENT (PROVE-LEMMA DPR-HACK1 (REWRITE) (EQUAL (ITIMES X (IPLUS (ITIMES C A) (ITIMES B Q))) (IPLUS (ITIMES C (ITIMES A X)) (ITIMES B (ITIMES Q X)))) ((ENABLE-THEORY INTEGERS GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-ITIMES . DPR-HACK1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-ITIMES . DPR-HACK1) (IMMEDIATE-DEPENDENTS0 ITIMES-DISTRIBUTES-OVER-IPLUS . DPR-HACK1) (IMMEDIATE-DEPENDENTS0 INTEGERS . DPR-HACK1) (IMMEDIATE-DEPENDENTS0 IPLUS . DPR-HACK1) (IMMEDIATE-DEPENDENTS0 ITIMES . DPR-HACK1) (LEMMAS ITIMES . DPR-HACK1))))) (PUT1-LST (QUOTE GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE) (QUOTE (IDATE 1000404112601 IMMEDIATE-DEPENDENTS0 (GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE-OFF1 GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE-OFF DIVIDES-PRODUCT-REDUCTION) EVENT (PROVE-LEMMA GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE (REWRITE) (IMPLIES (AND (NUMBERP X) (NUMBERP Y)) (EQUAL (GCD X Y) (IPLUS (ITIMES (CAR (GCD-FACTORS X Y)) X) (ITIMES (CDR (GCD-FACTORS X Y)) Y)))) ((USE (GCD-FACTORS-GIVES-LINEAR-COMBINATION)) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 GCD-FACTORS-GIVES-LINEAR-COMBINATION . GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE) (IMMEDIATE-DEPENDENTS0 GCD-FACTORS . GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE) (IMMEDIATE-DEPENDENTS0 ITIMES . GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE) (IMMEDIATE-DEPENDENTS0 IPLUS . GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE) (IMMEDIATE-DEPENDENTS0 GCD . GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE) (LEMMAS GCD . GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE))))) (PUT1-LST (QUOTE IQUOTIENT-ON) (QUOTE (IDATE 1000404112601 EVENT (TOGGLE IQUOTIENT-ON IQUOTIENT NIL) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 IQUOTIENT . IQUOTIENT-ON) (DISABLED-LEMMAS NIL IQUOTIENT IQUOTIENT-ON))))) (PUT1-LST (QUOTE IREMAINDER-ON) (QUOTE (IDATE 1000404112601 EVENT (TOGGLE IREMAINDER-ON IREMAINDER NIL) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 IREMAINDER . IREMAINDER-ON) (DISABLED-LEMMAS NIL IREMAINDER IREMAINDER-ON))))) (PUT1-LST (QUOTE GCD-FACTORS-GIVES-LINEAR-COMBINATION) (QUOTE (IDATE 1000404112601 IMMEDIATE-DEPENDENTS0 (GCD-FACTORS-GIVES-LINEAR-COMBINATION-OFF1 GCD-FACTORS-GIVES-LINEAR-COMBINATION-OFF GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE) EVENT (PROVE-LEMMA GCD-FACTORS-GIVES-LINEAR-COMBINATION NIL (IMPLIES (AND (NUMBERP X) (NUMBERP Y)) (EQUAL (IPLUS (ITIMES (CAR (GCD-FACTORS X Y)) X) (ITIMES (CDR (GCD-FACTORS X Y)) Y)) (GCD X Y)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIFF-DIFF-ARG2-CASESPLIT . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 DIFF-X-X . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 PLUS-DIFFERENCE-ARG2-CASESPLIT . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 LESSP-GCD . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES2 . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-LEQ-ARG1 . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES1 . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 DIFF-DIFF-ARG1 . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 DIFF-DIFF-ARG2 . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 EQUAL-GCD-0 . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 PLUS-DIFFERENCE-ARG2 . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 ITIMES-NEGATIVEP-ARG2 . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE-0 . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-LESSP-TIMES . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 TIMES-DISTRIBUTES-OVER-DIFFERENCE . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 INEG . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 IDIFFERENCE . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 ITIMES-DISTRIBUTES-OVER-IPLUS . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-IPLUS . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-IPLUS . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 IPLUS-LEFT-ID . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 INTEGERP . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 ITIMES-FIX-INT2 . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 ITIMES-NEGATIVEP-ARG1 . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-IPLUS . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 IDIFFERENCE-RIGHT-ID . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-IPLUS . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 INTEGERP-IF-NEGATIVEP-NON-ZERO . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 FIX-INT-ON-INTEGERS . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 IPLUS-0 . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 TIMES-DISTRIBUTES-OVER-PLUS . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 INTEGERP-IF-NUMBERP . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 TIMES-1-ARG1 . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 ITIMES-IS-TIMES . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 GCD-0 . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 LESSP-DIFFERENCE . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 PLUS-STOPPER . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 IPLUS-IS-PLUS . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 FIX-INT . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 INTEGERP-MINUS . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-ITIMES . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 GCD . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 GCD-FACTORS . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 ITIMES . GCD-FACTORS-GIVES-LINEAR-COMBINATION) (IMMEDIATE-DEPENDENTS0 IPLUS . GCD-FACTORS-GIVES-LINEAR-COMBINATION))))) (PUT1-LST (QUOTE *1*GCD-FACTORS) (QUOTE (MAIN-EVENT GCD-FACTORS))) (PUT1-LST (QUOTE GCD-FACTORS) (QUOTE (TYPE-PRESCRIPTION-LST ((GCD-FACTORS 16 NIL NIL)) TOTALP-LST ((GCD-FACTORS . T)) QUICK-BLOCK-INFO (QUESTIONABLE QUESTIONABLE) SDEFN (LAMBDA (X Y) (IF (EQUAL X (QUOTE 0)) (QUOTE (0 . 1)) (IF (NUMBERP X) (IF (EQUAL Y (QUOTE 0)) (QUOTE (1 . 0)) (IF (NUMBERP Y) (IF (LESSP X Y) (CONS (IDIFFERENCE (CAR (GCD-FACTORS X (DIFFERENCE Y X))) (CDR (GCD-FACTORS X (DIFFERENCE Y X)))) (CDR (GCD-FACTORS X (DIFFERENCE Y X)))) (CONS (CAR (GCD-FACTORS (DIFFERENCE X Y) Y)) (IDIFFERENCE (CDR (GCD-FACTORS (DIFFERENCE X Y) Y)) (CAR (GCD-FACTORS (DIFFERENCE X Y) Y))))) (QUOTE (1 . 0)))) (QUOTE (0 . 1))))) LISP-CODE *1*GCD-FACTORS SUBRP *1*FALSE 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 (ADD1 X) (FIX Y)) ORD-LESSP (ADD1-EQUAL ZEROP ORD-LESSP LESSP SUB1-ADD1 LESSP-DIFFERENCE FIX CDR-CONS CAR-CONS ORDINALP))) IDATE 1000404112553 CONTROLLER-POCKETS (3) SATELLITES (*1*GCD-FACTORS) IMMEDIATE-DEPENDENTS0 (GCD-FACTORS-OFF1 GCD-FACTORS-OFF GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE GCD-FACTORS-GIVES-LINEAR-COMBINATION) EVENT (DEFN GCD-FACTORS (X Y) (IF (ZEROP X) (QUOTE (0 . 1)) (IF (ZEROP Y) (QUOTE (1 . 0)) (IF (LESSP X Y) (CONS (IDIFFERENCE (CAR (GCD-FACTORS X (DIFFERENCE Y X))) (CDR (GCD-FACTORS X (DIFFERENCE Y X)))) (CDR (GCD-FACTORS X (DIFFERENCE Y X)))) (CONS (CAR (GCD-FACTORS (DIFFERENCE X Y) Y)) (IDIFFERENCE (CDR (GCD-FACTORS (DIFFERENCE X Y) Y)) (CAR (GCD-FACTORS (DIFFERENCE X Y) Y))))))) ((ORD-LESSP (CONS (ADD1 X) (FIX Y))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 IDIFFERENCE . 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GCD-QUOTIENT-QUOTIENT) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . GCD-QUOTIENT-QUOTIENT) (IMMEDIATE-DEPENDENTS0 QUOTIENT-PLUS . GCD-QUOTIENT-QUOTIENT) (IMMEDIATE-DEPENDENTS0 GCD-PLUS-INSTANCE . GCD-QUOTIENT-QUOTIENT) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-ELIM . GCD-QUOTIENT-QUOTIENT) (IMMEDIATE-DEPENDENTS0 LESSP-DIFFERENCE . GCD-QUOTIENT-QUOTIENT) (IMMEDIATE-DEPENDENTS0 GCD . GCD-QUOTIENT-QUOTIENT) (LEMMAS GCD . GCD-QUOTIENT-QUOTIENT))))) (PUT1-LST (QUOTE GCD-TIMES2) (QUOTE (IDATE 1000404112550 IMMEDIATE-DEPENDENTS0 (GCD-TIMES2-OFF) EVENT (PROVE-LEMMA GCD-TIMES2 (REWRITE) (EQUAL (GCD Y (TIMES X Y)) (FIX Y)) ((DISABLE FIX) (ENABLE COMMUTATIVITY-OF-TIMES) (USE (GCD-TIMES1 (X Y) (Y X))) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . GCD-TIMES2) (IMMEDIATE-DEPENDENTS0 GCD-TIMES1 . GCD-TIMES2) (IMMEDIATE-DEPENDENTS0 GCD . GCD-TIMES2) (LEMMAS GCD . GCD-TIMES2))))) (PUT1-LST (QUOTE GCD-TIMES1) (QUOTE (IDATE 1000404112550 IMMEDIATE-DEPENDENTS0 (GCD-TIMES1-OFF GCD-TIMES2) EVENT (PROVE-LEMMA GCD-TIMES1 (REWRITE) (EQUAL (GCD X (TIMES X Y)) (FIX X)) ((INDUCT (GCD-TIMES1-INDUCT X Y)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-1-ARG1 . GCD-TIMES1) (IMMEDIATE-DEPENDENTS0 TIMES-SUB1 . GCD-TIMES1) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-LEQ-ARG1 . GCD-TIMES1) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES2 . GCD-TIMES1) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES3 . GCD-TIMES1) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . GCD-TIMES1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . GCD-TIMES1) (IMMEDIATE-DEPENDENTS0 GCD-0 . GCD-TIMES1) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO . GCD-TIMES1) (IMMEDIATE-DEPENDENTS0 GCD-TIMES1-INDUCT . GCD-TIMES1) (IMMEDIATE-DEPENDENTS0 GCD . GCD-TIMES1) (LEMMAS GCD . GCD-TIMES1))))) (PUT1-LST (QUOTE *1*GCD-TIMES1-INDUCT) (QUOTE (MAIN-EVENT GCD-TIMES1-INDUCT))) (PUT1-LST (QUOTE GCD-TIMES1-INDUCT) (QUOTE (TYPE-PRESCRIPTION-LST ((GCD-TIMES1-INDUCT 2 NIL NIL)) TOTALP-LST ((GCD-TIMES1-INDUCT . T)) QUICK-BLOCK-INFO (UNCHANGING SELF-REFLEXIVE) SDEFN (LAMBDA (X Y) (IF (EQUAL Y (QUOTE 0)) (QUOTE *1*TRUE) (IF (NUMBERP Y) (GCD-TIMES1-INDUCT X (SUB1 Y)) (QUOTE *1*TRUE)))) LISP-CODE *1*GCD-TIMES1-INDUCT SUBRP *1*FALSE INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP Y)) NIL) (TESTS-AND-CASES ((NOT (ZEROP Y))) ((X (SUB1 Y))))) LEVEL-NO 1 JUSTIFICATIONS ((JUSTIFICATION (Y) (COUNT Y) LESSP (ZERO ZEROP COUNT-NUMBERP))) IDATE 1000404112550 CONTROLLER-POCKETS (2) SATELLITES (*1*GCD-TIMES1-INDUCT) IMMEDIATE-DEPENDENTS0 (GCD-TIMES1-INDUCT-OFF GCD-TIMES1) EVENT (DEFN GCD-TIMES1-INDUCT (X Y) (IF (ZEROP Y) (QUOTE *1*TRUE) (GCD-TIMES1-INDUCT X (SUB1 Y)))) LOCAL-UNDO-TUPLES ((DCELL . *1*GCD-TIMES1-INDUCT))))) (PUT1-LST (QUOTE GCD-REMAINDER-FACT2) (QUOTE (IDATE 1000404112550 IMMEDIATE-DEPENDENTS0 (GCD-REMAINDER-FACT2-OFF) EVENT (PROVE-LEMMA GCD-REMAINDER-FACT2 (REWRITE) (IMPLIES (AND (LESSP (QUOTE 1) B) (EQUAL (GCD B A) (QUOTE 1))) (NOT (EQUAL (REMAINDER A B) (QUOTE 0)))) ((ENABLE COMMUTATIVITY-OF-GCD GCD-REMAINDER-FACT1) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-GCD . GCD-REMAINDER-FACT2) (IMMEDIATE-DEPENDENTS0 GCD-REMAINDER-FACT1 . GCD-REMAINDER-FACT2) (IMMEDIATE-DEPENDENTS0 GCD . GCD-REMAINDER-FACT2) (LEMMAS EQUAL . GCD-REMAINDER-FACT2))))) (PUT1-LST (QUOTE GCD-REMAINDER-FACT1) (QUOTE (IDATE 1000404112550 IMMEDIATE-DEPENDENTS0 (GCD-REMAINDER-FACT1-OFF GCD-REMAINDER-FACT2) EVENT (PROVE-LEMMA GCD-REMAINDER-FACT1 (REWRITE) (IMPLIES (AND (LESSP (QUOTE 1) B) (EQUAL (GCD A B) (QUOTE 1))) (NOT (EQUAL (REMAINDER A B) (QUOTE 0)))) ((ENABLE GCD))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 GCD-0 . GCD-REMAINDER-FACT1) (IMMEDIATE-DEPENDENTS0 REMAINDER-NOOP . GCD-REMAINDER-FACT1) (IMMEDIATE-DEPENDENTS0 PLUS-STOPPER . GCD-REMAINDER-FACT1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-GCD . GCD-REMAINDER-FACT1) (IMMEDIATE-DEPENDENTS0 REMAINDER-1-ARG2 . GCD-REMAINDER-FACT1) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER . GCD-REMAINDER-FACT1) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . GCD-REMAINDER-FACT1) (IMMEDIATE-DEPENDENTS0 GCD . GCD-REMAINDER-FACT1) (LEMMAS EQUAL . GCD-REMAINDER-FACT1))))) (PUT1-LST (QUOTE RATIONAL-GENERALIZATION) (QUOTE (IDATE 1000404112550 IMMEDIATE-DEPENDENTS0 (R2 REQUAL-SIMPLE-RPLUS-X-X-REWRITE RPLUS-RZEROP R1 RATIONAL-GENERALIZATION-OFF SIMPLE-RPLUS-BRIDGE REQUAL-RZEROP-SIMPLE-RPLUS RATIONALP-SIMPLE-RTIMES SIMPLE-RPLUS-RZEROP TRANSITIVITY-OF-REQUAL-BRIDGE REQUAL-ASSOCIATIVITY-OF-SIMPLE-RPLUS) EVENT (PROVE-LEMMA RATIONAL-GENERALIZATION (GENERALIZE) (AND (IMPLIES (RATIONALP X) (INTEGERP (NUMERATOR X))) (AND (IMPLIES (RATIONALP X) (NUMBERP (DENOMINATOR X))) (IMPLIES (RATIONALP X) (NOT (ZEROP (DENOMINATOR X))))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RATIONAL . RATIONAL-GENERALIZATION) (IMMEDIATE-DEPENDENTS0 INTEGERP . RATIONAL-GENERALIZATION) (IMMEDIATE-DEPENDENTS0 RATIONALP . RATIONAL-GENERALIZATION) (GENERALIZE-LEMMAS NIL . 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(REWRITE-RULE REQUAL-SIMPLE-RPLUS-BRIDGE NIL (EQUAL (REQUAL (SIMPLE-RPLUS (REDUCE X) Y) Z) (REQUAL (SIMPLE-RPLUS X Y) Z)) NIL) (REWRITE-RULE EQUAL-REQUAL-REWRITE ((REQUAL B C)) (EQUAL (REQUAL B A) (REQUAL C A)) NIL) (REWRITE-RULE EQUAL-REQUAL-REWRITE ((REQUAL B C)) (EQUAL (REQUAL A B) (REQUAL C A)) NIL) (REWRITE-RULE EQUAL-REQUAL-REWRITE ((REQUAL B C)) (EQUAL (REQUAL A B) (REQUAL A C)) NIL) (REWRITE-RULE TRANSITIVITY-OF-REQUAL ((REQUAL B A) (REQUAL C B)) (REQUAL A C) NIL) (REWRITE-RULE TRANSITIVITY-OF-REQUAL ((REQUAL B A) (REQUAL B C)) (REQUAL A C) NIL) (REWRITE-RULE TRANSITIVITY-OF-REQUAL ((REQUAL A B) (REQUAL C B)) (REQUAL A C) NIL) (REWRITE-RULE TRANSITIVITY-OF-REQUAL ((REQUAL A B) (REQUAL B C)) (REQUAL A C) NIL) (REWRITE-RULE TRANSITIVITY-OF-REQUAL-BRIDGE ((REQUAL A B) (REQUAL B C)) (REQUAL A C) NIL) (REWRITE-RULE REQUAL-ASSOCIATIVITY-OF-SIMPLE-RPLUS NIL (REQUAL (SIMPLE-RPLUS (SIMPLE-RPLUS X Y) Z) (SIMPLE-RPLUS X (SIMPLE-RPLUS Y Z))) NIL) (REWRITE-RULE REQUAL-RNEG-RNEG NIL (REQUAL 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Y))) (REWRITE-RULE REQUAL-REDUCE-REDUCE-EQUAL NIL (EQUAL (REQUAL A B) (EQUAL (REDUCE A) (REDUCE B))) NIL)) TOTALP-LST ((REQUAL . T)) SDEFN (LAMBDA (X Y) (EQUAL (ITIMES (NUMERATOR (FIX-RATIONAL X)) (DENOMINATOR (FIX-RATIONAL Y))) (ITIMES (NUMERATOR (FIX-RATIONAL Y)) (DENOMINATOR (FIX-RATIONAL X))))) LISP-CODE *1*REQUAL SUBRP *1*FALSE LEVEL-NO 2 IDATE 1000404112548 SATELLITES (*1*REQUAL) IMMEDIATE-DEPENDENTS0 (REQUAL-SIMPLE-RPLUS-X-X-REWRITE REQUAL-RPLUS-X-SIMPLE-RNEG-X REQUAL-SIMPLE-RPLUS-X-SIMPLE-RNEG-X REQUAL-OFF REQUAL-RTIMES-RNEG REQUAL-SIMPLE-RTIMES-SIMPLE-RNEG REQUAL-RTIMES-RPLUS-BRIDGE REQUAL-SIMPLE-RTIMES-SIMPLE-RPLUS-ARG1 SIMPLE-RPLUS-BRIDGE REQUAL-RZEROP-SIMPLE-RPLUS REQUAL-SIMPLE-RTIMES-SIMPLE-RPLUS-WHEN-NOT-RZEROP SIMPLE-RPLUS-RZEROP REQUAL-ASSOCIATIVITY-OF-RTIMES REQUAL-SIMPLE-RTIMES-BRIDGE REQUAL-SIMPLE-RTIMES-REDUCE-ARG2 REQUAL-SIMPLE-RTIMES-REDUCE-ARG1 REQUAL-SIMPLE-RTIMES-REQUAL-ARG2 REQUAL-SIMPLE-RTIMES-REQUAL-ARG1 ASSOCIATIVITY-OF-SIMPLE-RTIMES ASSOCIATIVITY-OF-SIMPLE-RTIMES-WHEN-NOT-RZEROP REQUAL-RPLUS-RNEG REQUAL-RNEG-SIMPLE-RPLUS REQUAL-ASSOCIATIVITY-OF-RPLUS REQUAL-SIMPLE-RPLUS-BRIDGE EQUAL-REQUAL-REWRITE TRANSITIVITY-OF-REQUAL TRANSITIVITY-OF-REQUAL-BRIDGE REQUAL-ASSOCIATIVITY-OF-SIMPLE-RPLUS REQUAL-RNEG-RNEG SIMPLE-RNEG-SIMPLE-RNEG REQUAL-SIMPLE-RPLUS-REDUCE-ARG2 REQUAL-SIMPLE-RPLUS-REDUCE-ARG1 RPLUS-REDUCE-ARG2 RPLUS-REDUCE-ARG1 REQUAL-X-X RPLUS-REQUAL-ARG1 REQUAL-REDUCE2 REQUAL-REDUCE1 COMMUTATIVITY-OF-REQUAL REQUAL-REDUCE-REDUCE-EQUAL) EVENT (DEFN REQUAL (X Y) (EQUAL (ITIMES (NUMERATOR (FIX-RATIONAL X)) (DENOMINATOR (FIX-RATIONAL Y))) (ITIMES (NUMERATOR (FIX-RATIONAL Y)) (DENOMINATOR (FIX-RATIONAL X))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RATIONAL . REQUAL) (IMMEDIATE-DEPENDENTS0 FIX-RATIONAL . REQUAL) (IMMEDIATE-DEPENDENTS0 ITIMES . REQUAL) (DCELL . *1*REQUAL))))) (PUT1-LST (QUOTE *1*RLESSP) (QUOTE (MAIN-EVENT RLESSP))) (PUT1-LST (QUOTE RLESSP) (QUOTE (TYPE-PRESCRIPTION-LST ((RLESSP 3 NIL NIL)) TOTALP-LST ((RLESSP . T)) SDEFN (LAMBDA (X Y) (ILESSP (ITIMES (NUMERATOR (FIX-RATIONAL X)) (DENOMINATOR (FIX-RATIONAL Y))) (ITIMES (NUMERATOR (FIX-RATIONAL Y)) (DENOMINATOR (FIX-RATIONAL X))))) LISP-CODE *1*RLESSP SUBRP *1*FALSE LEVEL-NO 2 IDATE 1000404112548 SATELLITES (*1*RLESSP) IMMEDIATE-DEPENDENTS0 (RLESSP-OFF) EVENT (DEFN RLESSP (X Y) (ILESSP (ITIMES (NUMERATOR (FIX-RATIONAL X)) (DENOMINATOR (FIX-RATIONAL Y))) (ITIMES (NUMERATOR (FIX-RATIONAL Y)) (DENOMINATOR (FIX-RATIONAL X))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RATIONAL . RLESSP) (IMMEDIATE-DEPENDENTS0 FIX-RATIONAL . RLESSP) (IMMEDIATE-DEPENDENTS0 ITIMES . RLESSP) (IMMEDIATE-DEPENDENTS0 ILESSP . RLESSP) (DCELL . *1*RLESSP))))) (PUT1-LST (QUOTE *1*RMAGNITUDE) (QUOTE (MAIN-EVENT RMAGNITUDE))) (PUT1-LST (QUOTE RMAGNITUDE) (QUOTE (TYPE-PRESCRIPTION-LST ((RMAGNITUDE 64 NIL)) TOTALP-LST ((RMAGNITUDE . T)) SDEFN (LAMBDA (X) (REDUCE (SIMPLE-RMAGNITUDE X))) LISP-CODE *1*RMAGNITUDE SUBRP *1*FALSE LEVEL-NO 2 IDATE 1000404112548 SATELLITES (*1*RMAGNITUDE) IMMEDIATE-DEPENDENTS0 (RMAGNITUDE-OFF REDUCE-RMAGNITUDE FIX-RATIONAL-RMAGNITUDE RATIONALP-RMAGNITUDE) EVENT (DEFN RMAGNITUDE (X) (REDUCE (SIMPLE-RMAGNITUDE X))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SIMPLE-RMAGNITUDE . RMAGNITUDE) (IMMEDIATE-DEPENDENTS0 REDUCE . RMAGNITUDE) (DCELL . *1*RMAGNITUDE))))) (PUT1-LST (QUOTE *1*SIMPLE-RMAGNITUDE) (QUOTE (MAIN-EVENT SIMPLE-RMAGNITUDE))) (PUT1-LST (QUOTE SIMPLE-RMAGNITUDE) (QUOTE (TYPE-PRESCRIPTION-LST ((SIMPLE-RMAGNITUDE 64 T)) TOTALP-LST ((SIMPLE-RMAGNITUDE . T)) SDEFN (LAMBDA (X) (IF (NEGATIVEP (NUMERATOR (FIX-RATIONAL X))) (RNEG (FIX-RATIONAL X)) (FIX-RATIONAL X))) LISP-CODE *1*SIMPLE-RMAGNITUDE SUBRP *1*FALSE LEVEL-NO 2 IDATE 1000404112548 SATELLITES (*1*SIMPLE-RMAGNITUDE) IMMEDIATE-DEPENDENTS0 (SIMPLE-RMAGNITUDE-OFF RATIONALP-RMAGNITUDE RMAGNITUDE) EVENT (DEFN SIMPLE-RMAGNITUDE (X) (IF (NEGATIVEP (NUMERATOR (FIX-RATIONAL X))) (RNEG (FIX-RATIONAL X)) (FIX-RATIONAL X))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RNEG . SIMPLE-RMAGNITUDE) (IMMEDIATE-DEPENDENTS0 FIX-RATIONAL . SIMPLE-RMAGNITUDE) (IMMEDIATE-DEPENDENTS0 RATIONAL . SIMPLE-RMAGNITUDE) (DCELL . *1*SIMPLE-RMAGNITUDE))))) (PUT1-LST (QUOTE *1*RQUOTIENT) (QUOTE (MAIN-EVENT RQUOTIENT))) (PUT1-LST (QUOTE RQUOTIENT) (QUOTE (TYPE-PRESCRIPTION-LST ((RQUOTIENT 64 NIL NIL)) TOTALP-LST ((RQUOTIENT . T)) SDEFN (LAMBDA (X Y) (RTIMES X (RINVERSE Y))) LISP-CODE *1*RQUOTIENT SUBRP *1*FALSE LEVEL-NO 2 IDATE 1000404112548 SATELLITES (*1*RQUOTIENT) IMMEDIATE-DEPENDENTS0 (RQUOTIENT-OFF REDUCE-RQUOTIENT FIX-RATIONAL-RQUOTIENT RATIONALP-RQUOTIENT) EVENT (DEFN RQUOTIENT (X Y) (RTIMES X (RINVERSE Y))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RINVERSE . RQUOTIENT) (IMMEDIATE-DEPENDENTS0 RTIMES . RQUOTIENT) (DCELL . *1*RQUOTIENT))))) (PUT1-LST (QUOTE *1*RINVERSE) (QUOTE (MAIN-EVENT RINVERSE))) (PUT1-LST (QUOTE RINVERSE) (QUOTE (TYPE-PRESCRIPTION-LST ((RINVERSE 64 NIL)) TOTALP-LST ((RINVERSE . T)) SDEFN (LAMBDA (R) (REDUCE (SIMPLE-RINVERSE R))) LISP-CODE *1*RINVERSE SUBRP *1*FALSE LEVEL-NO 2 IDATE 1000404112548 SATELLITES (*1*RINVERSE) IMMEDIATE-DEPENDENTS0 (FIX-RATIONAL-RQUOTIENT RATIONALP-RQUOTIENT RQUOTIENT) EVENT (DEFN RINVERSE (R) (REDUCE (SIMPLE-RINVERSE R))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SIMPLE-RINVERSE . RINVERSE) (IMMEDIATE-DEPENDENTS0 REDUCE . RINVERSE) (DCELL . *1*RINVERSE))))) (PUT1-LST (QUOTE *1*SIMPLE-RINVERSE) (QUOTE (MAIN-EVENT SIMPLE-RINVERSE))) (PUT1-LST (QUOTE SIMPLE-RINVERSE) (QUOTE (TYPE-PRESCRIPTION-LST ((SIMPLE-RINVERSE 64 NIL)) TOTALP-LST ((SIMPLE-RINVERSE . T)) SDEFN (LAMBDA (R) (IF (RZEROP R) (QUOTE (*1*QUOTE RATIONAL 0 1)) (IF (NEGATIVEP (NUMERATOR R)) (RATIONAL (INEG (DENOMINATOR R)) (INEG (NUMERATOR R))) (RATIONAL (DENOMINATOR R) (NUMERATOR R))))) LISP-CODE *1*SIMPLE-RINVERSE SUBRP *1*FALSE LEVEL-NO 0 IDATE 1000404112548 SATELLITES (*1*SIMPLE-RINVERSE) IMMEDIATE-DEPENDENTS0 (RATIONALP-RQUOTIENT RINVERSE) EVENT (DEFN SIMPLE-RINVERSE (R) (IF (RZEROP R) (QUOTE (*1*QUOTE RATIONAL 0 1)) (IF (NEGATIVEP (NUMERATOR R)) (RATIONAL (INEG (DENOMINATOR R)) (INEG (NUMERATOR R))) (RATIONAL (DENOMINATOR R) (NUMERATOR R))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RATIONAL . SIMPLE-RINVERSE) (IMMEDIATE-DEPENDENTS0 INEG . SIMPLE-RINVERSE) (IMMEDIATE-DEPENDENTS0 RZEROP . SIMPLE-RINVERSE) (DCELL . *1*SIMPLE-RINVERSE))))) (PUT1-LST (QUOTE *1*RZEROP) (QUOTE (MAIN-EVENT RZEROP))) (PUT1-LST (QUOTE RZEROP) (QUOTE (TYPE-PRESCRIPTION-LST ((RZEROP 3 NIL)) LEMMAS ((REWRITE-RULE NUMERATOR-ZERO-RZEROP-BRIDGE ((EQUAL (NUMERATOR X) (QUOTE 0))) (RZEROP X) NIL)) TOTALP-LST ((RZEROP . T)) SDEFN (LAMBDA (X) (IF (RATIONALP X) (EQUAL (NUMERATOR X) (QUOTE 0)) (QUOTE *1*TRUE))) LISP-CODE *1*RZEROP SUBRP *1*FALSE LEVEL-NO 0 IDATE 1000404112548 SATELLITES (*1*RZEROP) IMMEDIATE-DEPENDENTS0 (R2 RNEGS-CANCEL-LIST CANCEL-ZERO-FACT EVAL$-RPLUS-TREE-ZERO RDIFFERENCE-RPLUS-HACK RPLUS-EVAL$-RPLUS-TREE EVAL$-RPLUS RPLUS-RZEROP R1 RZEROP-OFF SIMPLE-RPLUS-BRIDGE REQUAL-RZEROP-SIMPLE-RPLUS REQUAL-SIMPLE-RTIMES-SIMPLE-RPLUS-WHEN-NOT-RZEROP SIMPLE-RPLUS-RZEROP NUMERATOR-ZERO-RZEROP-BRIDGE ASSOCIATIVITY-OF-SIMPLE-RTIMES-WHEN-NOT-RZEROP SIMPLE-RTIMES-RZEROP RATIONALP-RQUOTIENT SIMPLE-RINVERSE) EVENT (DEFN RZEROP (X) (OR (NOT (RATIONALP X)) (EQUAL (NUMERATOR X) (QUOTE 0)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RATIONAL . RZEROP) (IMMEDIATE-DEPENDENTS0 RATIONALP . RZEROP) (DCELL . *1*RZEROP))))) (PUT1-LST (QUOTE *1*RTIMES) (QUOTE (MAIN-EVENT RTIMES))) (PUT1-LST (QUOTE RTIMES) (QUOTE (TYPE-PRESCRIPTION-LST ((RTIMES 64 NIL NIL)) LEMMAS ((REWRITE-RULE COMMUTATIVITY2-OF-RTIMES NIL (EQUAL (RTIMES X (RTIMES Y Z)) (RTIMES Y (RTIMES X Z))) ((X . Y))) (REWRITE-RULE RTIMES-RDIFFERENCE-ARG2 NIL (EQUAL (RTIMES X (RDIFFERENCE Y Z)) (RDIFFERENCE (RTIMES X Y) (RTIMES X Z))) NIL) (REWRITE-RULE RTIMES-RDIFFERENCE-ARG1 NIL (EQUAL (RTIMES (RDIFFERENCE X Y) Z) (RDIFFERENCE (RTIMES X Z) (RTIMES Y Z))) NIL) (REWRITE-RULE RTIMES-RNEG-ARG2 NIL (EQUAL (RTIMES X (RNEG Y)) (RNEG (RTIMES X Y))) NIL) (REWRITE-RULE RTIMES-RNEG-ARG1 NIL (EQUAL (RTIMES (RNEG X) Y) (RNEG (RTIMES X Y))) NIL) (REWRITE-RULE RTIMES-RPLUS-ARG2 NIL (EQUAL (RTIMES X (RPLUS Y Z)) (RPLUS (RTIMES X Y) (RTIMES X Z))) NIL) (REWRITE-RULE RTIMES-RPLUS-ARG1 NIL (EQUAL (RTIMES (RPLUS X Y) Z) (RPLUS (RTIMES X Z) (RTIMES Y Z))) NIL) (REWRITE-RULE ASSOCIATIVITY-OF-RTIMES NIL (EQUAL (RTIMES (RTIMES X Y) Z) (RTIMES X (RTIMES Y Z))) NIL) (REWRITE-RULE COMMUTATIVITY-OF-RTIMES NIL (EQUAL (RTIMES X Y) (RTIMES Y X)) ((X . Y)))) TOTALP-LST ((RTIMES . T)) SDEFN (LAMBDA (X Y) (REDUCE (SIMPLE-RTIMES X Y))) LISP-CODE *1*RTIMES SUBRP *1*FALSE LEVEL-NO 2 IDATE 1000404112548 SATELLITES (*1*RTIMES) IMMEDIATE-DEPENDENTS0 (COMMUTATIVITY2-OF-RTIMES RTIMES-OFF RTIMES-RDIFFERENCE-ARG2 RTIMES-RDIFFERENCE-ARG1 RTIMES-RNEG-ARG2 RTIMES-RNEG-ARG1 REQUAL-RTIMES-RNEG RTIMES-RPLUS-ARG2 RTIMES-RPLUS-ARG1 REQUAL-RTIMES-RPLUS-BRIDGE ASSOCIATIVITY-OF-RTIMES REQUAL-ASSOCIATIVITY-OF-RTIMES COMMUTATIVITY-OF-RTIMES REDUCE-RTIMES FIX-RATIONAL-RQUOTIENT FIX-RATIONAL-RTIMES RATIONALP-RQUOTIENT RATIONALP-RTIMES RQUOTIENT) EVENT (DEFN RTIMES (X Y) (REDUCE (SIMPLE-RTIMES X Y))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SIMPLE-RTIMES . RTIMES) (IMMEDIATE-DEPENDENTS0 REDUCE . 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T)) SDEFN (LAMBDA (X Y) (RATIONAL (ITIMES (NUMERATOR (FIX-RATIONAL X)) (NUMERATOR (FIX-RATIONAL Y))) (TIMES (DENOMINATOR (FIX-RATIONAL X)) (DENOMINATOR (FIX-RATIONAL Y))))) LISP-CODE *1*SIMPLE-RTIMES SUBRP *1*FALSE LEVEL-NO 2 IDATE 1000404112548 SATELLITES (*1*SIMPLE-RTIMES) IMMEDIATE-DEPENDENTS0 (SIMPLE-RTIMES-OFF REQUAL-SIMPLE-RTIMES-SIMPLE-RNEG REQUAL-SIMPLE-RTIMES-SIMPLE-RPLUS-ARG1 SIMPLE-RPLUS-BRIDGE REQUAL-SIMPLE-RTIMES-SIMPLE-RPLUS-WHEN-NOT-RZEROP FIX-RATIONAL-SIMPLE-RTIMES RATIONALP-SIMPLE-RTIMES REQUAL-SIMPLE-RTIMES-BRIDGE REQUAL-SIMPLE-RTIMES-REDUCE-ARG2 REQUAL-SIMPLE-RTIMES-REDUCE-ARG1 REQUAL-SIMPLE-RTIMES-REQUAL-ARG2 REQUAL-SIMPLE-RTIMES-REQUAL-ARG1 ASSOCIATIVITY-OF-SIMPLE-RTIMES ASSOCIATIVITY-OF-SIMPLE-RTIMES-WHEN-NOT-RZEROP SIMPLE-RTIMES-RZEROP COMMUTATIVITY-OF-SIMPLE-RTIMES RATIONALP-RTIMES RTIMES) EVENT (DEFN SIMPLE-RTIMES (X Y) (RATIONAL (ITIMES (NUMERATOR (FIX-RATIONAL X)) (NUMERATOR (FIX-RATIONAL Y))) (TIMES (DENOMINATOR (FIX-RATIONAL X)) (DENOMINATOR (FIX-RATIONAL Y))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RATIONAL . SIMPLE-RTIMES) (IMMEDIATE-DEPENDENTS0 FIX-RATIONAL . SIMPLE-RTIMES) (IMMEDIATE-DEPENDENTS0 ITIMES . SIMPLE-RTIMES) (DCELL . *1*SIMPLE-RTIMES))))) (PUT1-LST (QUOTE *1*RDIFFERENCE) (QUOTE (MAIN-EVENT RDIFFERENCE))) (PUT1-LST (QUOTE RDIFFERENCE) (QUOTE (TYPE-PRESCRIPTION-LST ((RDIFFERENCE 64 NIL NIL)) LEMMAS ((REWRITE-RULE RDIFFERENCE-RPLUS-HACK2 NIL (EQUAL (RDIFFERENCE (RPLUS B A) A) (REDUCE B)) NIL) (REWRITE-RULE RDIFFERENCE-RPLUS-HACK NIL (EQUAL (RDIFFERENCE (RPLUS A B) A) (REDUCE B)) NIL) (REWRITE-RULE RDIFFERENCE-X-X NIL (EQUAL (RDIFFERENCE X X) (QUOTE (*1*QUOTE RATIONAL 0 1))) NIL) (REWRITE-RULE RDIFFERENCE-REDUCE NIL (EQUAL (RDIFFERENCE X (REDUCE Y)) (RDIFFERENCE X Y)) NIL) (REWRITE-RULE RDIFFERENCE-REDUCE NIL (EQUAL (RDIFFERENCE (REDUCE X) Y) (RDIFFERENCE X Y)) NIL) (REWRITE-RULE RDIFFERENCE-RNEG-ARG2 NIL (EQUAL (RDIFFERENCE X (RNEG Y)) (RPLUS X Y)) NIL) (REWRITE-RULE RDIFFERENCE-RDIFFERENCE-ARG2 NIL (EQUAL (RDIFFERENCE X (RDIFFERENCE Y Z)) (RDIFFERENCE (RPLUS X Z) Y)) NIL) (REWRITE-RULE RDIFFERENCE-RDIFFERENCE-ARG1 NIL (EQUAL (RDIFFERENCE (RDIFFERENCE X Y) Z) (RDIFFERENCE X (RPLUS Y Z))) NIL)) TOTALP-LST ((RDIFFERENCE . T)) SDEFN (LAMBDA (A B) (RPLUS A (RNEG B))) LISP-CODE *1*RDIFFERENCE SUBRP *1*FALSE LEVEL-NO 2 IDATE 1000404112548 SATELLITES (*1*RDIFFERENCE) IMMEDIATE-DEPENDENTS0 (R2 EVAL$-RPLUS-TREE-DELETE EQUAL-RPLUS-RDIFFERENCE-HACK EQUAL-DIFFERENCE-HACK2 EQUAL-DIFFERENCE-HACK1 RPLUS-RDIFFERENCE-HACK RDIFFERENCE-RPLUS-HACK2 RDIFFERENCE-RPLUS-HACK RDIFFERENCE-X-X RDIFFERENCE-REDUCE RDIFFERENCE-OFF RDIFFERENCE-RNEG-ARG2 RNEG-RDIFFERENCE RTIMES-RDIFFERENCE-ARG2 RTIMES-RDIFFERENCE-ARG1 RPLUS-RNEG-ARG2 RPLUS-RNEG-ARG1 RDIFFERENCE-RDIFFERENCE-ARG2 RDIFFERENCE-RDIFFERENCE-ARG1 REDUCE-DIFFERENCE RPLUS-RDIFFERENCE-ARG2 RPLUS-RDIFFERENCE-ARG1 FIX-RATIONAL-RDIFFERENCE RATIONALP-RDIFFERENCE) EVENT (DEFN RDIFFERENCE (A B) (RPLUS A (RNEG B))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RNEG . RDIFFERENCE) (IMMEDIATE-DEPENDENTS0 RPLUS . RDIFFERENCE) (DCELL . *1*RDIFFERENCE))))) (PUT1-LST (QUOTE *1*RNEG) (QUOTE (MAIN-EVENT RNEG))) (PUT1-LST (QUOTE RNEG) (QUOTE (TYPE-PRESCRIPTION-LST ((RNEG 64 NIL)) LEMMAS ((REWRITE-RULE RNEG-RDIFFERENCE NIL (EQUAL (RNEG (RDIFFERENCE X Y)) (RDIFFERENCE Y X)) NIL) (REWRITE-RULE RNEG-RPLUS NIL (EQUAL (RNEG (RPLUS X Y)) (RPLUS (RNEG X) (RNEG Y))) NIL) (REWRITE-RULE RNEG-RNEG NIL (EQUAL (RNEG (RNEG X)) (REDUCE X)) NIL) (REWRITE-RULE RNEG-REDUCE NIL (EQUAL (RNEG (REDUCE X)) (RNEG X)) NIL)) TOTALP-LST ((RNEG . T)) SDEFN (LAMBDA (X) (REDUCE (SIMPLE-RNEG X))) LISP-CODE *1*RNEG SUBRP *1*FALSE LEVEL-NO 2 IDATE 1000404112548 SATELLITES (*1*RNEG) IMMEDIATE-DEPENDENTS0 (RDIFFERENCE-RPLUS-HACK RPLUS-X-RNEG-X RNEG-OFF RDIFFERENCE-RNEG-ARG2 RNEG-RDIFFERENCE RTIMES-RNEG-ARG2 RTIMES-RNEG-ARG1 REQUAL-RTIMES-RNEG RPLUS-RNEG-ARG2 RPLUS-RNEG-ARG1 RNEG-RPLUS REQUAL-RPLUS-RNEG REDUCE-RNEG RNEG-RNEG REQUAL-RNEG-RNEG RNEG-REDUCE FIX-RATIONAL-RDIFFERENCE FIX-RATIONAL-RNEG RATIONALP-RMAGNITUDE RATIONALP-RNEG SIMPLE-RMAGNITUDE RDIFFERENCE) EVENT (DEFN RNEG (X) (REDUCE (SIMPLE-RNEG X))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SIMPLE-RNEG . RNEG) (IMMEDIATE-DEPENDENTS0 REDUCE . RNEG) (DCELL . *1*RNEG))))) (PUT1-LST (QUOTE *1*SIMPLE-RNEG) (QUOTE (MAIN-EVENT SIMPLE-RNEG))) (PUT1-LST (QUOTE SIMPLE-RNEG) (QUOTE (TYPE-PRESCRIPTION-LST ((SIMPLE-RNEG 64 NIL)) LEMMAS ((REWRITE-RULE SIMPLE-RNEG-REDUCE NIL (EQUAL (SIMPLE-RNEG (REDUCE X)) (REDUCE (SIMPLE-RNEG X))) NIL)) TOTALP-LST ((SIMPLE-RNEG . T)) SDEFN (LAMBDA (X) (RATIONAL (INEG (NUMERATOR (FIX-RATIONAL X))) (DENOMINATOR (FIX-RATIONAL X)))) LISP-CODE *1*SIMPLE-RNEG SUBRP *1*FALSE LEVEL-NO 0 IDATE 1000404112548 SATELLITES (*1*SIMPLE-RNEG) IMMEDIATE-DEPENDENTS0 (REQUAL-RPLUS-X-SIMPLE-RNEG-X REQUAL-SIMPLE-RPLUS-X-SIMPLE-RNEG-X SIMPLE-RNEG-OFF REQUAL-SIMPLE-RTIMES-SIMPLE-RNEG REQUAL-RNEG-SIMPLE-RPLUS SIMPLE-RNEG-SIMPLE-RNEG SIMPLE-RNEG-REDUCE RATIONALP-RNEG RNEG) EVENT (DEFN SIMPLE-RNEG (X) (RATIONAL (INEG (NUMERATOR (FIX-RATIONAL X))) (DENOMINATOR (FIX-RATIONAL X)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RATIONAL . SIMPLE-RNEG) (IMMEDIATE-DEPENDENTS0 FIX-RATIONAL . SIMPLE-RNEG) (IMMEDIATE-DEPENDENTS0 INEG . SIMPLE-RNEG) (DCELL . *1*SIMPLE-RNEG))))) (PUT1-LST (QUOTE *1*RPLUS) (QUOTE (MAIN-EVENT RPLUS))) (PUT1-LST (QUOTE RPLUS) (QUOTE (TYPE-PRESCRIPTION-LST ((RPLUS 64 NIL NIL)) LEMMAS ((REWRITE-RULE CORRECTNESS-OF-CANCEL-RPLUS NIL *1*CANCEL-RPLUS NIL) (REWRITE-RULE EQUAL-DIFFERENCE-HACK2 ((EQUAL (REDUCE A) (RDIFFERENCE B C))) (EQUAL (RPLUS C A) (REDUCE B)) NIL) (REWRITE-RULE EQUAL-DIFFERENCE-HACK1 ((EQUAL A (RDIFFERENCE B C))) (EQUAL (RPLUS C A) (REDUCE B)) NIL) (REWRITE-RULE RPLUS-RDIFFERENCE-HACK NIL (EQUAL (RPLUS (RDIFFERENCE B A) A) (REDUCE B)) NIL) (REWRITE-RULE RPLUS-RDIFFERENCE-HACK NIL (EQUAL (RPLUS A (RDIFFERENCE B A)) (REDUCE B)) NIL) (REWRITE-RULE RPLUS-X-RNEG-X NIL (EQUAL (RPLUS X (RNEG X)) (QUOTE (*1*QUOTE RATIONAL 0 1))) NIL) (REWRITE-RULE RPLUS-RZEROP ((RZEROP X)) (EQUAL (RPLUS Y X) (REDUCE Y)) NIL) (REWRITE-RULE RPLUS-RZEROP ((RZEROP X)) (EQUAL (RPLUS X Y) (REDUCE Y)) NIL) (REWRITE-RULE RPLUS-RNEG-ARG2 NIL (EQUAL (RPLUS X (RNEG Y)) (RDIFFERENCE X Y)) NIL) (REWRITE-RULE RPLUS-RNEG-ARG1 NIL (EQUAL (RPLUS (RNEG X) Y) (RDIFFERENCE Y X)) NIL) (REWRITE-RULE RPLUS-REDUCE-ARG2-REWRITE NIL (EQUAL (RPLUS X (REDUCE Y)) (RPLUS X Y)) NIL) (REWRITE-RULE RPLUS-REDUCE-ARG1-REWRITE NIL (EQUAL (RPLUS (REDUCE X) Y) (RPLUS X Y)) NIL) (REWRITE-RULE RPLUS-RDIFFERENCE-ARG2 NIL (EQUAL (RPLUS X (RDIFFERENCE Y Z)) (RDIFFERENCE (RPLUS X Y) Z)) NIL) (REWRITE-RULE RPLUS-RDIFFERENCE-ARG1 NIL (EQUAL (RPLUS (RDIFFERENCE X Y) Z) (RDIFFERENCE (RPLUS X Z) Y)) NIL) (REWRITE-RULE COMMUTATIVITY2-OF-RPLUS NIL (EQUAL (RPLUS X (RPLUS Y Z)) (RPLUS Y (RPLUS X Z))) ((X . Y))) (REWRITE-RULE ASSOCIATIVITY-OF-RPLUS NIL (EQUAL (RPLUS (RPLUS X Y) Z) (RPLUS X (RPLUS Y Z))) NIL) (REWRITE-RULE NRATIONAL-RPLUS-ARG2 ((NOT (RATIONALP X))) (EQUAL (RPLUS Y X) (REDUCE Y)) NIL) (REWRITE-RULE NRATIONAL-RPLUS-ARG1 ((NOT (RATIONALP X))) (EQUAL (RPLUS X Y) (REDUCE Y)) NIL) (REWRITE-RULE COMMUTATIVITY-OF-RPLUS NIL (EQUAL (RPLUS X Y) (RPLUS Y X)) ((X . Y))) (REWRITE-RULE RPLUS-OPEN-UP NIL (EQUAL (RPLUS A B) (IF (RATIONALP A) (IF (RATIONALP B) (REDUCE (RATIONAL (IPLUS (ITIMES (NUMERATOR A) (DENOMINATOR B)) (ITIMES (NUMERATOR B) (DENOMINATOR A))) (ITIMES (DENOMINATOR A) (DENOMINATOR B)))) (REDUCE (FIX-RATIONAL A))) (REDUCE (FIX-RATIONAL B)))) NIL)) TOTALP-LST ((RPLUS . T)) SDEFN (LAMBDA (X Y) (REDUCE (SIMPLE-RPLUS X Y))) LISP-CODE *1*RPLUS SUBRP *1*FALSE LEVEL-NO 2 IDATE 1000404112548 SATELLITES (*1*RPLUS) IMMEDIATE-DEPENDENTS0 (RNEGS-CANCEL-LIST EVAL$-RPLUS-TREE-ZERO EQUAL-RPLUS-RDIFFERENCE-HACK EQUAL-RPLUS-X-X-REWRITE EQUAL-DIFFERENCE-HACK2 EQUAL-DIFFERENCE-HACK1 RPLUS-RDIFFERENCE-HACK RDIFFERENCE-RPLUS-HACK2 RDIFFERENCE-RPLUS-HACK RPLUS-X-RNEG-X REQUAL-RPLUS-X-SIMPLE-RNEG-X RPLUS-EVAL$-RPLUS-TREE EVAL$-RPLUS RPLUS-RZEROP RPLUS-OFF RDIFFERENCE-RNEG-ARG2 RTIMES-RPLUS-ARG2 RTIMES-RPLUS-ARG1 REQUAL-RTIMES-RPLUS-BRIDGE RPLUS-RNEG-ARG2 RPLUS-RNEG-ARG1 RDIFFERENCE-RDIFFERENCE-ARG2 RDIFFERENCE-RDIFFERENCE-ARG1 RNEG-RPLUS REQUAL-RPLUS-RNEG RPLUS-REDUCE-ARG2-REWRITE RPLUS-REDUCE-ARG1-REWRITE REDUCE-RPLUS RPLUS-RDIFFERENCE-ARG2 RPLUS-RDIFFERENCE-ARG1 COMMUTATIVITY2-OF-RPLUS ASSOCIATIVITY-OF-RPLUS REQUAL-ASSOCIATIVITY-OF-RPLUS NRATIONAL-RPLUS-ARG2 NRATIONAL-RPLUS-ARG1 REQUAL-SIMPLE-RPLUS-REDUCE-ARG2 REQUAL-SIMPLE-RPLUS-REDUCE-ARG1 RPLUS-REDUCE-ARG2 RPLUS-REDUCE-ARG1 RPLUS-REQUAL-ARG1 COMMUTATIVITY-OF-RPLUS RPLUS-OPEN-UP FIX-RATIONAL-RDIFFERENCE FIX-RATIONAL-RPLUS RATIONALP-RPLUS RDIFFERENCE) EVENT (DEFN RPLUS (X Y) (REDUCE (SIMPLE-RPLUS X Y))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SIMPLE-RPLUS . RPLUS) (IMMEDIATE-DEPENDENTS0 REDUCE . RPLUS) (DCELL . *1*RPLUS))))) (PUT1-LST (QUOTE *1*SIMPLE-RPLUS) (QUOTE (MAIN-EVENT SIMPLE-RPLUS))) (PUT1-LST (QUOTE SIMPLE-RPLUS) (QUOTE (TYPE-PRESCRIPTION-LST ((SIMPLE-RPLUS 64 NIL NIL)) LEMMAS ((REWRITE-RULE COMMUTATIVITY-OF-SIMPLE-RPLUS NIL (EQUAL (SIMPLE-RPLUS X Y) (SIMPLE-RPLUS Y X)) ((X . Y))) (REWRITE-RULE SIMPLE-RPLUS-FIX-RATIONAL-ARG2 NIL (EQUAL (SIMPLE-RPLUS X (FIX-RATIONAL Y)) (SIMPLE-RPLUS X Y)) NIL) (REWRITE-RULE SIMPLE-RPLUS-FIX-RATIONAL-ARG1 NIL (EQUAL (SIMPLE-RPLUS (FIX-RATIONAL X) Y) (SIMPLE-RPLUS X Y)) NIL) (REWRITE-RULE NRATIONAL-SIMPLE-RPLUS-ARG2 ((NOT (RATIONALP X))) (EQUAL (SIMPLE-RPLUS Y X) (FIX-RATIONAL Y)) NIL) (REWRITE-RULE NRATIONAL-SIMPLE-RPLUS-ARG1 ((NOT (RATIONALP X))) (EQUAL (SIMPLE-RPLUS X Y) (FIX-RATIONAL Y)) NIL)) TOTALP-LST ((SIMPLE-RPLUS . T)) SDEFN (LAMBDA (X Y) (RATIONAL (IPLUS (ITIMES (NUMERATOR (FIX-RATIONAL X)) (DENOMINATOR (FIX-RATIONAL Y))) (ITIMES (NUMERATOR (FIX-RATIONAL Y)) (DENOMINATOR (FIX-RATIONAL X)))) (ITIMES (DENOMINATOR (FIX-RATIONAL X)) (DENOMINATOR (FIX-RATIONAL Y))))) LISP-CODE *1*SIMPLE-RPLUS SUBRP *1*FALSE LEVEL-NO 2 IDATE 1000404112548 SATELLITES (*1*SIMPLE-RPLUS) IMMEDIATE-DEPENDENTS0 (REQUAL-SIMPLE-RPLUS-X-X-REWRITE REQUAL-SIMPLE-RPLUS-X-SIMPLE-RNEG-X RPLUS-RZEROP SIMPLE-RPLUS-OFF REQUAL-SIMPLE-RTIMES-SIMPLE-RPLUS-ARG1 SIMPLE-RPLUS-BRIDGE COMMUTATIVITY-OF-SIMPLE-RPLUS REQUAL-RZEROP-SIMPLE-RPLUS REQUAL-SIMPLE-RTIMES-SIMPLE-RPLUS-WHEN-NOT-RZEROP SIMPLE-RPLUS-RZEROP REQUAL-RNEG-SIMPLE-RPLUS REQUAL-SIMPLE-RPLUS-BRIDGE REQUAL-ASSOCIATIVITY-OF-SIMPLE-RPLUS FIX-RATIONAL-SIMPLE-RPLUS RATIONALP-SIMPLE-RPLUS SIMPLE-RPLUS-FIX-RATIONAL-ARG2 SIMPLE-RPLUS-FIX-RATIONAL-ARG1 NRATIONAL-SIMPLE-RPLUS-ARG2 NRATIONAL-SIMPLE-RPLUS-ARG1 NRATIONAL-RPLUS-ARG1 REQUAL-SIMPLE-RPLUS-REDUCE-ARG2 REQUAL-SIMPLE-RPLUS-REDUCE-ARG1 COMMUTATIVITY-OF-RPLUS RPLUS-OPEN-UP RATIONALP-RPLUS RPLUS) EVENT (DEFN SIMPLE-RPLUS (X Y) (RATIONAL (IPLUS (ITIMES (NUMERATOR (FIX-RATIONAL X)) (DENOMINATOR (FIX-RATIONAL Y))) (ITIMES (NUMERATOR (FIX-RATIONAL Y)) (DENOMINATOR (FIX-RATIONAL X)))) (ITIMES (DENOMINATOR (FIX-RATIONAL X)) (DENOMINATOR (FIX-RATIONAL Y))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RATIONAL . SIMPLE-RPLUS) (IMMEDIATE-DEPENDENTS0 FIX-RATIONAL . SIMPLE-RPLUS) (IMMEDIATE-DEPENDENTS0 ITIMES . SIMPLE-RPLUS) (IMMEDIATE-DEPENDENTS0 IPLUS . SIMPLE-RPLUS) (DCELL . *1*SIMPLE-RPLUS))))) (PUT1-LST (QUOTE *1*REDUCE) (QUOTE (MAIN-EVENT REDUCE))) (PUT1-LST (QUOTE REDUCE) (QUOTE (TYPE-PRESCRIPTION-LST ((REDUCE 64 NIL)) LEMMAS ((REWRITE-RULE REDUCE-EVAL$-RPLUS-TREE NIL (EQUAL (REDUCE (EVAL$ (QUOTE *1*TRUE) (RPLUS-TREE Y) A)) (EVAL$ (QUOTE *1*TRUE) (RPLUS-TREE Y) A)) NIL) (REWRITE-RULE RPLUS-RZEROP-BRIDGE2 ((NUMBERP V) (NOT (EQUAL V (QUOTE 0)))) (EQUAL (REDUCE (RATIONAL (MINUS (TIMES D V)) (TIMES V W))) (REDUCE (RATIONAL (MINUS D) W))) NIL) (REWRITE-RULE RPLUS-RZEROP-BRIDGE ((NUMBERP V) (NOT (EQUAL V (QUOTE 0))) (NUMBERP Z)) (EQUAL (REDUCE (RATIONAL (TIMES V Z) (TIMES V W))) (REDUCE (RATIONAL Z W))) NIL) (REWRITE-RULE REDUCE-RNEG NIL (EQUAL (REDUCE (RNEG X)) (RNEG X)) NIL) (REWRITE-RULE REDUCE-RMAGNITUDE NIL (EQUAL (REDUCE (RMAGNITUDE X)) (RMAGNITUDE X)) NIL) (REWRITE-RULE REDUCE-RQUOTIENT NIL (EQUAL (REDUCE (RQUOTIENT X Y)) (RQUOTIENT X Y)) NIL) (REWRITE-RULE REDUCE-DIFFERENCE NIL (EQUAL (REDUCE (RDIFFERENCE X Y)) (RDIFFERENCE X Y)) NIL) (REWRITE-RULE REDUCE-RTIMES NIL (EQUAL (REDUCE (RTIMES X Y)) (RTIMES X Y)) NIL) (REWRITE-RULE REDUCE-RPLUS NIL (EQUAL (REDUCE (RPLUS X Y)) (RPLUS X Y)) NIL) (REWRITE-RULE REDUCE-0 NIL (EQUAL (REDUCE (RATIONAL (QUOTE 0) X)) (QUOTE (*1*QUOTE RATIONAL 0 1))) NIL) (REWRITE-RULE REDUCE-NRATIONALP ((NOT (RATIONALP X))) (EQUAL (REDUCE X) (QUOTE (*1*QUOTE RATIONAL 0 1))) NIL) (REWRITE-RULE REDUCE-REDUCE NIL (EQUAL (REDUCE (REDUCE X)) (REDUCE X)) NIL)) TOTALP-LST ((REDUCE . T)) SDEFN (LAMBDA (R) (IF (RATIONALP R) (IF (NEGATIVEP (NUMERATOR R)) (RATIONAL (MINUS (QUOTIENT (NEGATIVE-GUTS (NUMERATOR R)) (GCD (NEGATIVE-GUTS (NUMERATOR R)) (DENOMINATOR R)))) (QUOTIENT (DENOMINATOR R) (GCD (NEGATIVE-GUTS (NUMERATOR R)) (DENOMINATOR R)))) (RATIONAL (QUOTIENT (NUMERATOR R) (GCD (NUMERATOR R) (DENOMINATOR R))) (QUOTIENT (DENOMINATOR R) (GCD (NUMERATOR R) (DENOMINATOR R))))) (QUOTE (*1*QUOTE RATIONAL 0 1)))) LISP-CODE *1*REDUCE SUBRP *1*FALSE LEVEL-NO 2 IDATE 1000404112548 SATELLITES (*1*REDUCE) IMMEDIATE-DEPENDENTS0 (EVAL$-RPLUS-TREE-RPLUS-FRINGE RNEGS-CANCEL-LIST EVAL$-RPLUS-TREE-ZERO EQUAL-RPLUS-RDIFFERENCE-HACK EQUAL-RPLUS-X-X-REWRITE EQUAL-DIFFERENCE-HACK2 EQUAL-DIFFERENCE-HACK1 RPLUS-RDIFFERENCE-HACK RDIFFERENCE-RPLUS-HACK2 RDIFFERENCE-RPLUS-HACK RPLUS-X-RNEG-X RDIFFERENCE-REDUCE REDUCE-EVAL$-RPLUS-TREE EVAL$-REDUCE RPLUS-RZEROP RPLUS-RZEROP-BRIDGE2 RPLUS-RZEROP-BRIDGE REDUCE-OFF REQUAL-SIMPLE-RTIMES-BRIDGE REQUAL-SIMPLE-RTIMES-REDUCE-ARG2 REQUAL-SIMPLE-RTIMES-REDUCE-ARG1 RPLUS-REDUCE-ARG2-REWRITE RPLUS-REDUCE-ARG1-REWRITE REDUCE-RNEG REDUCE-RMAGNITUDE REDUCE-RQUOTIENT REDUCE-DIFFERENCE REDUCE-RTIMES REDUCE-RPLUS REQUAL-SIMPLE-RPLUS-BRIDGE NRATIONAL-RPLUS-ARG2 NRATIONAL-RPLUS-ARG1 RNEG-RNEG RNEG-REDUCE SIMPLE-RNEG-REDUCE REDUCE-0 RATIONAL-INEG-NUMERATOR-REDUCE-BRIDGE NUMBERP-NUMERATOR-REDUCE REDUCE-NRATIONALP REQUAL-SIMPLE-RPLUS-REDUCE-ARG2 REQUAL-SIMPLE-RPLUS-REDUCE-ARG1 RPLUS-REDUCE-ARG2 RPLUS-REDUCE-ARG1 RPLUS-OPEN-UP REDUCE-REDUCE REQUAL-REDUCE2 REQUAL-REDUCE1 REQUAL-REDUCE-REDUCE-EQUAL FIX-RATIONAL-REDUCE RATIONALP-REDUCE RMAGNITUDE RINVERSE RTIMES RNEG RPLUS) EVENT (DEFN REDUCE (R) (IF (RATIONALP R) (IF (NEGATIVEP (NUMERATOR R)) (RATIONAL (MINUS (QUOTIENT (NEGATIVE-GUTS (NUMERATOR R)) (GCD (NEGATIVE-GUTS (NUMERATOR R)) (DENOMINATOR R)))) (QUOTIENT (DENOMINATOR R) (GCD (NEGATIVE-GUTS (NUMERATOR R)) (DENOMINATOR R)))) (RATIONAL (QUOTIENT (NUMERATOR R) (GCD (NUMERATOR R) (DENOMINATOR R))) (QUOTIENT (DENOMINATOR R) (GCD (NUMERATOR R) (DENOMINATOR R))))) (QUOTE (*1*QUOTE RATIONAL 0 1)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RATIONAL . REDUCE) (IMMEDIATE-DEPENDENTS0 GCD . REDUCE) (IMMEDIATE-DEPENDENTS0 RATIONALP . REDUCE) (DCELL . *1*REDUCE))))) (PUT1-LST (QUOTE *1*FIX-RATIONAL) (QUOTE (MAIN-EVENT FIX-RATIONAL))) (PUT1-LST (QUOTE FIX-RATIONAL) (QUOTE (TYPE-PRESCRIPTION-LST ((FIX-RATIONAL 64 T)) LEMMAS ((REWRITE-RULE FIX-RATIONAL-SIMPLE-RTIMES NIL (EQUAL (FIX-RATIONAL (SIMPLE-RTIMES X Y)) (SIMPLE-RTIMES X Y)) NIL) (REWRITE-RULE FIX-RATIONAL-SIMPLE-RPLUS NIL (EQUAL (FIX-RATIONAL (SIMPLE-RPLUS X Y)) (SIMPLE-RPLUS X Y)) NIL) (REWRITE-RULE FIX-RATIONAL-OF-RATIONALP ((RATIONALP X)) (EQUAL (FIX-RATIONAL X) X) NIL) (REWRITE-RULE FIX-RATIONAL-RMAGNITUDE NIL (EQUAL (FIX-RATIONAL (RMAGNITUDE X)) (RMAGNITUDE X)) NIL) (REWRITE-RULE FIX-RATIONAL-RQUOTIENT NIL (EQUAL (FIX-RATIONAL (RQUOTIENT X Y)) (RQUOTIENT X Y)) NIL) (REWRITE-RULE FIX-RATIONAL-RDIFFERENCE NIL (EQUAL (FIX-RATIONAL (RDIFFERENCE X Y)) (RDIFFERENCE X Y)) NIL) (REWRITE-RULE FIX-RATIONAL-RNEG NIL (EQUAL (FIX-RATIONAL (RNEG X)) (RNEG X)) NIL) (REWRITE-RULE FIX-RATIONAL-RTIMES NIL (EQUAL (FIX-RATIONAL (RTIMES X Y)) (RTIMES X Y)) NIL) (REWRITE-RULE FIX-RATIONAL-FIX-RATIONAL NIL (EQUAL (FIX-RATIONAL (FIX-RATIONAL X)) (FIX-RATIONAL X)) NIL) (REWRITE-RULE FIX-RATIONAL-RPLUS NIL (EQUAL (FIX-RATIONAL (RPLUS X Y)) (RPLUS X Y)) NIL) (REWRITE-RULE FIX-RATIONAL-REDUCE NIL (EQUAL (FIX-RATIONAL (REDUCE X)) (REDUCE X)) NIL)) TOTALP-LST ((FIX-RATIONAL . T)) SDEFN (LAMBDA (X) (IF (RATIONALP X) X (QUOTE (*1*QUOTE RATIONAL 0 1)))) LISP-CODE *1*FIX-RATIONAL SUBRP *1*FALSE LEVEL-NO 0 IDATE 1000404112548 SATELLITES (*1*FIX-RATIONAL) IMMEDIATE-DEPENDENTS0 (REQUAL-SIMPLE-RPLUS-X-X-REWRITE REQUAL-SIMPLE-RPLUS-X-SIMPLE-RNEG-X RPLUS-RZEROP FIX-RATIONAL-OFF REQUAL-SIMPLE-RTIMES-SIMPLE-RNEG SIMPLE-RPLUS-BRIDGE COMMUTATIVITY-OF-SIMPLE-RPLUS REQUAL-RZEROP-SIMPLE-RPLUS FIX-RATIONAL-SIMPLE-RTIMES RATIONALP-SIMPLE-RTIMES SIMPLE-RPLUS-RZEROP REQUAL-SIMPLE-RTIMES-REQUAL-ARG1 ASSOCIATIVITY-OF-SIMPLE-RTIMES ASSOCIATIVITY-OF-SIMPLE-RTIMES-WHEN-NOT-RZEROP SIMPLE-RTIMES-RZEROP COMMUTATIVITY-OF-SIMPLE-RTIMES REQUAL-RNEG-SIMPLE-RPLUS TRANSITIVITY-OF-REQUAL-BRIDGE REQUAL-ASSOCIATIVITY-OF-SIMPLE-RPLUS FIX-RATIONAL-SIMPLE-RPLUS RATIONALP-SIMPLE-RPLUS FIX-RATIONAL-OF-RATIONALP SIMPLE-RPLUS-FIX-RATIONAL-ARG2 SIMPLE-RPLUS-FIX-RATIONAL-ARG1 NRATIONAL-SIMPLE-RPLUS-ARG2 NRATIONAL-SIMPLE-RPLUS-ARG1 NRATIONAL-RPLUS-ARG1 SIMPLE-RNEG-SIMPLE-RNEG SIMPLE-RNEG-REDUCE NUMBERP-NUMERATOR-REDUCE REQUAL-X-X RPLUS-REQUAL-ARG1 RPLUS-OPEN-UP REQUAL-REDUCE1 REQUAL-REDUCE-REDUCE-EQUAL FIX-RATIONAL-RMAGNITUDE FIX-RATIONAL-RQUOTIENT FIX-RATIONAL-RDIFFERENCE FIX-RATIONAL-RNEG FIX-RATIONAL-RTIMES FIX-RATIONAL-FIX-RATIONAL FIX-RATIONAL-RPLUS FIX-RATIONAL-REDUCE RATIONALP-RMAGNITUDE RATIONALP-RNEG RATIONALP-RTIMES RATIONALP-FIX-RATIONAL RATIONALP-RPLUS REQUAL RLESSP SIMPLE-RMAGNITUDE SIMPLE-RTIMES SIMPLE-RNEG SIMPLE-RPLUS) EVENT (DEFN FIX-RATIONAL (X) (IF (RATIONALP X) X (QUOTE (*1*QUOTE RATIONAL 0 1)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 RATIONAL . 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INTEGERP-IQUOTIENT))))) (PUT1-LST (QUOTE IQUO-IREM-UNIQUENESS) (QUOTE (IDATE 1000404112527 EVENT (PROVE-LEMMA IQUO-IREM-UNIQUENESS NIL (IMPLIES (AND (INTEGERP I) (AND (INTEGERP J) (AND (INTEGERP R) (AND (INTEGERP Q) (AND (NOT (EQUAL J (QUOTE 0))) (AND (EQUAL I (IPLUS R (ITIMES J Q))) (IF (ILEQ (QUOTE 0) I) (AND (ILEQ (QUOTE 0) R) (ILESSP R (IABS J))) (AND (ILEQ R (QUOTE 0)) (ILESSP (INEG (IABS J)) R))))))))) (AND (EQUAL R (IREM I J)) (EQUAL Q (IQUO I J)))) ((ENABLE IREM IABS IDIFFERENCE IPLUS INEG ILEQ FIX-INT ITIMES IQUO IZEROP ILESSP INTEGERP QUOTIENT-DIFFERENCE-LESSP-ARG2) (ENABLE-THEORY ARITHMETIC GROUND-ZERO) (DO-NOT-INDUCT T) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LESSP-PLUS-TIMES1 . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES2 . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-ELIM . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 FIX-INT . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES1 . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 IDIFFERENCE . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 DIFF-X-X . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES-CANCELLATION1 . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 IZEROP . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 QUOTIENT-TIMES-INSTANCE . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES1-INSTANCE . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 QUOTIENT-LESSP-ARG1 . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 DIFF-ADD1-ARG2 . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 QUOTIENT-DIFFERENCE-LESSP-ARG2 . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE-0 . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-LEQ-ARG1 . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-DIFFERENCE-PLUS . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-LESSP-PLUS . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 PLUS-STOPPER . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 QUOTIENT-PLUS . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 EQUAL-PLUS-0 . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 LESSP-PLUS-TIMES2 . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 DIFF-DIFF-ARG1 . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 REMAINDER-NOOP . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 QUOTIENT-DIFFERENCE3 . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 DIFF-ADD1-ARG2-CASESPLIT . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 ARITHMETIC . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 IQUO . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 IREM . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 INEG . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 IABS . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 ILESSP . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 ILEQ . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 ITIMES . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 IPLUS . IQUO-IREM-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 INTEGERP . IQUO-IREM-UNIQUENESS))))) (PUT1-LST (QUOTE DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO) (QUOTE (IDATE 1000404112525 EVENT (PROVE-LEMMA DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO NIL (IMPLIES (AND (INTEGERP I) (AND (INTEGERP J) (NOT (EQUAL J (QUOTE 0))))) (AND (EQUAL (IPLUS (IREM I J) (ITIMES J (IQUO I J))) I) (IF (ILEQ (QUOTE 0) I) (AND (ILEQ (QUOTE 0) (IREM I J)) (ILESSP (IREM I J) (IABS J))) (AND (ILEQ (IREM I J) (QUOTE 0)) (ILESSP (INEG (IABS J)) (IREM I J)))))) ((USE (DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART1 (I I) (J J)) (DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2 (I I) (J J)) (DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3 (I I) (J J))) (ENABLE INTEGERP ILESSP ILEQ) (DO-NOT-INDUCT T) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART1 . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO) (IMMEDIATE-DEPENDENTS0 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2 . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO) (IMMEDIATE-DEPENDENTS0 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3 . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO) (IMMEDIATE-DEPENDENTS0 INEG . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO) (IMMEDIATE-DEPENDENTS0 IABS . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO) (IMMEDIATE-DEPENDENTS0 ILESSP . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO) (IMMEDIATE-DEPENDENTS0 ILEQ . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO) (IMMEDIATE-DEPENDENTS0 IQUO . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO) (IMMEDIATE-DEPENDENTS0 ITIMES . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO) (IMMEDIATE-DEPENDENTS0 IREM . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO) (IMMEDIATE-DEPENDENTS0 IPLUS . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO) (IMMEDIATE-DEPENDENTS0 INTEGERP . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO))))) (PUT1-LST (QUOTE DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3) (QUOTE (IDATE 1000404112525 IMMEDIATE-DEPENDENTS0 (DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO) EVENT (PROVE-LEMMA DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3 NIL (IMPLIES (AND (INTEGERP I) (AND (INTEGERP J) (AND (NOT (EQUAL J (QUOTE 0))) (ILESSP I (QUOTE 0))))) (AND (ILEQ (IREM I J) (QUOTE 0)) (ILESSP (INEG (IABS J)) (IREM I J)))) ((ENABLE IABS IREM ILESSP ILEQ IDIFFERENCE IPLUS INEG ITIMES IQUO IZEROP INTEGERP FIX-INT) (ENABLE-THEORY ARITHMETIC GROUND-ZERO) (DO-NOT-INDUCT T) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQUAL-PLUS-0 . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3) (IMMEDIATE-DEPENDENTS0 LESSP-PLUS-TIMES1 . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-LESSP-PLUS . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-DIFFERENCE-PLUS . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3) (IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE-0 . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3) (IMMEDIATE-DEPENDENTS0 IPLUS . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3) (IMMEDIATE-DEPENDENTS0 IDIFFERENCE . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3) (IMMEDIATE-DEPENDENTS0 IQUO . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3) (IMMEDIATE-DEPENDENTS0 IZEROP . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3) (IMMEDIATE-DEPENDENTS0 EQUAL-QUOTIENT-0 . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3) (IMMEDIATE-DEPENDENTS0 FIX-INT . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3) (IMMEDIATE-DEPENDENTS0 ITIMES . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3) (IMMEDIATE-DEPENDENTS0 ARITHMETIC . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3) (IMMEDIATE-DEPENDENTS0 IABS . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3) (IMMEDIATE-DEPENDENTS0 INEG . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3) (IMMEDIATE-DEPENDENTS0 IREM . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3) (IMMEDIATE-DEPENDENTS0 ILEQ . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3) (IMMEDIATE-DEPENDENTS0 ILESSP . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3) (IMMEDIATE-DEPENDENTS0 INTEGERP . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3))))) (PUT1-LST (QUOTE DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2) (QUOTE (IDATE 1000404112523 IMMEDIATE-DEPENDENTS0 (DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO) EVENT (PROVE-LEMMA DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2 NIL (IMPLIES (AND (INTEGERP I) (AND (INTEGERP J) (AND (NOT (EQUAL J (QUOTE 0))) (ILEQ (QUOTE 0) I)))) (AND (ILEQ (QUOTE 0) (IREM I J)) (ILESSP (IREM I J) (IABS J)))) ((ENABLE IABS IREM ILESSP ILEQ IDIFFERENCE IPLUS INEG ITIMES IQUO IZEROP INTEGERP FIX-INT) (ENABLE-THEORY ARITHMETIC GROUND-ZERO) (DO-NOT-INDUCT T) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2) (IMMEDIATE-DEPENDENTS0 LESSP-PLUS-TIMES1 . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2) (IMMEDIATE-DEPENDENTS0 LESSP-PLUS-TIMES2 . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-DIFFERENCE-PLUS . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2) (IMMEDIATE-DEPENDENTS0 PLUS-STOPPER . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2) (IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE-0 . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2) (IMMEDIATE-DEPENDENTS0 IPLUS . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2) (IMMEDIATE-DEPENDENTS0 IDIFFERENCE . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2) (IMMEDIATE-DEPENDENTS0 EQUAL-QUOTIENT-0 . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2) (IMMEDIATE-DEPENDENTS0 INEG . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2) (IMMEDIATE-DEPENDENTS0 ITIMES . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2) (IMMEDIATE-DEPENDENTS0 IQUO . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2) (IMMEDIATE-DEPENDENTS0 IZEROP . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2) (IMMEDIATE-DEPENDENTS0 FIX-INT . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2) (IMMEDIATE-DEPENDENTS0 ARITHMETIC . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2) (IMMEDIATE-DEPENDENTS0 IABS . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2) (IMMEDIATE-DEPENDENTS0 ILESSP . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2) (IMMEDIATE-DEPENDENTS0 IREM . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2) (IMMEDIATE-DEPENDENTS0 ILEQ . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2) (IMMEDIATE-DEPENDENTS0 INTEGERP . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2))))) (PUT1-LST (QUOTE DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART1) (QUOTE (IDATE 1000404112521 IMMEDIATE-DEPENDENTS0 (DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO) EVENT (PROVE-LEMMA DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART1 NIL (IMPLIES (INTEGERP I) (EQUAL (IPLUS (IREM I J) (ITIMES J (IQUO I J))) I)) ((ENABLE IREM INTEGERP FIX-INT CORRECTNESS-OF-CANCEL-IDIFFERENCE FIX-INT-FIX-INT IPLUS-IDIFFERENCE-ARG1) (DO-NOT-INDUCT T) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 FIX-INT . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART1) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-IDIFFERENCE . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART1) (IMMEDIATE-DEPENDENTS0 IPLUS-IDIFFERENCE-ARG1 . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART1) (IMMEDIATE-DEPENDENTS0 IQUO . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART1) (IMMEDIATE-DEPENDENTS0 ITIMES . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART1) (IMMEDIATE-DEPENDENTS0 IREM . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART1) (IMMEDIATE-DEPENDENTS0 IPLUS . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART1) (IMMEDIATE-DEPENDENTS0 INTEGERP . DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART1))))) (PUT1-LST (QUOTE *1*IREM) (QUOTE (MAIN-EVENT IREM))) (PUT1-LST (QUOTE IREM) (QUOTE (TYPE-PRESCRIPTION-LST ((IREM 36 NIL NIL)) LEMMAS ((REWRITE-RULE IREM-FIX-INT2 NIL (EQUAL (IREM I (FIX-INT J)) (IREM I J)) NIL) (REWRITE-RULE IREM-FIX-INT1 NIL (EQUAL (IREM (FIX-INT I) J) (IREM I J)) NIL)) TOTALP-LST ((IREM . T)) SDEFN (LAMBDA (I J) (IDIFFERENCE (FIX-INT I) (ITIMES J (IQUO I J)))) LISP-CODE *1*IREM SUBRP *1*FALSE LEVEL-NO 2 IDATE 1000404112521 SATELLITES (*1*IREM) IMMEDIATE-DEPENDENTS0 (IREM-OFF FIX-INT-IREM IREM-FIX-INT2 IREM-FIX-INT1 INTEGERP-IREM IQUO-IREM-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART1) EVENT (DEFN IREM (I J) (IDIFFERENCE (FIX-INT I) (ITIMES J (IQUO I J)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 IQUO . IREM) (IMMEDIATE-DEPENDENTS0 ITIMES . IREM) (IMMEDIATE-DEPENDENTS0 FIX-INT . IREM) (IMMEDIATE-DEPENDENTS0 IDIFFERENCE . IREM) (DCELL . *1*IREM))))) (PUT1-LST (QUOTE *1*IQUO) (QUOTE (MAIN-EVENT IQUO))) (PUT1-LST (QUOTE IQUO) (QUOTE (TYPE-PRESCRIPTION-LST ((IQUO 36 NIL NIL)) LEMMAS ((REWRITE-RULE IQUO-FIX-INT2 NIL (EQUAL (IQUO I (FIX-INT J)) (IQUO I J)) NIL) (REWRITE-RULE IQUO-FIX-INT1 NIL (EQUAL (IQUO (FIX-INT I) J) (IQUO I J)) NIL)) TOTALP-LST ((IQUO . T)) SDEFN (LAMBDA (I J) (IF (IZEROP J) (QUOTE 0) (IF (NEGATIVEP I) (IF (NEGATIVEP J) (QUOTIENT (NEGATIVE-GUTS I) (NEGATIVE-GUTS J)) (FIX-INT (MINUS (QUOTIENT (NEGATIVE-GUTS I) J)))) (IF (NEGATIVEP J) (FIX-INT (MINUS (QUOTIENT I (NEGATIVE-GUTS J)))) (QUOTIENT I J))))) LISP-CODE *1*IQUO SUBRP *1*FALSE LEVEL-NO 2 IDATE 1000404112521 SATELLITES (*1*IQUO) IMMEDIATE-DEPENDENTS0 (IQUO-OFF FIX-INT-IQUO IQUO-FIX-INT2 IQUO-FIX-INT1 INTEGERP-IQUO IQUO-IREM-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART1 IREM) EVENT (DEFN IQUO (I J) (IF (IZEROP J) (QUOTE 0) (IF (NEGATIVEP I) (IF (NEGATIVEP J) (QUOTIENT (NEGATIVE-GUTS I) (NEGATIVE-GUTS J)) (FIX-INT (MINUS (QUOTIENT (NEGATIVE-GUTS I) J)))) (IF (NEGATIVEP J) (FIX-INT (MINUS (QUOTIENT I (NEGATIVE-GUTS J)))) (QUOTIENT I J))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 FIX-INT . IQUO) (IMMEDIATE-DEPENDENTS0 IZEROP . IQUO) (DCELL . *1*IQUO))))) (PUT1-LST (QUOTE IDIV-IMOD-UNIQUENESS) (QUOTE (IDATE 1000404112521 EVENT (PROVE-LEMMA IDIV-IMOD-UNIQUENESS NIL (IMPLIES (AND (INTEGERP I) (AND (INTEGERP J) (AND (INTEGERP R) (AND (INTEGERP Q) (AND (NOT (EQUAL J (QUOTE 0))) (AND (EQUAL I (IPLUS R (ITIMES J Q))) (IF (ILESSP (QUOTE 0) J) (AND (ILEQ (QUOTE 0) R) (ILESSP R J)) (AND (ILEQ R (QUOTE 0)) (ILESSP J R))))))))) (AND (EQUAL R (IMOD I J)) (EQUAL Q (IDIV I J)))) ((ENABLE IMOD IABS IDIFFERENCE IPLUS INEG ILEQ FIX-INT ITIMES IDIV IZEROP ILESSP INTEGERP QUOTIENT-DIFFERENCE-LESSP-ARG2) (ENABLE-THEORY ARITHMETIC GROUND-ZERO) (DO-NOT-INDUCT T) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIFFERENCE-LEQ-ARG1 . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 LESSP-DIFFERENCE . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 LESSP-PLUS-TIMES2 . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES2 . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 DIFF-DIFF-ARG2 . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 DIFF-DIFF-ARG1 . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 REMAINDER-DIFFERENCE2 . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 FIX-INT . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES1 . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 IDIFFERENCE . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 IZEROP . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES1-INSTANCE . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 QUOTIENT-TIMES-INSTANCE . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 QUOTIENT-LESSP-ARG1 . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 DIFF-ADD1-ARG2 . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 QUOTIENT-DIFFERENCE-LESSP-ARG2 . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE-0 . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 INEG . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 REMAINDER-NOOP . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 PLUS-STOPPER . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 QUOTIENT-PLUS . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 DIFF-X-X . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES-CANCELLATION1 . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-DIFFERENCE-PLUS . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-LESSP-PLUS . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 EQUAL-PLUS-0 . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 ARITHMETIC . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 IDIV . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 IMOD . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 ILEQ . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 ILESSP . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 ITIMES . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 IPLUS . IDIV-IMOD-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 INTEGERP . IDIV-IMOD-UNIQUENESS))))) (PUT1-LST (QUOTE DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF) (QUOTE (IDATE 1000404112520 EVENT (PROVE-LEMMA DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF NIL (IMPLIES (AND (INTEGERP I) (AND (INTEGERP J) (NOT (EQUAL J (QUOTE 0))))) (AND (EQUAL (IPLUS (IMOD I J) (ITIMES J (IDIV I J))) I) (IF (ILESSP (QUOTE 0) J) (AND (ILEQ (QUOTE 0) (IMOD I J)) (ILESSP (IMOD I J) J)) (AND (ILEQ (IMOD I J) (QUOTE 0)) (ILESSP J (IMOD I J)))))) ((USE (DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART1 (I I) (J J)) (DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2 (I I) (J J)) (DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3 (I I) (J J))) (ENABLE INTEGERP ILESSP) (DO-NOT-INDUCT T) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART1 . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF) (IMMEDIATE-DEPENDENTS0 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2 . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF) (IMMEDIATE-DEPENDENTS0 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3 . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF) (IMMEDIATE-DEPENDENTS0 ILEQ . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF) (IMMEDIATE-DEPENDENTS0 ILESSP . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF) (IMMEDIATE-DEPENDENTS0 IDIV . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF) (IMMEDIATE-DEPENDENTS0 ITIMES . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF) (IMMEDIATE-DEPENDENTS0 IMOD . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF) (IMMEDIATE-DEPENDENTS0 IPLUS . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF) (IMMEDIATE-DEPENDENTS0 INTEGERP . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF))))) (PUT1-LST (QUOTE DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3) (QUOTE (IDATE 1000404112520 IMMEDIATE-DEPENDENTS0 (DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF) EVENT (PROVE-LEMMA DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3 NIL (IMPLIES (AND (INTEGERP J) (ILESSP J (QUOTE 0))) (AND (ILEQ (IMOD I J) (QUOTE 0)) (ILESSP J (IMOD I J)))) ((ENABLE IMOD ILESSP ILEQ IDIFFERENCE IPLUS INEG ITIMES IDIV IZEROP INTEGERP FIX-INT) (ENABLE-THEORY ARITHMETIC GROUND-ZERO) (DO-NOT-INDUCT T) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LESSP-PLUS-TIMES1 . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-DIFFERENCE-PLUS . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3) (IMMEDIATE-DEPENDENTS0 QUOTIENT-LESSP-ARG1 . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-LESSP-PLUS . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3) (IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE-0 . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3) (IMMEDIATE-DEPENDENTS0 TIMES-ADD1 . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3) (IMMEDIATE-DEPENDENTS0 EQUAL-PLUS-0 . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3) (IMMEDIATE-DEPENDENTS0 REMAINDER-NOOP . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3) (IMMEDIATE-DEPENDENTS0 REMAINDER-OF-NON-NUMBER . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3) (IMMEDIATE-DEPENDENTS0 DIFF-X-X . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3) (IMMEDIATE-DEPENDENTS0 IPLUS . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3) (IMMEDIATE-DEPENDENTS0 TIMES-QUOTIENT . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3) (IMMEDIATE-DEPENDENTS0 ITIMES . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3) (IMMEDIATE-DEPENDENTS0 INEG . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3) (IMMEDIATE-DEPENDENTS0 IDIFFERENCE . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3) (IMMEDIATE-DEPENDENTS0 IDIV . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3) (IMMEDIATE-DEPENDENTS0 IZEROP . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3) (IMMEDIATE-DEPENDENTS0 EQUAL-QUOTIENT-0 . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3) (IMMEDIATE-DEPENDENTS0 FIX-INT . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3) (IMMEDIATE-DEPENDENTS0 ARITHMETIC . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3) (IMMEDIATE-DEPENDENTS0 IMOD . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3) (IMMEDIATE-DEPENDENTS0 ILEQ . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3) (IMMEDIATE-DEPENDENTS0 ILESSP . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3) (IMMEDIATE-DEPENDENTS0 INTEGERP . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3))))) (PUT1-LST (QUOTE DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (QUOTE (IDATE 1000404112518 IMMEDIATE-DEPENDENTS0 (DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF) EVENT (PROVE-LEMMA DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2 NIL (IMPLIES (ILESSP (QUOTE 0) J) (AND (ILEQ (QUOTE 0) (IMOD I J)) (ILESSP (IMOD I J) J))) ((ENABLE IMOD ILESSP ILEQ IDIFFERENCE IPLUS INEG ITIMES IDIV IZEROP INTEGERP FIX-INT) (ENABLE-THEORY ARITHMETIC GROUND-ZERO) (DO-NOT-INDUCT T) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LESSP-PLUS-TIMES1 . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (IMMEDIATE-DEPENDENTS0 LESSP-PLUS-TIMES2 . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-DIFFERENCE-PLUS . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-LESSP-PLUS . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (IMMEDIATE-DEPENDENTS0 EQUAL-PLUS-0 . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (IMMEDIATE-DEPENDENTS0 TIMES-ADD1 . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (IMMEDIATE-DEPENDENTS0 REMAINDER-NOOP . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (IMMEDIATE-DEPENDENTS0 TIMES-QUOTIENT . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (IMMEDIATE-DEPENDENTS0 DIFF-X-X . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (IMMEDIATE-DEPENDENTS0 QUOTIENT-LESSP-ARG1 . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (IMMEDIATE-DEPENDENTS0 PLUS-STOPPER . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE-0 . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (IMMEDIATE-DEPENDENTS0 IPLUS . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (IMMEDIATE-DEPENDENTS0 ITIMES . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (IMMEDIATE-DEPENDENTS0 INEG . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (IMMEDIATE-DEPENDENTS0 IDIFFERENCE . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (IMMEDIATE-DEPENDENTS0 IDIV . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (IMMEDIATE-DEPENDENTS0 IZEROP . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (IMMEDIATE-DEPENDENTS0 EQUAL-QUOTIENT-0 . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (IMMEDIATE-DEPENDENTS0 FIX-INT . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (IMMEDIATE-DEPENDENTS0 INTEGERP . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (IMMEDIATE-DEPENDENTS0 ARITHMETIC . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (IMMEDIATE-DEPENDENTS0 IMOD . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (IMMEDIATE-DEPENDENTS0 ILEQ . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2) (IMMEDIATE-DEPENDENTS0 ILESSP . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2))))) (PUT1-LST (QUOTE DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART1) (QUOTE (IDATE 1000404112516 IMMEDIATE-DEPENDENTS0 (DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF) EVENT (PROVE-LEMMA DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART1 NIL (IMPLIES (INTEGERP I) (EQUAL (IPLUS (IMOD I J) (ITIMES J (IDIV I J))) I)) ((ENABLE IMOD INTEGERP FIX-INT CORRECTNESS-OF-CANCEL-IDIFFERENCE FIX-INT-FIX-INT IPLUS-IDIFFERENCE-ARG1) (DO-NOT-INDUCT T) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 FIX-INT . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART1) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-IDIFFERENCE . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART1) (IMMEDIATE-DEPENDENTS0 IPLUS-IDIFFERENCE-ARG1 . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART1) (IMMEDIATE-DEPENDENTS0 IDIV . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART1) (IMMEDIATE-DEPENDENTS0 ITIMES . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART1) (IMMEDIATE-DEPENDENTS0 IMOD . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART1) (IMMEDIATE-DEPENDENTS0 IPLUS . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART1) (IMMEDIATE-DEPENDENTS0 INTEGERP . DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART1))))) (PUT1-LST (QUOTE *1*IMOD) (QUOTE (MAIN-EVENT IMOD))) (PUT1-LST (QUOTE IMOD) (QUOTE (TYPE-PRESCRIPTION-LST ((IMOD 36 NIL NIL)) LEMMAS ((REWRITE-RULE IMOD-FIX-INT2 NIL (EQUAL (IMOD I (FIX-INT J)) (IMOD I J)) NIL) (REWRITE-RULE IMOD-FIX-INT1 NIL (EQUAL (IMOD (FIX-INT I) J) (IMOD I J)) NIL)) TOTALP-LST ((IMOD . T)) SDEFN (LAMBDA (I J) (IDIFFERENCE (FIX-INT I) (ITIMES J (IDIV I J)))) LISP-CODE *1*IMOD SUBRP *1*FALSE LEVEL-NO 2 IDATE 1000404112516 SATELLITES (*1*IMOD) IMMEDIATE-DEPENDENTS0 (IMOD-OFF FIX-INT-IMOD IMOD-FIX-INT2 IMOD-FIX-INT1 INTEGERP-IMOD IDIV-IMOD-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART1) EVENT (DEFN IMOD (I J) (IDIFFERENCE (FIX-INT I) (ITIMES J (IDIV I J)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 IDIV . IMOD) (IMMEDIATE-DEPENDENTS0 ITIMES . IMOD) (IMMEDIATE-DEPENDENTS0 FIX-INT . IMOD) (IMMEDIATE-DEPENDENTS0 IDIFFERENCE . IMOD) (DCELL . *1*IMOD))))) (PUT1-LST (QUOTE *1*IDIV) (QUOTE (MAIN-EVENT IDIV))) (PUT1-LST (QUOTE IDIV) (QUOTE (TYPE-PRESCRIPTION-LST ((IDIV 36 NIL NIL)) LEMMAS ((REWRITE-RULE IDIV-FIX-INT2 NIL (EQUAL (IDIV I (FIX-INT J)) (IDIV I J)) NIL) (REWRITE-RULE IDIV-FIX-INT1 NIL (EQUAL (IDIV (FIX-INT I) J) (IDIV I J)) NIL)) TOTALP-LST ((IDIV . T)) SDEFN (LAMBDA (I J) (IF (IZEROP J) (QUOTE 0) (IF (NEGATIVEP I) (IF (NEGATIVEP J) (QUOTIENT (NEGATIVE-GUTS I) (NEGATIVE-GUTS J)) (IF (EQUAL (REMAINDER (NEGATIVE-GUTS I) J) (QUOTE 0)) (FIX-INT (MINUS (QUOTIENT (NEGATIVE-GUTS I) J))) (FIX-INT (MINUS (ADD1 (QUOTIENT (NEGATIVE-GUTS I) J)))))) (IF (NEGATIVEP J) (IF (EQUAL (REMAINDER I (NEGATIVE-GUTS J)) (QUOTE 0)) (FIX-INT (MINUS (QUOTIENT I (NEGATIVE-GUTS J)))) (FIX-INT (MINUS (ADD1 (QUOTIENT I (NEGATIVE-GUTS J)))))) (QUOTIENT I J))))) LISP-CODE *1*IDIV SUBRP *1*FALSE LEVEL-NO 2 IDATE 1000404112516 SATELLITES (*1*IDIV) IMMEDIATE-DEPENDENTS0 (IDIV-OFF FIX-INT-IDIV IDIV-FIX-INT2 IDIV-FIX-INT1 INTEGERP-IDIV IDIV-IMOD-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART1 IMOD) EVENT (DEFN IDIV (I J) (IF (IZEROP J) (QUOTE 0) (IF (NEGATIVEP I) (IF (NEGATIVEP J) (QUOTIENT (NEGATIVE-GUTS I) (NEGATIVE-GUTS J)) (IF (EQUAL (REMAINDER (NEGATIVE-GUTS I) J) (QUOTE 0)) (FIX-INT (MINUS (QUOTIENT (NEGATIVE-GUTS I) J))) (FIX-INT (MINUS (ADD1 (QUOTIENT (NEGATIVE-GUTS I) J)))))) (IF (NEGATIVEP J) (IF (EQUAL (REMAINDER I (NEGATIVE-GUTS J)) (QUOTE 0)) (FIX-INT (MINUS (QUOTIENT I (NEGATIVE-GUTS J)))) (FIX-INT (MINUS (ADD1 (QUOTIENT I (NEGATIVE-GUTS J)))))) (QUOTIENT I J))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 FIX-INT . IDIV) (IMMEDIATE-DEPENDENTS0 IZEROP . IDIV) (DCELL . *1*IDIV))))) (PUT1-LST (QUOTE IQUOTIENT-IREMAINDER-UNIQUENESS) (QUOTE (IDATE 1000404112516 EVENT (PROVE-LEMMA IQUOTIENT-IREMAINDER-UNIQUENESS NIL (IMPLIES (AND (INTEGERP I) (AND (INTEGERP J) (AND (INTEGERP R) (AND (INTEGERP Q) (AND (NOT (EQUAL J (QUOTE 0))) (AND (EQUAL I (IPLUS R (ITIMES J Q))) (AND (ILEQ (QUOTE 0) R) (ILESSP R (IABS J))))))))) (AND (EQUAL R (IREMAINDER I J)) (EQUAL Q (IQUOTIENT I J)))) ((ENABLE IREMAINDER IABS IDIFFERENCE IPLUS INEG ILEQ FIX-INT ITIMES IQUOTIENT IZEROP ILESSP INTEGERP QUOTIENT-DIFFERENCE-LESSP-ARG2) (ENABLE-THEORY ARITHMETIC GROUND-ZERO) (DO-NOT-INDUCT T) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LESSP-TIMES2 . IQUOTIENT-IREMAINDER-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 DIFF-DIFF-ARG2 . IQUOTIENT-IREMAINDER-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 DIFF-DIFF-ARG1 . IQUOTIENT-IREMAINDER-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 DIFF-X-X . IQUOTIENT-IREMAINDER-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES-CANCELLATION1 . IQUOTIENT-IREMAINDER-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 REMAINDER-NOOP . IQUOTIENT-IREMAINDER-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 REMAINDER-DIFFERENCE2 . IQUOTIENT-IREMAINDER-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 FIX-INT . IQUOTIENT-IREMAINDER-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . IQUOTIENT-IREMAINDER-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . IQUOTIENT-IREMAINDER-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES1 . IQUOTIENT-IREMAINDER-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 IDIFFERENCE . IQUOTIENT-IREMAINDER-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 IZEROP . IQUOTIENT-IREMAINDER-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES1-INSTANCE . IQUOTIENT-IREMAINDER-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 QUOTIENT-TIMES-INSTANCE . IQUOTIENT-IREMAINDER-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 QUOTIENT-LESSP-ARG1 . IQUOTIENT-IREMAINDER-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 DIFF-ADD1-ARG2 . IQUOTIENT-IREMAINDER-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 QUOTIENT-DIFFERENCE-LESSP-ARG2 . IQUOTIENT-IREMAINDER-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE-0 . IQUOTIENT-IREMAINDER-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . IQUOTIENT-IREMAINDER-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 PLUS-STOPPER . IQUOTIENT-IREMAINDER-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 INEG . IQUOTIENT-IREMAINDER-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 QUOTIENT-PLUS . IQUOTIENT-IREMAINDER-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-DIFFERENCE-PLUS . IQUOTIENT-IREMAINDER-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 LESSP-PLUS-TIMES2 . IQUOTIENT-IREMAINDER-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 ARITHMETIC . IQUOTIENT-IREMAINDER-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 IQUOTIENT . IQUOTIENT-IREMAINDER-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 IREMAINDER . IQUOTIENT-IREMAINDER-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 IABS . IQUOTIENT-IREMAINDER-UNIQUENESS) (IMMEDIATE-DEPENDENTS0 ILESSP . 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CORRECTNESS-OF-CANCEL-IDIFFERENCE) (IMMEDIATE-DEPENDENTS0 IPLUS-0 . CORRECTNESS-OF-CANCEL-IDIFFERENCE) (IMMEDIATE-DEPENDENTS0 IPLUS-INEG2 . CORRECTNESS-OF-CANCEL-IDIFFERENCE) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-IPLUS . CORRECTNESS-OF-CANCEL-IDIFFERENCE) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-IPLUS . CORRECTNESS-OF-CANCEL-IDIFFERENCE) (IMMEDIATE-DEPENDENTS0 IPLUS-TREE-IPLUS-FRINGE . CORRECTNESS-OF-CANCEL-IDIFFERENCE) (IMMEDIATE-DEPENDENTS0 IPLUS-FIX-INT1 . CORRECTNESS-OF-CANCEL-IDIFFERENCE) (IMMEDIATE-DEPENDENTS0 IDIFFERENCE . CORRECTNESS-OF-CANCEL-IDIFFERENCE) (IMMEDIATE-DEPENDENTS0 IPLUS-TREE-DELETE . CORRECTNESS-OF-CANCEL-IDIFFERENCE) (IMMEDIATE-DEPENDENTS0 INEG-INEG . CORRECTNESS-OF-CANCEL-IDIFFERENCE) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-IPLUS . CORRECTNESS-OF-CANCEL-IDIFFERENCE) (IMMEDIATE-DEPENDENTS0 IPLUS-FIX-INT2 . CORRECTNESS-OF-CANCEL-IDIFFERENCE) (IMMEDIATE-DEPENDENTS0 INEG-IPLUS . CORRECTNESS-OF-CANCEL-IDIFFERENCE) (IMMEDIATE-DEPENDENTS0 SETS-AND-BAGS . CORRECTNESS-OF-CANCEL-IDIFFERENCE) (IMMEDIATE-DEPENDENTS0 CANCEL-IDIFFERENCE . CORRECTNESS-OF-CANCEL-IDIFFERENCE) (LEMMAS IDIFFERENCE . CORRECTNESS-OF-CANCEL-IDIFFERENCE))))) (PUT1-LST (QUOTE *1*CANCEL-IDIFFERENCE) (QUOTE (MAIN-EVENT CANCEL-IDIFFERENCE))) (PUT1-LST (QUOTE CANCEL-IDIFFERENCE) (QUOTE (TYPE-PRESCRIPTION-LST ((CANCEL-IDIFFERENCE 16 T)) TOTALP-LST ((CANCEL-IDIFFERENCE . T)) SDEFN (LAMBDA (X) (IF (LISTP X) (IF (EQUAL (CAR X) (QUOTE IDIFFERENCE)) (IF (LISTP (CAR (CDR X))) (IF (EQUAL (CAR (CAR (CDR X))) (QUOTE IPLUS)) (IF (LISTP (CAR (CDR (CDR X)))) (IF (EQUAL (CAR (CAR (CDR (CDR X)))) (QUOTE IPLUS)) (CONS (QUOTE IDIFFERENCE) (CONS (IPLUS-TREE (BAGDIFF (IPLUS-FRINGE (CAR (CDR X))) (BAGINT (IPLUS-FRINGE (CAR (CDR X))) (IPLUS-FRINGE (CAR (CDR (CDR X))))))) (CONS (IPLUS-TREE (BAGDIFF (IPLUS-FRINGE (CAR (CDR (CDR X)))) (BAGINT (IPLUS-FRINGE (CAR (CDR X))) (IPLUS-FRINGE (CAR (CDR (CDR X))))))) (QUOTE NIL)))) (IF (MEMBER (CAR (CDR (CDR X))) (IPLUS-FRINGE (CAR (CDR X)))) (IPLUS-TREE (DELETE (CAR (CDR (CDR X))) (IPLUS-FRINGE (CAR (CDR X))))) X)) (IF (MEMBER (CAR (CDR (CDR X))) (IPLUS-FRINGE (CAR (CDR X)))) (IPLUS-TREE (DELETE (CAR (CDR (CDR X))) (IPLUS-FRINGE (CAR (CDR X))))) X)) (IF (LISTP (CAR (CDR (CDR X)))) (IF (EQUAL (CAR (CAR (CDR (CDR X)))) (QUOTE IPLUS)) (IF (MEMBER (CAR (CDR X)) (IPLUS-FRINGE (CAR (CDR (CDR X))))) (CONS (QUOTE INEG) (CONS (IPLUS-TREE (DELETE (CAR (CDR X)) (IPLUS-FRINGE (CAR (CDR (CDR X)))))) (QUOTE NIL))) X) X) X)) (IF (LISTP (CAR (CDR (CDR X)))) (IF (EQUAL (CAR (CAR (CDR (CDR X)))) (QUOTE IPLUS)) (IF (MEMBER (CAR (CDR X)) (IPLUS-FRINGE (CAR (CDR (CDR X))))) (CONS (QUOTE INEG) (CONS (IPLUS-TREE (DELETE (CAR (CDR X)) (IPLUS-FRINGE (CAR (CDR (CDR X)))))) (QUOTE NIL))) X) X) X)) X) X)) LISP-CODE *1*CANCEL-IDIFFERENCE SUBRP *1*FALSE LEVEL-NO 2 IDATE 1000404112506 SATELLITES (*1*CANCEL-IDIFFERENCE) IMMEDIATE-DEPENDENTS0 (CANCEL-IDIFFERENCE-OFF CORRECTNESS-OF-CANCEL-IDIFFERENCE) EVENT (DEFN CANCEL-IDIFFERENCE (X) (IF (AND (LISTP X) (EQUAL (CAR X) (QUOTE IDIFFERENCE))) (IF (AND (LISTP (CAR (CDR X))) (AND (EQUAL (CAR (CAR (CDR X))) (QUOTE IPLUS)) (AND (LISTP (CAR (CDR (CDR X)))) (EQUAL (CAR (CAR (CDR (CDR X)))) (QUOTE IPLUS))))) (CONS (QUOTE IDIFFERENCE) (CONS (IPLUS-TREE (BAGDIFF (IPLUS-FRINGE (CAR (CDR X))) (BAGINT (IPLUS-FRINGE (CAR (CDR X))) (IPLUS-FRINGE (CAR (CDR (CDR X))))))) (CONS (IPLUS-TREE (BAGDIFF (IPLUS-FRINGE (CAR (CDR (CDR X)))) (BAGINT (IPLUS-FRINGE (CAR (CDR X))) (IPLUS-FRINGE (CAR (CDR (CDR X))))))) (QUOTE NIL)))) (IF (AND (LISTP (CAR (CDR X))) (AND (EQUAL (CAR (CAR (CDR X))) (QUOTE IPLUS)) (MEMBER (CAR (CDR (CDR X))) (IPLUS-FRINGE (CAR (CDR X)))))) (IPLUS-TREE (DELETE (CAR (CDR (CDR X))) (IPLUS-FRINGE (CAR (CDR X))))) (IF (AND (LISTP (CAR (CDR (CDR X)))) (AND (EQUAL (CAR (CAR (CDR (CDR X)))) (QUOTE IPLUS)) (MEMBER (CAR (CDR X)) (IPLUS-FRINGE (CAR (CDR (CDR X))))))) (CONS (QUOTE INEG) (CONS (IPLUS-TREE (DELETE (CAR (CDR X)) (IPLUS-FRINGE (CAR (CDR (CDR X)))))) (QUOTE NIL))) X))) X)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DELETE . CANCEL-IDIFFERENCE) (IMMEDIATE-DEPENDENTS0 BAGINT . CANCEL-IDIFFERENCE) (IMMEDIATE-DEPENDENTS0 IPLUS-FRINGE . CANCEL-IDIFFERENCE) (IMMEDIATE-DEPENDENTS0 BAGDIFF . CANCEL-IDIFFERENCE) (IMMEDIATE-DEPENDENTS0 IPLUS-TREE . CANCEL-IDIFFERENCE) (DCELL . *1*CANCEL-IDIFFERENCE))))) (PUT1-LST (QUOTE IPLUS-IDIFFERENCE-IDIFFERENCE) (QUOTE (IDATE 1000404112506 IMMEDIATE-DEPENDENTS0 (INTEGERS) EVENT (PROVE-LEMMA IPLUS-IDIFFERENCE-IDIFFERENCE (REWRITE) (EQUAL (IPLUS (IDIFFERENCE A B) (IDIFFERENCE C D)) (IDIFFERENCE (IPLUS A C) (IPLUS B D))) ((ENABLE IDIFFERENCE ASSOCIATIVITY-OF-IPLUS COMMUTATIVITY-OF-IPLUS INEG-IPLUS CORRECTNESS-OF-CANCEL-IPLUS) (DO-NOT-INDUCT T) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-IPLUS . IPLUS-IDIFFERENCE-IDIFFERENCE) (IMMEDIATE-DEPENDENTS0 INEG-IPLUS . IPLUS-IDIFFERENCE-IDIFFERENCE) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-IPLUS . IPLUS-IDIFFERENCE-IDIFFERENCE) (IMMEDIATE-DEPENDENTS0 IDIFFERENCE . IPLUS-IDIFFERENCE-IDIFFERENCE) (IMMEDIATE-DEPENDENTS0 IPLUS . IPLUS-IDIFFERENCE-IDIFFERENCE) (LEMMAS IPLUS . IPLUS-IDIFFERENCE-IDIFFERENCE))))) (PUT1-LST (QUOTE CORRECTNESS-OF-CANCEL-IPLUS) (QUOTE (IDATE 1000404112506 IMMEDIATE-DEPENDENTS0 (REQUAL-SIMPLE-RPLUS-X-X-REWRITE RPLUS-REQUAL-ARG1 GCD-FACTORS-GIVES-LINEAR-COMBINATION INTEGERS IPLUS-IDIFFERENCE-IDIFFERENCE) EVENT (PROVE-LEMMA CORRECTNESS-OF-CANCEL-IPLUS ((META EQUAL)) (EQUAL (EVAL$ (QUOTE *1*TRUE) X A) (EVAL$ (QUOTE *1*TRUE) (CANCEL-IPLUS X) A)) ((ENABLE CANCEL-IPLUS FIX-INT EQUAL-IDIFFERENCE-0 EVAL$-QUOTE IDIFFERENCE-CANCELLATION-1 INTEGERP-EVAL$-IPLUS IPLUS-TREE-BAGDIFF IPLUS-TREE-DELETE IPLUS-TREE-IPLUS-FRINGE NOT-INTEGERP-IMPLIES-NOT-EQUAL-IPLUS) (ENABLE-THEORY SETS-AND-BAGS GROUND-ZERO) (DISABLE EVAL$) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SUBBAGP-BAGINT1 . CORRECTNESS-OF-CANCEL-IPLUS) (IMMEDIATE-DEPENDENTS0 IPLUS-TREE-BAGDIFF . CORRECTNESS-OF-CANCEL-IPLUS) (IMMEDIATE-DEPENDENTS0 SUBBAGP-BAGINT2 . CORRECTNESS-OF-CANCEL-IPLUS) (IMMEDIATE-DEPENDENTS0 IDIFFERENCE-CANCELLATION-1 . CORRECTNESS-OF-CANCEL-IPLUS) (IMMEDIATE-DEPENDENTS0 NOT-INTEGERP-IMPLIES-NOT-EQUAL-IPLUS . CORRECTNESS-OF-CANCEL-IPLUS) (IMMEDIATE-DEPENDENTS0 EVAL$-QUOTE . CORRECTNESS-OF-CANCEL-IPLUS) (IMMEDIATE-DEPENDENTS0 INTEGERP-EVAL$-IPLUS . CORRECTNESS-OF-CANCEL-IPLUS) (IMMEDIATE-DEPENDENTS0 FIX-INT . CORRECTNESS-OF-CANCEL-IPLUS) (IMMEDIATE-DEPENDENTS0 IPLUS-TREE-IPLUS-FRINGE . CORRECTNESS-OF-CANCEL-IPLUS) (IMMEDIATE-DEPENDENTS0 IPLUS-TREE-DELETE . CORRECTNESS-OF-CANCEL-IPLUS) (IMMEDIATE-DEPENDENTS0 EQUAL-IDIFFERENCE-0 . CORRECTNESS-OF-CANCEL-IPLUS) (IMMEDIATE-DEPENDENTS0 SETS-AND-BAGS . CORRECTNESS-OF-CANCEL-IPLUS) (IMMEDIATE-DEPENDENTS0 CANCEL-IPLUS . CORRECTNESS-OF-CANCEL-IPLUS) (LEMMAS EQUAL . CORRECTNESS-OF-CANCEL-IPLUS))))) (PUT1-LST (QUOTE NOT-INTEGERP-IMPLIES-NOT-EQUAL-IPLUS) (QUOTE (IDATE 1000404112505 IMMEDIATE-DEPENDENTS0 (NOT-INTEGERP-IMPLIES-NOT-EQUAL-IPLUS-OFF CORRECTNESS-OF-CANCEL-IPLUS) EVENT (PROVE-LEMMA NOT-INTEGERP-IMPLIES-NOT-EQUAL-IPLUS (REWRITE) (IMPLIES (NOT (INTEGERP A)) (EQUAL (EQUAL A (IPLUS B C)) (QUOTE *1*FALSE))) ((USE (INTEGERP-IPLUS (X B) (Y C))) (ENABLE INTEGERP) (DO-NOT-INDUCT T) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 INTEGERP-IPLUS . NOT-INTEGERP-IMPLIES-NOT-EQUAL-IPLUS) (IMMEDIATE-DEPENDENTS0 IPLUS . NOT-INTEGERP-IMPLIES-NOT-EQUAL-IPLUS) (IMMEDIATE-DEPENDENTS0 INTEGERP . NOT-INTEGERP-IMPLIES-NOT-EQUAL-IPLUS) (LEMMAS EQUAL . NOT-INTEGERP-IMPLIES-NOT-EQUAL-IPLUS))))) (PUT1-LST (QUOTE IPLUS-TREE-BAGDIFF) (QUOTE (IDATE 1000404112505 IMMEDIATE-DEPENDENTS0 (IPLUS-TREE-BAGDIFF-OFF CORRECTNESS-OF-CANCEL-IDIFFERENCE CORRECTNESS-OF-CANCEL-IPLUS) EVENT (PROVE-LEMMA IPLUS-TREE-BAGDIFF (REWRITE) (IMPLIES (SUBBAGP X Y) (EQUAL (EVAL$ (QUOTE *1*TRUE) (IPLUS-TREE (BAGDIFF Y X)) A) (IDIFFERENCE (EVAL$ (QUOTE *1*TRUE) (IPLUS-TREE Y) A) (EVAL$ (QUOTE *1*TRUE) (IPLUS-TREE X) A)))) ((ENABLE SUBBAGP BAGDIFF FIX-INT COMMUTATIVITY-OF-IPLUS IDIFFERENCE-0 IDIFFERENCE-FIX-INT IDIFFERENCE-IDIFFERENCE INTEGERP-EVAL$-IPLUS-TREE IPLUS-LEFT-ID IPLUS-RIGHT-ID IPLUS-TREE IPLUS-TREE-DELETE) (ENABLE-THEORY SETS-AND-BAGS GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 MEMBER-DELETE . IPLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 IPLUS-RIGHT-ID . IPLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-IPLUS . IPLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 SUBBAGP-CDR2 . IPLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 INTEGERP-EVAL$-IPLUS-TREE . IPLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 IPLUS-LEFT-ID . IPLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 IDIFFERENCE-0 . IPLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 FIX-INT . IPLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 IPLUS-TREE-DELETE . IPLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 IDIFFERENCE-IDIFFERENCE . IPLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 SETS-AND-BAGS . IPLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 IDIFFERENCE . IPLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 BAGDIFF . IPLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 IPLUS-TREE . IPLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 SUBBAGP . IPLUS-TREE-BAGDIFF) (LEMMAS EVAL$ . IPLUS-TREE-BAGDIFF))))) (PUT1-LST (QUOTE IPLUS-TREE-DELETE) (QUOTE (IDATE 1000404112502 IMMEDIATE-DEPENDENTS0 (IPLUS-TREE-DELETE-OFF CORRECTNESS-OF-CANCEL-IDIFFERENCE CORRECTNESS-OF-CANCEL-IPLUS IPLUS-TREE-BAGDIFF) EVENT (PROVE-LEMMA IPLUS-TREE-DELETE (REWRITE) (EQUAL (EVAL$ (QUOTE *1*TRUE) (IPLUS-TREE (DELETE X Y)) A) (IF (MEMBER X Y) (IDIFFERENCE (EVAL$ (QUOTE *1*TRUE) (IPLUS-TREE Y) A) (EVAL$ (QUOTE *1*TRUE) X A)) (EVAL$ (QUOTE *1*TRUE) (IPLUS-TREE Y) A))) ((ENABLE DELETE IPLUS-TREE FIX-INT COMMUTATIVITY-OF-IPLUS IDIFFERENCE-IPLUS IDIFFERENCE-IPLUS-CANONICALIZER1 IDIFFERENCE-RIGHT-ID IDIFFERENCE-X-X INTEGERP-EVAL$-IPLUS-TREE INTEGERP-IDIFFERENCE INTEGERP-IPLUS IPLUS-0 IPLUS-LEFT-ID IPLUS-RIGHT-ID) (ENABLE-THEORY SETS-AND-BAGS GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 INTEGERP-IDIFFERENCE . IPLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 IPLUS-LEFT-ID . IPLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 IPLUS-RIGHT-ID . IPLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 IPLUS-0 . IPLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-IPLUS . IPLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 IDIFFERENCE-IPLUS-CANONICALIZER1 . IPLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 LISTP-DELETE . IPLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 INTEGERP-EVAL$-IPLUS-TREE . IPLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 IDIFFERENCE-IPLUS . IPLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 IDIFFERENCE-X-X . IPLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 IDIFFERENCE-RIGHT-ID . IPLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 FIX-INT . IPLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 MEMBER-NON-LIST . IPLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE-NON-MEMBER . IPLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 SETS-AND-BAGS . IPLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 IDIFFERENCE . IPLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE . IPLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 IPLUS-TREE . IPLUS-TREE-DELETE) (LEMMAS EVAL$ . IPLUS-TREE-DELETE))))) (PUT1-LST (QUOTE IPLUS-TREE-IPLUS-FRINGE) (QUOTE (IDATE 1000404112458 IMMEDIATE-DEPENDENTS0 (IPLUS-TREE-IPLUS-FRINGE-OFF CORRECTNESS-OF-CANCEL-IDIFFERENCE CORRECTNESS-OF-CANCEL-IPLUS) EVENT (PROVE-LEMMA IPLUS-TREE-IPLUS-FRINGE (REWRITE) (EQUAL (EVAL$ (QUOTE *1*TRUE) (IPLUS-TREE (IPLUS-FRINGE X)) A) (FIX-INT (EVAL$ (QUOTE *1*TRUE) X A))) ((ENABLE IPLUS-FRINGE IPLUS-TREE FIX-INT COMMUTATIVITY-OF-IPLUS EVAL$-IPLUS-TREE-APPEND INTEGERP-EVAL$-BRIDGE INTEGERP-EVAL$-IPLUS INTEGERP-IPLUS INTEGERP-IPLUS IPLUS-0 IPLUS-LEFT-ID IPLUS-RIGHT-ID) (INDUCT (IPLUS-FRINGE X)) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 IPLUS-LEFT-ID . IPLUS-TREE-IPLUS-FRINGE) (IMMEDIATE-DEPENDENTS0 IPLUS-RIGHT-ID . IPLUS-TREE-IPLUS-FRINGE) (IMMEDIATE-DEPENDENTS0 IPLUS-0 . IPLUS-TREE-IPLUS-FRINGE) (IMMEDIATE-DEPENDENTS0 EVAL$-IPLUS-TREE-APPEND . IPLUS-TREE-IPLUS-FRINGE) (IMMEDIATE-DEPENDENTS0 INTEGERP-EVAL$-IPLUS . IPLUS-TREE-IPLUS-FRINGE) (IMMEDIATE-DEPENDENTS0 INTEGERP-EVAL$-BRIDGE . IPLUS-TREE-IPLUS-FRINGE) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-IPLUS . IPLUS-TREE-IPLUS-FRINGE) (IMMEDIATE-DEPENDENTS0 FIX-INT . IPLUS-TREE-IPLUS-FRINGE) (IMMEDIATE-DEPENDENTS0 IPLUS-FRINGE . IPLUS-TREE-IPLUS-FRINGE) (IMMEDIATE-DEPENDENTS0 IPLUS-TREE . IPLUS-TREE-IPLUS-FRINGE) (LEMMAS EVAL$ . IPLUS-TREE-IPLUS-FRINGE))))) (PUT1-LST (QUOTE EVAL$-IPLUS-TREE-APPEND) (QUOTE (IDATE 1000404112456 IMMEDIATE-DEPENDENTS0 (EVAL$-IPLUS-TREE-APPEND-OFF IPLUS-TREE-IPLUS-FRINGE) EVENT (PROVE-LEMMA EVAL$-IPLUS-TREE-APPEND (REWRITE) (EQUAL (EVAL$ (QUOTE *1*TRUE) (IPLUS-TREE (APPEND X Y)) A) (IPLUS (EVAL$ (QUOTE *1*TRUE) (IPLUS-TREE X) A) (EVAL$ (QUOTE *1*TRUE) (IPLUS-TREE Y) A))) ((ENABLE FIX-INT IPLUS-TREE APPEND COMMUTATIVITY-OF-IPLUS COMMUTATIVITY2-OF-IPLUS INTEGERP-EVAL$-BRIDGE INTEGERP-EVAL$-IPLUS-TREE INTEGERP-IPLUS IPLUS-0 IPLUS-CANCELLATION IPLUS-LEFT-ID IPLUS-RIGHT-ID) (INDUCT (EVAL$-IPLUS-TREE-APPEND-INDUCTION X Y A)) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 INTEGERP-EVAL$-BRIDGE . EVAL$-IPLUS-TREE-APPEND) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-IPLUS . EVAL$-IPLUS-TREE-APPEND) (IMMEDIATE-DEPENDENTS0 IPLUS-RIGHT-ID . EVAL$-IPLUS-TREE-APPEND) (IMMEDIATE-DEPENDENTS0 IPLUS-LEFT-ID . EVAL$-IPLUS-TREE-APPEND) (IMMEDIATE-DEPENDENTS0 INTEGERP-EVAL$-IPLUS-TREE . EVAL$-IPLUS-TREE-APPEND) (IMMEDIATE-DEPENDENTS0 FIX-INT . EVAL$-IPLUS-TREE-APPEND) (IMMEDIATE-DEPENDENTS0 IPLUS-0 . EVAL$-IPLUS-TREE-APPEND) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-IPLUS . EVAL$-IPLUS-TREE-APPEND) (IMMEDIATE-DEPENDENTS0 EVAL$-IPLUS-TREE-APPEND-INDUCTION . EVAL$-IPLUS-TREE-APPEND) (IMMEDIATE-DEPENDENTS0 IPLUS . EVAL$-IPLUS-TREE-APPEND) (IMMEDIATE-DEPENDENTS0 IPLUS-TREE . EVAL$-IPLUS-TREE-APPEND) (LEMMAS EVAL$ . EVAL$-IPLUS-TREE-APPEND))))) (PUT1-LST (QUOTE *1*EVAL$-IPLUS-TREE-APPEND-INDUCTION) (QUOTE (MAIN-EVENT EVAL$-IPLUS-TREE-APPEND-INDUCTION))) (PUT1-LST (QUOTE EVAL$-IPLUS-TREE-APPEND-INDUCTION) (QUOTE (TYPE-PRESCRIPTION-LST ((EVAL$-IPLUS-TREE-APPEND-INDUCTION 8 NIL NIL NIL)) TOTALP-LST ((EVAL$-IPLUS-TREE-APPEND-INDUCTION . T)) QUICK-BLOCK-INFO (SELF-REFLEXIVE UNCHANGING UNCHANGING) SDEFN (LAMBDA (A B C) (IF (LISTP A) (EVAL$-IPLUS-TREE-APPEND-INDUCTION (CDR A) B C) (QUOTE NIL))) LISP-CODE *1*EVAL$-IPLUS-TREE-APPEND-INDUCTION SUBRP *1*FALSE INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP A)) (((CDR A) B C))) (TESTS-AND-CASES ((NOT (LISTP A))) NIL)) LEVEL-NO 1 JUSTIFICATIONS ((JUSTIFICATION (A) (COUNT A) LESSP (ZERO CDR-LESSP))) IDATE 1000404112452 CONTROLLER-POCKETS (1) SATELLITES (*1*EVAL$-IPLUS-TREE-APPEND-INDUCTION) IMMEDIATE-DEPENDENTS0 (EVAL$-IPLUS-TREE-APPEND) EVENT (DEFN EVAL$-IPLUS-TREE-APPEND-INDUCTION (A B C) (IF (LISTP A) (EVAL$-IPLUS-TREE-APPEND-INDUCTION (CDR A) B C) (QUOTE NIL))) LOCAL-UNDO-TUPLES ((DCELL . *1*EVAL$-IPLUS-TREE-APPEND-INDUCTION))))) (PUT1-LST (QUOTE INTEGERP-EVAL$-BRIDGE) (QUOTE (IDATE 1000404112452 IMMEDIATE-DEPENDENTS0 (INTEGERP-EVAL$-BRIDGE-OFF IPLUS-TREE-IPLUS-FRINGE EVAL$-IPLUS-TREE-APPEND) EVENT (PROVE-LEMMA INTEGERP-EVAL$-BRIDGE (REWRITE) (IMPLIES (EQUAL (EVAL$ (QUOTE *1*TRUE) Z A) (EVAL$ (QUOTE *1*TRUE) (IPLUS-TREE X) A)) (INTEGERP (EVAL$ (QUOTE *1*TRUE) Z A))) ((USE (INTEGERP-EVAL$-IPLUS-TREE (L X) (A A))) (DISABLE EVAL$) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 INTEGERP-EVAL$-IPLUS-TREE . 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Y))) (REWRITE-RULE ITIMES-DISTRIBUTES-OVER-IPLUS NIL (EQUAL (ITIMES (IPLUS X Y) Z) (IPLUS (ITIMES X Z) (ITIMES Y Z))) NIL) (REWRITE-RULE ITIMES-DISTRIBUTES-OVER-IPLUS NIL (EQUAL (ITIMES X (IPLUS Y Z)) (IPLUS (ITIMES X Y) (ITIMES X Z))) NIL) (REWRITE-RULE COMMUTATIVITY-OF-ITIMES NIL (EQUAL (ITIMES X Y) (ITIMES Y X)) ((X . Y))) (REWRITE-RULE ITIMES-FIX-INT2 NIL (EQUAL (ITIMES A (FIX-INT B)) (ITIMES A B)) NIL) (REWRITE-RULE ITIMES-FIX-INT1 NIL (EQUAL (ITIMES (FIX-INT A) B) (ITIMES A B)) NIL) (REWRITE-RULE ITIMES-ZERO2 ((IZEROP Y)) (EQUAL (ITIMES X Y) (QUOTE 0)) NIL) (REWRITE-RULE ITIMES-ZERO1 ((IZEROP X)) (EQUAL (ITIMES X Y) (QUOTE 0)) NIL)) TOTALP-LST ((ITIMES . T)) SDEFN (LAMBDA (I J) (IF (NEGATIVEP I) (IF (NEGATIVEP J) (TIMES (NEGATIVE-GUTS I) (NEGATIVE-GUTS J)) (FIX-INT (MINUS (TIMES (NEGATIVE-GUTS I) J)))) (IF (NEGATIVEP J) (FIX-INT (MINUS (TIMES I (NEGATIVE-GUTS J)))) (TIMES I J)))) LISP-CODE *1*ITIMES SUBRP *1*FALSE LEVEL-NO 2 IDATE 1000404112444 SATELLITES (*1*ITIMES) IMMEDIATE-DEPENDENTS0 (REQUAL-SIMPLE-RPLUS-X-X-REWRITE REQUAL-SIMPLE-RPLUS-X-SIMPLE-RNEG-X RPLUS-RZEROP REQUAL-SIMPLE-RTIMES-SIMPLE-RNEG SIMPLE-RPLUS-BRIDGE REQUAL-RZEROP-SIMPLE-RPLUS REQUAL-SIMPLE-RTIMES-SIMPLE-RPLUS-WHEN-NOT-RZEROP FIX-RATIONAL-SIMPLE-RTIMES RATIONALP-SIMPLE-RTIMES SIMPLE-RPLUS-RZEROP REQUAL-SIMPLE-RTIMES-REQUAL-ARG1 ASSOCIATIVITY-OF-SIMPLE-RTIMES ASSOCIATIVITY-OF-SIMPLE-RTIMES-WHEN-NOT-RZEROP REQUAL-RNEG-SIMPLE-RPLUS TRANSITIVITY-OF-REQUAL-BRIDGE SIMPLE-RNEG-SIMPLE-RNEG RPLUS-REQUAL-ARG1 RPLUS-OPEN-UP REQUAL-REDUCE1 COMMUTATIVITY-OF-REQUAL ITIMES-OFF1 REMAINDER-0-SUFFICIENCY DPR-HACK5 DPR-HACK4 DPR-HACK3 DPR-HACK2 DPR-HACK1 GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE GCD-FACTORS-GIVES-LINEAR-COMBINATION ITIMES-ON ITIMES-IS-TIMES ITIMES-NEGATIVEP-ARG2 ITIMES-NEGATIVEP-ARG1 ITIMES-INEG-ARG2 ITIMES-INEG-ARG1 REQUAL RLESSP SIMPLE-RTIMES SIMPLE-RPLUS ITIMES-OFF IQUO-IREM-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART1 IREM IDIV-IMOD-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART1 IMOD IQUOTIENT-IREMAINDER-UNIQUENESS DIVISION-THEOREM DIVISION-THEOREM-PART3 DIVISION-THEOREM-PART2 DIVISION-THEOREM-PART1 IREMAINDER ITIMES-1-ARG1 EQUAL-ITIMES-MINUS-1 EQUAL-ITIMES-1 EQUAL-ITIMES-0 ITIMES-DISTRIBUTES-OVER-IDIFFERENCE ITIMES-DISTRIBUTES-OVER-IDIFFERENCE-PROOF ASSOCIATIVITY-OF-ITIMES COMMUTATIVITY2-OF-ITIMES ITIMES-DISTRIBUTES-OVER-IPLUS ITIMES-DISTRIBUTES-OVER-IPLUS-PROOF COMMUTATIVITY-OF-ITIMES ITIMES-FIX-INT2 ITIMES-FIX-INT1 ITIMES-ZERO2 ITIMES-ZERO1 FIX-INT-ITIMES INTEGERP-ITIMES) EVENT (DEFN ITIMES (I J) (IF (NEGATIVEP I) (IF (NEGATIVEP J) (TIMES (NEGATIVE-GUTS I) (NEGATIVE-GUTS J)) (FIX-INT (MINUS (TIMES (NEGATIVE-GUTS I) J)))) (IF (NEGATIVEP J) (FIX-INT (MINUS (TIMES I (NEGATIVE-GUTS J)))) (TIMES I J)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 FIX-INT . 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T)) SDEFN (LAMBDA (I) (IF (NEGATIVEP I) (NEGATIVE-GUTS I) (IF (NUMBERP I) I (QUOTE 0)))) LISP-CODE *1*IABS SUBRP *1*FALSE LEVEL-NO 0 IDATE 1000404112444 SATELLITES (*1*IABS) IMMEDIATE-DEPENDENTS0 (IABS-OFF IQUO-IREM-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2 IQUOTIENT-IREMAINDER-UNIQUENESS DIVISION-THEOREM DIVISION-THEOREM-PART3 FIX-INT-IABS INTEGERP-IABS) EVENT (DEFN IABS (I) (IF (NEGATIVEP I) (NEGATIVE-GUTS I) (FIX I))) LOCAL-UNDO-TUPLES ((DCELL . *1*IABS))))) (PUT1-LST (QUOTE *1*IDIFFERENCE) (QUOTE (MAIN-EVENT IDIFFERENCE))) (PUT1-LST (QUOTE IDIFFERENCE) (QUOTE (TYPE-PRESCRIPTION-LST ((IDIFFERENCE 36 NIL NIL)) LEMMAS ((REWRITE-RULE CORRECTNESS-OF-CANCEL-IDIFFERENCE NIL *1*CANCEL-IDIFFERENCE NIL) (REWRITE-RULE IDIFFERENCE-0 NIL (EQUAL (IDIFFERENCE X (QUOTE 0)) (FIX-INT X)) NIL) (REWRITE-RULE IDIFFERENCE-FIX-INT NIL (EQUAL (IDIFFERENCE A (FIX-INT B)) (IDIFFERENCE A B)) NIL) (REWRITE-RULE IDIFFERENCE-IDIFFERENCE NIL (EQUAL (IDIFFERENCE (IDIFFERENCE X Y) Z) (IDIFFERENCE X (IPLUS Y Z))) NIL) (REWRITE-RULE IDIFFERENCE-RIGHT-ID ((NOT (INTEGERP B))) (EQUAL (IDIFFERENCE A B) (FIX-INT A)) NIL) (REWRITE-RULE IDIFFERENCE-IPLUS NIL (EQUAL (IDIFFERENCE (IPLUS Y X) X) (FIX-INT Y)) NIL) (REWRITE-RULE IDIFFERENCE-IPLUS NIL (EQUAL (IDIFFERENCE (IPLUS X Y) X) (FIX-INT Y)) NIL) (REWRITE-RULE IDIFFERENCE-IPLUS-CANONICALIZER1 NIL (EQUAL (IDIFFERENCE (IPLUS A B) C) (IPLUS A (IDIFFERENCE B C))) NIL) (REWRITE-RULE IDIFFERENCE-X-X NIL (EQUAL (IDIFFERENCE X X) (QUOTE 0)) NIL)) TOTALP-LST ((IDIFFERENCE . T)) SDEFN (LAMBDA (X Y) (IPLUS X (INEG Y))) LISP-CODE *1*IDIFFERENCE SUBRP *1*FALSE LEVEL-NO 1 IDATE 1000404112444 SATELLITES (*1*IDIFFERENCE) IMMEDIATE-DEPENDENTS0 (IDIFFERENCE-OFF1 DIVIDES-PRODUCT-REDUCTION DPR-HACK2 GCD-FACTORS-GIVES-LINEAR-COMBINATION GCD-FACTORS IDIFFERENCE-ON IDIFFERENCE-OFF IQUO-IREM-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2 IREM IDIV-IMOD-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2 IMOD IQUOTIENT-IREMAINDER-UNIQUENESS DIVISION-THEOREM-PART3 DIVISION-THEOREM-PART2 IREMAINDER ITIMES-DISTRIBUTES-OVER-IDIFFERENCE ITIMES-DISTRIBUTES-OVER-IDIFFERENCE-PROOF CORRECTNESS-OF-CANCEL-IDIFFERENCE IPLUS-IDIFFERENCE-IDIFFERENCE IPLUS-TREE-BAGDIFF IPLUS-TREE-DELETE EQUAL-IDIFFERENCE-0 IDIFFERENCE-CANCELLATION-1 IDIFFERENCE-0 IDIFFERENCE-FIX-INT IDIFFERENCE-IDIFFERENCE IDIFFERENCE-RIGHT-ID IDIFFERENCE-IPLUS IDIFFERENCE-IPLUS-CANONICALIZER1 IDIFFERENCE-X-X IPLUS-IDIFFERENCE-ARG2 IPLUS-IDIFFERENCE-ARG1 INEG-IDIFFERENCE FIX-INT-IDIFFERENCE INTEGERP-IDIFFERENCE) EVENT (DEFN IDIFFERENCE (X Y) (IPLUS X (INEG Y))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 INEG . IDIFFERENCE) (IMMEDIATE-DEPENDENTS0 IPLUS . IDIFFERENCE) (DCELL . *1*IDIFFERENCE))))) (PUT1-LST (QUOTE *1*INEG) (QUOTE (MAIN-EVENT INEG))) (PUT1-LST (QUOTE INEG) (QUOTE (TYPE-PRESCRIPTION-LST ((INEG 36 NIL)) LEMMAS ((REWRITE-RULE INEG-FIX-INT NIL (EQUAL (INEG (FIX-INT X)) (INEG X)) NIL) (REWRITE-RULE INEG-IDIFFERENCE NIL (EQUAL (INEG (IDIFFERENCE A B)) (IPLUS (INEG A) B)) NIL) (REWRITE-RULE INEG-INEG NIL (EQUAL (INEG (INEG X)) (FIX-INT X)) NIL) (REWRITE-RULE INEG-IPLUS NIL (EQUAL (INEG (IPLUS A B)) (IPLUS (INEG A) (INEG B))) NIL) (REWRITE-RULE INEG-ID ((NOT (INTEGERP X))) (EQUAL (INEG X) (QUOTE 0)) NIL)) TOTALP-LST ((INEG . T)) SDEFN (LAMBDA (X) (IF (NEGATIVEP X) (NEGATIVE-GUTS X) (IF (EQUAL X (QUOTE 0)) (QUOTE 0) (IF (NUMBERP X) (MINUS X) (QUOTE 0))))) LISP-CODE *1*INEG SUBRP *1*FALSE LEVEL-NO 0 IDATE 1000404112444 SATELLITES (*1*INEG) IMMEDIATE-DEPENDENTS0 (REQUAL-SIMPLE-RPLUS-X-SIMPLE-RNEG-X REQUAL-SIMPLE-RTIMES-SIMPLE-RNEG SIMPLE-RPLUS-BRIDGE REQUAL-RNEG-SIMPLE-RPLUS TRANSITIVITY-OF-REQUAL-BRIDGE NEGATIVE-GUTS-INEG SIMPLE-RNEG-SIMPLE-RNEG SIMPLE-RNEG-REDUCE RATIONAL-INEG-NUMERATOR-REDUCE-BRIDGE NUMBERP-INEG NEGATIVEP-INEG REQUAL-REDUCE-REDUCE-EQUAL INEG-OFF1 DIVIDES-PRODUCT-REDUCTION DPR-HACK2 GCD-FACTORS-GIVES-LINEAR-COMBINATION INEG-ON EQUAL-INEG-INEG ITIMES-NEGATIVEP-ARG2 ITIMES-NEGATIVEP-ARG1 ITIMES-INEG-ARG2 ITIMES-INEG-ARG1 SIMPLE-RINVERSE SIMPLE-RNEG INEG-OFF IQUO-IREM-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2 IDIV-IMOD-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2 IQUOTIENT-IREMAINDER-UNIQUENESS DIVISION-THEOREM-PART3 DIVISION-THEOREM-PART2 ITIMES-DISTRIBUTES-OVER-IDIFFERENCE-PROOF EQUAL-IDIFFERENCE-0 IDIFFERENCE-CANCELLATION-1 IDIFFERENCE-0 IDIFFERENCE-FIX-INT IDIFFERENCE-IDIFFERENCE IDIFFERENCE-RIGHT-ID IDIFFERENCE-IPLUS IDIFFERENCE-IPLUS-CANONICALIZER1 IDIFFERENCE-X-X IPLUS-INEG2 IPLUS-INEG1 INEG-FIX-INT INEG-IDIFFERENCE INEG-INEG INEG-IPLUS INEG-ID FIX-INT-INEG INTEGERP-INEG IDIFFERENCE) EVENT (DEFN INEG (X) (IF (NEGATIVEP X) (NEGATIVE-GUTS X) (IF (ZEROP X) (QUOTE 0) (MINUS X)))) LOCAL-UNDO-TUPLES ((DCELL . *1*INEG))))) (PUT1-LST (QUOTE *1*IPLUS) (QUOTE (MAIN-EVENT IPLUS))) (PUT1-LST (QUOTE IPLUS) (QUOTE (TYPE-PRESCRIPTION-LST ((IPLUS 36 NIL NIL)) LEMMAS ((REWRITE-RULE DPR-HACK4 NIL (EQUAL (IPLUS (ITIMES C (ITIMES A X)) (ITIMES C (ITIMES B Y))) (ITIMES C (IPLUS (ITIMES A X) (ITIMES B Y)))) NIL) (REWRITE-RULE DPR-HACK3 NIL (EQUAL (IPLUS (ITIMES C (ITIMES A X)) (ITIMES B (ITIMES C Y))) (IPLUS (ITIMES C (ITIMES A X)) (ITIMES C (ITIMES B Y)))) NIL) (REWRITE-RULE IPLUS-IS-PLUS ((NUMBERP X) (NUMBERP Y)) (EQUAL (IPLUS X Y) (PLUS X Y)) NIL) (REWRITE-RULE IPLUS-IDIFFERENCE-IDIFFERENCE NIL (EQUAL (IPLUS (IDIFFERENCE A B) (IDIFFERENCE C D)) (IDIFFERENCE (IPLUS A C) (IPLUS B D))) NIL) (REWRITE-RULE IPLUS-IDIFFERENCE-ARG2 NIL (EQUAL (IPLUS A (IDIFFERENCE B C)) (IDIFFERENCE (IPLUS A B) C)) NIL) (REWRITE-RULE IPLUS-IDIFFERENCE-ARG1 NIL (EQUAL (IPLUS (IDIFFERENCE A B) C) (IDIFFERENCE (IPLUS A C) B)) NIL) (REWRITE-RULE IPLUS-FIX-INT2 NIL (EQUAL (IPLUS A (FIX-INT B)) (IPLUS A B)) NIL) (REWRITE-RULE IPLUS-FIX-INT1 NIL (EQUAL (IPLUS (FIX-INT A) B) (IPLUS A B)) NIL) (REWRITE-RULE IPLUS-INEG2 NIL (EQUAL (IPLUS (INEG A) A) (QUOTE 0)) NIL) (REWRITE-RULE IPLUS-INEG1 NIL (EQUAL (IPLUS A (INEG A)) (QUOTE 0)) NIL) (REWRITE-RULE ASSOCIATIVITY-OF-IPLUS NIL (EQUAL (IPLUS (IPLUS X Y) Z) (IPLUS X (IPLUS Y Z))) NIL) (REWRITE-RULE COMMUTATIVITY-OF-IPLUS NIL (EQUAL (IPLUS X Y) (IPLUS Y X)) ((X . Y))) (REWRITE-RULE COMMUTATIVITY2-OF-IPLUS NIL (EQUAL (IPLUS X (IPLUS Y Z)) (IPLUS Y (IPLUS X Z))) ((X . Y))) (REWRITE-RULE IPLUS-0 NIL (EQUAL (IPLUS (QUOTE 0) X) (FIX-INT X)) NIL) (REWRITE-RULE IPLUS-RIGHT-ID ((NOT (INTEGERP Y))) (EQUAL (IPLUS X Y) (FIX-INT X)) NIL) (REWRITE-RULE IPLUS-LEFT-ID ((NOT (INTEGERP X))) (EQUAL (IPLUS X Y) (FIX-INT Y)) NIL)) TOTALP-LST ((IPLUS . T)) SDEFN (LAMBDA (X Y) (IF (NEGATIVEP X) (IF (NEGATIVEP Y) (IF (EQUAL (NEGATIVE-GUTS X) (QUOTE 0)) (IF (EQUAL (NEGATIVE-GUTS Y) (QUOTE 0)) (QUOTE 0) (MINUS (PLUS (NEGATIVE-GUTS X) (NEGATIVE-GUTS Y)))) (MINUS (PLUS (NEGATIVE-GUTS X) (NEGATIVE-GUTS Y)))) (IF (LESSP Y (NEGATIVE-GUTS X)) (MINUS (DIFFERENCE (NEGATIVE-GUTS X) Y)) (DIFFERENCE Y (NEGATIVE-GUTS X)))) (IF (NEGATIVEP Y) (IF (LESSP X (NEGATIVE-GUTS Y)) (MINUS (DIFFERENCE (NEGATIVE-GUTS Y) X)) (DIFFERENCE X (NEGATIVE-GUTS Y))) (PLUS X Y)))) LISP-CODE *1*IPLUS SUBRP *1*FALSE LEVEL-NO 1 IDATE 1000404112444 SATELLITES (*1*IPLUS) IMMEDIATE-DEPENDENTS0 (REQUAL-SIMPLE-RPLUS-X-X-REWRITE REQUAL-SIMPLE-RPLUS-X-SIMPLE-RNEG-X RPLUS-RZEROP SIMPLE-RPLUS-BRIDGE REQUAL-RZEROP-SIMPLE-RPLUS REQUAL-SIMPLE-RTIMES-SIMPLE-RPLUS-WHEN-NOT-RZEROP SIMPLE-RPLUS-RZEROP REQUAL-RNEG-SIMPLE-RPLUS RPLUS-OPEN-UP IPLUS-OFF1 DIVIDES-PRODUCT-REDUCTION DPR-HACK5 DPR-HACK4 DPR-HACK3 DPR-HACK2 DPR-HACK1 GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE GCD-FACTORS-GIVES-LINEAR-COMBINATION IPLUS-ON IPLUS-IS-PLUS SIMPLE-RPLUS IPLUS-OFF IQUO-IREM-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART1 IDIV-IMOD-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART1 IQUOTIENT-IREMAINDER-UNIQUENESS DIVISION-THEOREM DIVISION-THEOREM-PART3 DIVISION-THEOREM-PART2 DIVISION-THEOREM-PART1 ITIMES-DISTRIBUTES-OVER-IDIFFERENCE-PROOF ITIMES-DISTRIBUTES-OVER-IPLUS ITIMES-DISTRIBUTES-OVER-IPLUS-PROOF IPLUS-IDIFFERENCE-IDIFFERENCE NOT-INTEGERP-IMPLIES-NOT-EQUAL-IPLUS EVAL$-IPLUS-TREE-APPEND INTEGERP-EVAL$-IPLUS EQUAL-IDIFFERENCE-0 IDIFFERENCE-CANCELLATION-1 IDIFFERENCE-0 IDIFFERENCE-FIX-INT IDIFFERENCE-IDIFFERENCE IDIFFERENCE-RIGHT-ID IDIFFERENCE-IPLUS IDIFFERENCE-IPLUS-CANONICALIZER1 IDIFFERENCE-X-X IPLUS-IDIFFERENCE-ARG2 IPLUS-IDIFFERENCE-ARG1 IPLUS-FIX-INT2 IPLUS-FIX-INT1 IPLUS-INEG2 IPLUS-INEG1 IPLUS-CANCELLATION ASSOCIATIVITY-OF-IPLUS COMMUTATIVITY-OF-IPLUS COMMUTATIVITY2-OF-IPLUS IPLUS-0 IPLUS-RIGHT-ID IPLUS-LEFT-ID INEG-IDIFFERENCE INEG-IPLUS FIX-INT-IPLUS INTEGERP-IPLUS IDIFFERENCE) EVENT (DEFN IPLUS (X Y) (IF (NEGATIVEP X) (IF (NEGATIVEP Y) (IF (AND (ZEROP (NEGATIVE-GUTS X)) (ZEROP (NEGATIVE-GUTS Y))) (QUOTE 0) (MINUS (PLUS (NEGATIVE-GUTS X) (NEGATIVE-GUTS Y)))) (IF (LESSP Y (NEGATIVE-GUTS X)) (MINUS (DIFFERENCE (NEGATIVE-GUTS X) Y)) (DIFFERENCE Y (NEGATIVE-GUTS X)))) (IF (NEGATIVEP Y) (IF (LESSP X (NEGATIVE-GUTS Y)) (MINUS (DIFFERENCE (NEGATIVE-GUTS Y) X)) (DIFFERENCE X (NEGATIVE-GUTS Y))) (PLUS X Y)))) LOCAL-UNDO-TUPLES ((DCELL . *1*IPLUS))))) (PUT1-LST (QUOTE *1*ILEQ) (QUOTE (MAIN-EVENT ILEQ))) (PUT1-LST (QUOTE ILEQ) (QUOTE (TYPE-PRESCRIPTION-LST ((ILEQ 3 NIL NIL)) TOTALP-LST ((ILEQ . T)) SDEFN (LAMBDA (I J) (IF (ILESSP I J) (QUOTE *1*TRUE) (EQUAL I J))) LISP-CODE *1*ILEQ SUBRP *1*FALSE LEVEL-NO 0 IDATE 1000404112444 SATELLITES (*1*ILEQ) IMMEDIATE-DEPENDENTS0 (ILEQ-OFF IQUO-IREM-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2 IDIV-IMOD-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2 IQUOTIENT-IREMAINDER-UNIQUENESS DIVISION-THEOREM DIVISION-THEOREM-PART2) EVENT (DEFN ILEQ (I J) (OR (ILESSP I J) (EQUAL I J))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ILESSP . ILEQ) (DCELL . *1*ILEQ))))) (PUT1-LST (QUOTE *1*ILESSP) (QUOTE (MAIN-EVENT ILESSP))) (PUT1-LST (QUOTE ILESSP) (QUOTE (TYPE-PRESCRIPTION-LST ((ILESSP 3 NIL NIL)) TOTALP-LST ((ILESSP . T)) SDEFN (LAMBDA (I J) (IF (NEGATIVEP I) (IF (NEGATIVEP J) (LESSP (NEGATIVE-GUTS J) (NEGATIVE-GUTS I)) (QUOTE *1*TRUE)) (IF (NEGATIVEP J) (QUOTE *1*FALSE) (LESSP I J)))) LISP-CODE *1*ILESSP SUBRP *1*FALSE LEVEL-NO 0 IDATE 1000404112444 SATELLITES (*1*ILESSP) IMMEDIATE-DEPENDENTS0 (ILESSP-OFF1 ILESSP-ON RLESSP ILESSP-OFF IQUO-IREM-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2 IDIV-IMOD-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2 IQUOTIENT-IREMAINDER-UNIQUENESS DIVISION-THEOREM DIVISION-THEOREM-PART3 DIVISION-THEOREM-PART2 ILEQ) EVENT (DEFN ILESSP (I J) (IF (NEGATIVEP I) (IF (NEGATIVEP J) (LESSP (NEGATIVE-GUTS J) (NEGATIVE-GUTS I)) (QUOTE *1*TRUE)) (IF (NEGATIVEP J) (QUOTE *1*FALSE) (LESSP I J)))) LOCAL-UNDO-TUPLES ((DCELL . *1*ILESSP))))) (PUT1-LST (QUOTE *1*IZEROP) (QUOTE (MAIN-EVENT IZEROP))) (PUT1-LST (QUOTE IZEROP) (QUOTE (TYPE-PRESCRIPTION-LST ((IZEROP 3 NIL)) TOTALP-LST ((IZEROP . T)) SDEFN (LAMBDA (I) (IF (INTEGERP I) (EQUAL I (QUOTE 0)) (QUOTE *1*TRUE))) LISP-CODE *1*IZEROP SUBRP *1*FALSE LEVEL-NO 0 IDATE 1000404112444 SATELLITES (*1*IZEROP) IMMEDIATE-DEPENDENTS0 (REQUAL-SIMPLE-RPLUS-X-X-REWRITE REQUAL-SIMPLE-RPLUS-X-SIMPLE-RNEG-X RPLUS-RZEROP REQUAL-SIMPLE-RTIMES-SIMPLE-RNEG SIMPLE-RPLUS-BRIDGE FIX-RATIONAL-SIMPLE-RTIMES RATIONALP-SIMPLE-RTIMES SIMPLE-RTIMES-RZEROP REQUAL-RNEG-SIMPLE-RPLUS IZEROP-OFF1 DIVIDES-PRODUCT-REDUCTION REMAINDER-0-SUFFICIENCY DPR-HACK2 IZEROP-ON ITIMES-INEG-ARG2 ITIMES-INEG-ARG1 IZEROP-OFF IQUO-FIX-INT2 IDIV-FIX-INT2 IQUOTIENT-FIX-INT2 IQUO-IREM-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2 IQUO IDIV-IMOD-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2 IDIV IQUOTIENT-IREMAINDER-UNIQUENESS DIVISION-THEOREM-PART3 DIVISION-THEOREM-PART2 IQUOTIENT EQUAL-ITIMES-0 ITIMES-ZERO2 ITIMES-ZERO1) EVENT (DEFN IZEROP (I) (IF (INTEGERP I) (EQUAL I (QUOTE 0)) (QUOTE *1*TRUE))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 INTEGERP . IZEROP) (DCELL . *1*IZEROP))))) (PUT1-LST (QUOTE *1*FIX-INT) (QUOTE (MAIN-EVENT FIX-INT))) (PUT1-LST (QUOTE FIX-INT) (QUOTE (TYPE-PRESCRIPTION-LST ((FIX-INT 4 T)) LEMMAS ((REWRITE-RULE FIX-INT-ON-INTEGERS ((INTEGERP X)) (EQUAL (FIX-INT X) X) NIL) (REWRITE-RULE FIX-INT-IREM NIL (EQUAL (FIX-INT (IREM I J)) (IREM I J)) NIL) (REWRITE-RULE FIX-INT-IQUO NIL (EQUAL (FIX-INT (IQUO I J)) (IQUO I J)) NIL) (REWRITE-RULE FIX-INT-IMOD NIL (EQUAL (FIX-INT (IMOD I J)) (IMOD I J)) NIL) (REWRITE-RULE FIX-INT-IDIV NIL (EQUAL (FIX-INT (IDIV I J)) (IDIV I J)) NIL) (REWRITE-RULE FIX-INT-IREMAINDER NIL (EQUAL (FIX-INT (IREMAINDER I J)) (IREMAINDER I J)) NIL) (REWRITE-RULE FIX-INT-IQUOTIENT NIL (EQUAL (FIX-INT (IQUOTIENT I J)) (IQUOTIENT I J)) NIL) (REWRITE-RULE FIX-INT-ITIMES NIL (EQUAL (FIX-INT (ITIMES X Y)) (ITIMES X Y)) NIL) (REWRITE-RULE FIX-INT-IABS NIL (EQUAL (FIX-INT (IABS X)) (IABS X)) NIL) (REWRITE-RULE FIX-INT-INEG NIL (EQUAL (FIX-INT (INEG X)) (INEG X)) NIL) (REWRITE-RULE FIX-INT-IDIFFERENCE NIL (EQUAL (FIX-INT (IDIFFERENCE A B)) (IDIFFERENCE A B)) NIL) (REWRITE-RULE FIX-INT-IPLUS NIL (EQUAL (FIX-INT (IPLUS A B)) (IPLUS A B)) NIL) (REWRITE-RULE FIX-INT-FIX-INT NIL (EQUAL (FIX-INT (FIX-INT X)) (FIX-INT X)) NIL)) TOTALP-LST ((FIX-INT . T)) SDEFN (LAMBDA (X) (IF (INTEGERP X) X (QUOTE 0))) LISP-CODE *1*FIX-INT SUBRP *1*FALSE LEVEL-NO 0 IDATE 1000404112444 SATELLITES (*1*FIX-INT) IMMEDIATE-DEPENDENTS0 (REQUAL-SIMPLE-RPLUS-X-X-REWRITE REQUAL-SIMPLE-RPLUS-X-SIMPLE-RNEG-X RPLUS-RZEROP SIMPLE-RPLUS-RZEROP REQUAL-SIMPLE-RTIMES-REQUAL-ARG1 ASSOCIATIVITY-OF-SIMPLE-RTIMES-WHEN-NOT-RZEROP TRANSITIVITY-OF-REQUAL-BRIDGE NRATIONAL-SIMPLE-RPLUS-ARG2 NRATIONAL-SIMPLE-RPLUS-ARG1 NRATIONAL-RPLUS-ARG1 REQUAL-REDUCE1 FIX-INT-OFF1 REMAINDER-0-SUFFICIENCY GCD-FACTORS-GIVES-LINEAR-COMBINATION FIX-INT-ON ITIMES-NEGATIVEP-ARG2 ITIMES-NEGATIVEP-ARG1 ITIMES-INEG-ARG2 ITIMES-INEG-ARG1 FIX-INT-ON-INTEGERS FIX-INT-OFF FIX-INT-IREM FIX-INT-IQUO FIX-INT-IMOD FIX-INT-IDIV FIX-INT-IREMAINDER FIX-INT-IQUOTIENT IREM-FIX-INT2 IREM-FIX-INT1 IQUO-FIX-INT2 IQUO-FIX-INT1 IMOD-FIX-INT2 IMOD-FIX-INT1 IDIV-FIX-INT2 IDIV-FIX-INT1 IREMAINDER-FIX-INT2 IREMAINDER-FIX-INT1 IQUOTIENT-FIX-INT2 IQUOTIENT-FIX-INT1 INTEGERP-IQUO INTEGERP-IDIV INTEGERP-IQUOTIENT IQUO-IREM-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART1 IREM IQUO IDIV-IMOD-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART1 IMOD IDIV IQUOTIENT-IREMAINDER-UNIQUENESS DIVISION-THEOREM-PART3 DIVISION-THEOREM-PART2 DIVISION-THEOREM-PART1 IREMAINDER IQUOTIENT ITIMES-1-ARG1 EQUAL-ITIMES-MINUS-1 EQUAL-ITIMES-1 EQUAL-ITIMES-0 ITIMES-DISTRIBUTES-OVER-IDIFFERENCE-PROOF ASSOCIATIVITY-OF-ITIMES COMMUTATIVITY2-OF-ITIMES ITIMES-DISTRIBUTES-OVER-IPLUS-PROOF COMMUTATIVITY-OF-ITIMES ITIMES-FIX-INT2 ITIMES-FIX-INT1 ITIMES-ZERO2 ITIMES-ZERO1 CORRECTNESS-OF-CANCEL-IPLUS IPLUS-TREE-BAGDIFF IPLUS-TREE-DELETE IPLUS-TREE-IPLUS-FRINGE EVAL$-IPLUS-TREE-APPEND EQUAL-IDIFFERENCE-0 IDIFFERENCE-CANCELLATION-1 IDIFFERENCE-0 IDIFFERENCE-FIX-INT IDIFFERENCE-RIGHT-ID IDIFFERENCE-IPLUS IPLUS-FIX-INT2 IPLUS-FIX-INT1 IPLUS-CANCELLATION IPLUS-0 IPLUS-RIGHT-ID IPLUS-LEFT-ID INEG-FIX-INT INEG-INEG FIX-INT-ITIMES FIX-INT-IABS FIX-INT-INEG FIX-INT-IDIFFERENCE FIX-INT-IPLUS FIX-INT-FIX-INT INTEGERP-ITIMES INTEGERP-FIX-INT ITIMES) EVENT (DEFN FIX-INT (X) (IF (INTEGERP X) X (QUOTE 0))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 INTEGERP . FIX-INT) (DCELL . *1*FIX-INT))))) (PUT1-LST (QUOTE *1*INTEGERP) (QUOTE (MAIN-EVENT INTEGERP))) (PUT1-LST (QUOTE INTEGERP) (QUOTE (TYPE-PRESCRIPTION-LST ((INTEGERP 3 NIL)) LEMMAS ((REWRITE-RULE RATIONALP-MEANS ((RATIONALP X)) (INTEGERP (NUMERATOR X)) NIL) (REWRITE-RULE INTEGERP-IF-NUMBERP ((NUMBERP X)) (INTEGERP X) NIL) (REWRITE-RULE INTEGERP-IF-NEGATIVEP-NON-ZERO ((NEGATIVEP X) (NOT (EQUAL X (QUOTE (*1*QUOTE MINUS 0))))) (INTEGERP X) NIL) (REWRITE-RULE INTEGERP-MINUS NIL (EQUAL (INTEGERP (MINUS X)) (LESSP (QUOTE 0) X)) NIL) (REWRITE-RULE INTEGERP-IREM NIL (INTEGERP (IREM I J)) NIL) (REWRITE-RULE INTEGERP-IQUO NIL (INTEGERP (IQUO I J)) NIL) (REWRITE-RULE INTEGERP-IMOD NIL (INTEGERP (IMOD I J)) NIL) (REWRITE-RULE INTEGERP-IDIV NIL (INTEGERP (IDIV I J)) NIL) (REWRITE-RULE INTEGERP-IREMAINDER NIL (INTEGERP (IREMAINDER I J)) NIL) (REWRITE-RULE INTEGERP-IQUOTIENT NIL (INTEGERP (IQUOTIENT I J)) NIL) (REWRITE-RULE INTEGERP-EVAL$-BRIDGE ((EQUAL (EVAL$ (QUOTE *1*TRUE) Z A) (EVAL$ (QUOTE *1*TRUE) (IPLUS-TREE X) A))) (INTEGERP (EVAL$ (QUOTE *1*TRUE) Z A)) NIL) (REWRITE-RULE INTEGERP-EVAL$-IPLUS-TREE NIL (INTEGERP (EVAL$ (QUOTE *1*TRUE) (IPLUS-TREE L) A)) NIL) (REWRITE-RULE INTEGERP-EVAL$-IPLUS ((LISTP X) (EQUAL (CAR X) (QUOTE IPLUS))) (INTEGERP (EVAL$ (QUOTE *1*TRUE) X A)) NIL) (REWRITE-RULE INTEGERP-ITIMES NIL (INTEGERP (ITIMES X Y)) NIL) (REWRITE-RULE INTEGERP-IABS NIL (INTEGERP (IABS X)) NIL) (REWRITE-RULE INTEGERP-INEG NIL (INTEGERP (INEG X)) NIL) (REWRITE-RULE INTEGERP-IDIFFERENCE NIL (INTEGERP (IDIFFERENCE X Y)) NIL) (REWRITE-RULE INTEGERP-IPLUS NIL (INTEGERP (IPLUS X Y)) NIL) (REWRITE-RULE INTEGERP-FIX-INT NIL (INTEGERP (FIX-INT X)) NIL)) TOTALP-LST ((INTEGERP . T)) SDEFN (LAMBDA (X) (IF (NUMBERP X) (QUOTE *1*TRUE) (IF (NEGATIVEP X) (IF (EQUAL (NEGATIVE-GUTS X) (QUOTE 0)) (QUOTE *1*FALSE) (QUOTE *1*TRUE)) (QUOTE *1*FALSE)))) LISP-CODE *1*INTEGERP SUBRP *1*FALSE LEVEL-NO 0 IDATE 1000404112444 SATELLITES (*1*INTEGERP) IMMEDIATE-DEPENDENTS0 (REQUAL-SIMPLE-RPLUS-X-X-REWRITE REQUAL-SIMPLE-RPLUS-X-SIMPLE-RNEG-X RPLUS-RZEROP RPLUS-RZEROP-BRIDGE2 RPLUS-RZEROP-BRIDGE REQUAL-SIMPLE-RTIMES-SIMPLE-RNEG SIMPLE-RPLUS-BRIDGE COMMUTATIVITY-OF-SIMPLE-RPLUS REQUAL-RZEROP-SIMPLE-RPLUS FIX-RATIONAL-SIMPLE-RTIMES RATIONALP-SIMPLE-RTIMES SIMPLE-RPLUS-RZEROP REQUAL-SIMPLE-RTIMES-REQUAL-ARG1 ASSOCIATIVITY-OF-SIMPLE-RTIMES-WHEN-NOT-RZEROP SIMPLE-RTIMES-RZEROP COMMUTATIVITY-OF-SIMPLE-RTIMES REQUAL-RNEG-SIMPLE-RPLUS TRANSITIVITY-OF-REQUAL-BRIDGE REQUAL-ASSOCIATIVITY-OF-SIMPLE-RPLUS RATIONALP-SIMPLE-RPLUS FIX-RATIONAL-OF-RATIONALP MEANS-RATIONALP RATIONALP-MEANS SIMPLE-RNEG-SIMPLE-RNEG SIMPLE-RNEG-REDUCE REDUCE-0 RATIONAL-INEG-NUMERATOR-REDUCE-BRIDGE NUMBERP-NUMERATOR-REDUCE REDUCE-NRATIONALP REQUAL-X-X RPLUS-REQUAL-ARG1 RPLUS-OPEN-UP REDUCE-REDUCE REQUAL-REDUCE1 REQUAL-REDUCE-REDUCE-EQUAL NEGATIVEP-IF-INTEGERP-AND-NOT-NUMBERP NUMBERP-IF-INTEGERP-AND-NOT-NEGATIVEP GCD-FACTORS-GIVES-LINEAR-COMBINATION INTEGERP-ON RATIONAL-GENERALIZATION RATIONALP-FIX-RATIONAL RATIONALP-REDUCE EQUAL-INEG-INEG INTEGERP-IF-NUMBERP INTEGERP-IF-NEGATIVEP-NON-ZERO FIX-INT-ON-INTEGERS INTEGERP-MINUS RATIONALP INTEGERP-OFF FIX-INT-IQUO FIX-INT-IDIV FIX-INT-IQUOTIENT IQUO-FIX-INT2 IQUO-FIX-INT1 IDIV-FIX-INT2 IDIV-FIX-INT1 IQUOTIENT-FIX-INT2 IQUOTIENT-FIX-INT1 INTEGERP-IREM INTEGERP-IQUO INTEGERP-IMOD INTEGERP-IDIV INTEGERP-IREMAINDER INTEGERP-IQUOTIENT IQUO-IREM-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART1 IDIV-IMOD-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART1 IQUOTIENT-IREMAINDER-UNIQUENESS DIVISION-THEOREM DIVISION-THEOREM-PART3 DIVISION-THEOREM-PART2 DIVISION-THEOREM-PART1 ITIMES-1-ARG1 EQUAL-ITIMES-MINUS-1 EQUAL-ITIMES-1 EQUAL-ITIMES-0 ITIMES-DISTRIBUTES-OVER-IDIFFERENCE-PROOF ASSOCIATIVITY-OF-ITIMES COMMUTATIVITY2-OF-ITIMES ITIMES-DISTRIBUTES-OVER-IPLUS-PROOF COMMUTATIVITY-OF-ITIMES ITIMES-FIX-INT2 ITIMES-FIX-INT1 ITIMES-ZERO2 ITIMES-ZERO1 NOT-INTEGERP-IMPLIES-NOT-EQUAL-IPLUS INTEGERP-EVAL$-BRIDGE INTEGERP-EVAL$-IPLUS-TREE INTEGERP-EVAL$-IPLUS EQUAL-IDIFFERENCE-0 IDIFFERENCE-CANCELLATION-1 IDIFFERENCE-0 IDIFFERENCE-FIX-INT IDIFFERENCE-RIGHT-ID IDIFFERENCE-IPLUS IPLUS-FIX-INT2 IPLUS-FIX-INT1 IPLUS-CANCELLATION IPLUS-0 IPLUS-RIGHT-ID IPLUS-LEFT-ID INEG-FIX-INT INEG-INEG INEG-ID FIX-INT-ITIMES FIX-INT-IABS FIX-INT-INEG FIX-INT-IPLUS FIX-INT-FIX-INT INTEGERP-ITIMES INTEGERP-IABS INTEGERP-INEG INTEGERP-IDIFFERENCE INTEGERP-IPLUS INTEGERP-FIX-INT IZEROP FIX-INT) EVENT (DEFN INTEGERP (X) (OR (NUMBERP X) (AND (NEGATIVEP X) (NOT (ZEROP (NEGATIVE-GUTS X)))))) LOCAL-UNDO-TUPLES ((DCELL . *1*INTEGERP))))) (PUT1-LST (QUOTE ARITHMETIC) (QUOTE (IDATE 1000404112444 IMMEDIATE-DEPENDENTS0 (REQUAL-SIMPLE-RTIMES-REQUAL-ARG1 ASSOCIATIVITY-OF-SIMPLE-RTIMES-WHEN-NOT-RZEROP RPLUS-REQUAL-ARG1 COMMUTATIVITY-OF-RPLUS IQUO-IREM-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2 IDIV-IMOD-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2 IQUOTIENT-IREMAINDER-UNIQUENESS QUOTIENT-DIFFERENCE-LESSP-ARG2 DIVISION-THEOREM-PART3 DIVISION-THEOREM-PART2 QUOTIENT-REMAINDER-UNIQUENESS) EVENT (DEFTHEORY ARITHMETIC (ADDITION MULTIPLICATION REMAINDERS QUOTIENTS EXPONENTIATION LOGS GCDS)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ADDITION . ARITHMETIC) (IMMEDIATE-DEPENDENTS0 MULTIPLICATION . ARITHMETIC) (IMMEDIATE-DEPENDENTS0 REMAINDERS . ARITHMETIC) (IMMEDIATE-DEPENDENTS0 QUOTIENTS . ARITHMETIC) (IMMEDIATE-DEPENDENTS0 EXPONENTIATION . ARITHMETIC) (IMMEDIATE-DEPENDENTS0 LOGS . ARITHMETIC) (IMMEDIATE-DEPENDENTS0 GCDS . ARITHMETIC))))) (PUT1-LST (QUOTE GCDS) (QUOTE (IDATE 1000404112444 IMMEDIATE-DEPENDENTS0 (ARITHMETIC) EVENT (DEFTHEORY GCDS (COMMUTATIVITY2-OF-GCD ASSOCIATIVITY-OF-GCD COMMON-DIVISOR-DIVIDES-GCD DISTRIBUTIVITY-OF-TIMES-OVER-GCD LESSP-GCD EQUAL-GCD-0 GCD-0 GCD-IDEMPOTENCE GCD-X-X REMAINDER-GCD GCD-PLUS GCD-PLUS-INSTANCE GCD-1 COMMUTATIVITY-OF-GCD)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-GCD . GCDS) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-GCD . GCDS) (IMMEDIATE-DEPENDENTS0 COMMON-DIVISOR-DIVIDES-GCD . GCDS) (IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-TIMES-OVER-GCD . GCDS) (IMMEDIATE-DEPENDENTS0 LESSP-GCD . GCDS) (IMMEDIATE-DEPENDENTS0 EQUAL-GCD-0 . GCDS) (IMMEDIATE-DEPENDENTS0 GCD-0 . GCDS) (IMMEDIATE-DEPENDENTS0 GCD-IDEMPOTENCE . GCDS) (IMMEDIATE-DEPENDENTS0 GCD-X-X . GCDS) (IMMEDIATE-DEPENDENTS0 REMAINDER-GCD . GCDS) (IMMEDIATE-DEPENDENTS0 GCD-PLUS . GCDS) (IMMEDIATE-DEPENDENTS0 GCD-PLUS-INSTANCE . GCDS) (IMMEDIATE-DEPENDENTS0 GCD-1 . GCDS) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-GCD . GCDS))))) (PUT1-LST (QUOTE GCD-IDEMPOTENCE) (QUOTE (IDATE 1000404112444 IMMEDIATE-DEPENDENTS0 (GCDS) EVENT (PROVE-LEMMA GCD-IDEMPOTENCE (REWRITE) (AND (EQUAL (GCD X (GCD X Y)) (GCD X Y)) (EQUAL (GCD Y (GCD X Y)) (GCD X Y))) ((ENABLE GCD GCD-X-X GCD-PLUS REMAINDER-GCD GCD-1 COMMUTATIVITY-OF-GCD) (ENABLE-THEORY ADDITION GROUND-ZERO) (INDUCT (GCD X Y)) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-LESSP-PLUS . GCD-IDEMPOTENCE) (IMMEDIATE-DEPENDENTS0 EQUAL-PLUS-0 . GCD-IDEMPOTENCE) (IMMEDIATE-DEPENDENTS0 REMAINDER-GCD . GCD-IDEMPOTENCE) (IMMEDIATE-DEPENDENTS0 GCD-PLUS . GCD-IDEMPOTENCE) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-ELIM . GCD-IDEMPOTENCE) (IMMEDIATE-DEPENDENTS0 GCD-X-X . GCD-IDEMPOTENCE) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-GCD . GCD-IDEMPOTENCE) (IMMEDIATE-DEPENDENTS0 ADDITION . GCD-IDEMPOTENCE) (IMMEDIATE-DEPENDENTS0 GCD . GCD-IDEMPOTENCE) (LEMMAS GCD . GCD-IDEMPOTENCE) (LEMMAS GCD . GCD-IDEMPOTENCE))))) (PUT1-LST (QUOTE GCD-X-X) (QUOTE (IDATE 1000404112443 IMMEDIATE-DEPENDENTS0 (GCDS GCD-IDEMPOTENCE) EVENT (PROVE-LEMMA GCD-X-X (REWRITE) (EQUAL (GCD X X) (FIX X)) ((ENABLE GCD) (ENABLE-THEORY ADDITION GROUND-ZERO) (INDUCT (SINGLE-NUMBER-INDUCTION X)) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIFF-X-X . GCD-X-X) (IMMEDIATE-DEPENDENTS0 SINGLE-NUMBER-INDUCTION . GCD-X-X) (IMMEDIATE-DEPENDENTS0 ADDITION . GCD-X-X) (IMMEDIATE-DEPENDENTS0 GCD . GCD-X-X) (LEMMAS GCD . GCD-X-X))))) (PUT1-LST (QUOTE COMMUTATIVITY2-OF-GCD) (QUOTE (IDATE 1000404112443 IMMEDIATE-DEPENDENTS0 (GCDS) EVENT (PROVE-LEMMA COMMUTATIVITY2-OF-GCD (REWRITE) (EQUAL (GCD B (GCD A C)) (GCD A (GCD B C))) ((ENABLE EQUAL-GCD-0 REMAINDER-GCD) (USE (GCD-IS-THE-GREATEST (X A) (Y (GCD B C)) (Z (GCD B (GCD A C)))) (GCD-IS-THE-GREATEST (X B) (Y (GCD A C)) (Z (GCD A (GCD B C)))) (COMMUTATIVITY2-OF-GCD-ZERO-CASE (A A) (B B) (C C)) (TRANSITIVITY-OF-DIVIDES (A A) (B (GCD A C)) (C (GCD B (GCD A C)))) (TRANSITIVITY-OF-DIVIDES (A C) (B (GCD A C)) (C (GCD B (GCD A C)))) (TRANSITIVITY-OF-DIVIDES (A B) (B (GCD B C)) (C (GCD A (GCD B C)))) (TRANSITIVITY-OF-DIVIDES (A C) (B (GCD B C)) (C (GCD A (GCD B C)))) (COMMON-DIVISOR-DIVIDES-GCD (X B) (Y C) (Z (GCD B (GCD A C)))) (COMMON-DIVISOR-DIVIDES-GCD (X A) (Y C) (Z (GCD A (GCD B C))))) (DO-NOT-INDUCT T) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQUAL-GCD-0 . COMMUTATIVITY2-OF-GCD) (IMMEDIATE-DEPENDENTS0 REMAINDER-GCD . COMMUTATIVITY2-OF-GCD) (IMMEDIATE-DEPENDENTS0 GCD-IS-THE-GREATEST . COMMUTATIVITY2-OF-GCD) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-GCD-ZERO-CASE . COMMUTATIVITY2-OF-GCD) (IMMEDIATE-DEPENDENTS0 TRANSITIVITY-OF-DIVIDES . COMMUTATIVITY2-OF-GCD) (IMMEDIATE-DEPENDENTS0 COMMON-DIVISOR-DIVIDES-GCD . COMMUTATIVITY2-OF-GCD) (IMMEDIATE-DEPENDENTS0 GCD . COMMUTATIVITY2-OF-GCD) (LEMMAS GCD . COMMUTATIVITY2-OF-GCD))))) (PUT1-LST (QUOTE COMMUTATIVITY2-OF-GCD-ZERO-CASE) (QUOTE (IDATE 1000404112442 IMMEDIATE-DEPENDENTS0 (COMMUTATIVITY2-OF-GCD) EVENT (PROVE-LEMMA COMMUTATIVITY2-OF-GCD-ZERO-CASE NIL (IMPLIES (OR (ZEROP A) (OR (ZEROP B) (ZEROP C))) (EQUAL (GCD B (GCD A C)) (GCD A (GCD B C)))) ((ENABLE GCD GCD-0 COMMUTATIVITY-OF-GCD) (DO-NOT-INDUCT T) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-GCD . COMMUTATIVITY2-OF-GCD-ZERO-CASE) (IMMEDIATE-DEPENDENTS0 GCD-0 . COMMUTATIVITY2-OF-GCD-ZERO-CASE) (IMMEDIATE-DEPENDENTS0 GCD . COMMUTATIVITY2-OF-GCD-ZERO-CASE))))) (PUT1-LST (QUOTE ASSOCIATIVITY-OF-GCD) (QUOTE (IDATE 1000404112442 IMMEDIATE-DEPENDENTS0 (GCDS) EVENT (PROVE-LEMMA ASSOCIATIVITY-OF-GCD (REWRITE) (EQUAL (GCD (GCD A B) C) (GCD A (GCD B C))) ((ENABLE EQUAL-GCD-0 REMAINDER-GCD) (USE (GCD-IS-THE-GREATEST (X A) (Y (GCD B C)) (Z (GCD (GCD A B) C))) (GCD-IS-THE-GREATEST (X (GCD A B)) (Y C) (Z (GCD A (GCD B C)))) (ASSOCIATIVITY-OF-GCD-ZERO-CASE (A A) (B B) (C C)) (TRANSITIVITY-OF-DIVIDES (A A) (B (GCD A B)) (C (GCD (GCD A B) C))) (TRANSITIVITY-OF-DIVIDES (A B) (B (GCD A B)) (C (GCD (GCD A B) C))) (TRANSITIVITY-OF-DIVIDES (A B) (B (GCD B C)) (C (GCD A (GCD B C)))) (TRANSITIVITY-OF-DIVIDES (A C) (B (GCD B C)) (C (GCD A (GCD B C)))) (COMMON-DIVISOR-DIVIDES-GCD (X B) (Y C) (Z (GCD (GCD A B) C))) (COMMON-DIVISOR-DIVIDES-GCD (X A) (Y B) (Z (GCD A (GCD B C))))) (DO-NOT-INDUCT T) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQUAL-GCD-0 . ASSOCIATIVITY-OF-GCD) (IMMEDIATE-DEPENDENTS0 REMAINDER-GCD . ASSOCIATIVITY-OF-GCD) (IMMEDIATE-DEPENDENTS0 GCD-IS-THE-GREATEST . ASSOCIATIVITY-OF-GCD) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-GCD-ZERO-CASE . ASSOCIATIVITY-OF-GCD) (IMMEDIATE-DEPENDENTS0 TRANSITIVITY-OF-DIVIDES . ASSOCIATIVITY-OF-GCD) (IMMEDIATE-DEPENDENTS0 COMMON-DIVISOR-DIVIDES-GCD . ASSOCIATIVITY-OF-GCD) (IMMEDIATE-DEPENDENTS0 GCD . ASSOCIATIVITY-OF-GCD) (LEMMAS GCD . ASSOCIATIVITY-OF-GCD))))) (PUT1-LST (QUOTE ASSOCIATIVITY-OF-GCD-ZERO-CASE) (QUOTE (IDATE 1000404112442 IMMEDIATE-DEPENDENTS0 (ASSOCIATIVITY-OF-GCD) EVENT (PROVE-LEMMA ASSOCIATIVITY-OF-GCD-ZERO-CASE NIL (IMPLIES (OR (ZEROP A) (OR (ZEROP B) (ZEROP C))) (EQUAL (GCD (GCD A B) C) (GCD A (GCD B C)))) ((ENABLE GCD GCD-0) (DO-NOT-INDUCT T) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 GCD-0 . ASSOCIATIVITY-OF-GCD-ZERO-CASE) (IMMEDIATE-DEPENDENTS0 GCD . ASSOCIATIVITY-OF-GCD-ZERO-CASE))))) (PUT1-LST (QUOTE COMMON-DIVISOR-DIVIDES-GCD) (QUOTE (IDATE 1000404112442 IMMEDIATE-DEPENDENTS0 (GCDS COMMUTATIVITY2-OF-GCD ASSOCIATIVITY-OF-GCD) EVENT (PROVE-LEMMA COMMON-DIVISOR-DIVIDES-GCD (REWRITE) (IMPLIES (AND (EQUAL (REMAINDER X Z) (QUOTE 0)) (EQUAL (REMAINDER Y Z) (QUOTE 0))) (EQUAL (REMAINDER (GCD X Y) Z) (QUOTE 0))) ((ENABLE GCD COMMUTATIVITY-OF-GCD DISTRIBUTIVITY-OF-TIMES-OVER-GCD EQUAL-GCD-0) (ENABLE-THEORY ADDITION MULTIPLICATION REMAINDERS GROUND-ZERO) (DO-NOT-INDUCT T) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-TIMES-OVER-GCD . COMMON-DIVISOR-DIVIDES-GCD) (IMMEDIATE-DEPENDENTS0 REMAINDER-NOOP . COMMON-DIVISOR-DIVIDES-GCD) (IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES1-INSTANCE . COMMON-DIVISOR-DIVIDES-GCD) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . COMMON-DIVISOR-DIVIDES-GCD) (IMMEDIATE-DEPENDENTS0 PLUS-STOPPER . COMMON-DIVISOR-DIVIDES-GCD) (IMMEDIATE-DEPENDENTS0 REMAINDER-ZERO . COMMON-DIVISOR-DIVIDES-GCD) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-GCD . COMMON-DIVISOR-DIVIDES-GCD) (IMMEDIATE-DEPENDENTS0 REMAINDER-OF-NON-NUMBER . COMMON-DIVISOR-DIVIDES-GCD) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER . COMMON-DIVISOR-DIVIDES-GCD) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . COMMON-DIVISOR-DIVIDES-GCD) (IMMEDIATE-DEPENDENTS0 ADDITION . COMMON-DIVISOR-DIVIDES-GCD) (IMMEDIATE-DEPENDENTS0 MULTIPLICATION . COMMON-DIVISOR-DIVIDES-GCD) (IMMEDIATE-DEPENDENTS0 REMAINDERS . COMMON-DIVISOR-DIVIDES-GCD) (IMMEDIATE-DEPENDENTS0 GCD . COMMON-DIVISOR-DIVIDES-GCD) (LEMMAS REMAINDER . COMMON-DIVISOR-DIVIDES-GCD))))) (PUT1-LST (QUOTE GCD-IS-THE-GREATEST) (QUOTE (IDATE 1000404112442 IMMEDIATE-DEPENDENTS0 (COMMUTATIVITY2-OF-GCD ASSOCIATIVITY-OF-GCD) EVENT (PROVE-LEMMA GCD-IS-THE-GREATEST NIL (IMPLIES (AND (NOT (ZEROP X)) (AND (NOT (ZEROP Y)) (AND (EQUAL (REMAINDER X Z) (QUOTE 0)) (EQUAL (REMAINDER Y Z) (QUOTE 0))))) (IF (LESSP (GCD X Y) Z) (QUOTE *1*FALSE) (QUOTE *1*TRUE))) ((ENABLE GCD COMMUTATIVITY-OF-GCD DISTRIBUTIVITY-OF-TIMES-OVER-GCD EQUAL-GCD-0) (ENABLE-THEORY ADDITION MULTIPLICATION REMAINDERS GROUND-ZERO) (DO-NOT-INDUCT T) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-TIMES-OVER-GCD . GCD-IS-THE-GREATEST) (IMMEDIATE-DEPENDENTS0 EQUAL-GCD-0 . GCD-IS-THE-GREATEST) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES2 . GCD-IS-THE-GREATEST) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . GCD-IS-THE-GREATEST) (IMMEDIATE-DEPENDENTS0 PLUS-STOPPER . GCD-IS-THE-GREATEST) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . GCD-IS-THE-GREATEST) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-GCD . GCD-IS-THE-GREATEST) (IMMEDIATE-DEPENDENTS0 REMAINDER-ZERO . GCD-IS-THE-GREATEST) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER . GCD-IS-THE-GREATEST) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . GCD-IS-THE-GREATEST) (IMMEDIATE-DEPENDENTS0 ADDITION . GCD-IS-THE-GREATEST) (IMMEDIATE-DEPENDENTS0 MULTIPLICATION . GCD-IS-THE-GREATEST) (IMMEDIATE-DEPENDENTS0 REMAINDERS . GCD-IS-THE-GREATEST) (IMMEDIATE-DEPENDENTS0 GCD . GCD-IS-THE-GREATEST))))) (PUT1-LST (QUOTE DISTRIBUTIVITY-OF-TIMES-OVER-GCD) (QUOTE (IDATE 1000404112441 IMMEDIATE-DEPENDENTS0 (RPLUS-RZEROP-BRIDGE2 RPLUS-RZEROP-BRIDGE TIMES-GCD-FACT GCDS COMMON-DIVISOR-DIVIDES-GCD GCD-IS-THE-GREATEST) EVENT (PROVE-LEMMA DISTRIBUTIVITY-OF-TIMES-OVER-GCD (REWRITE) (AND (EQUAL (GCD (TIMES X Z) (TIMES Y Z)) (TIMES Z (GCD X Y))) (AND (EQUAL (GCD (TIMES Z X) (TIMES Y Z)) (TIMES Z (GCD X Y))) (AND (EQUAL (GCD (TIMES X Z) (TIMES Z Y)) (TIMES Z (GCD X Y))) (EQUAL (GCD (TIMES Z X) (TIMES Z Y)) (TIMES Z (GCD X Y)))))) ((USE (DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF (X X) (Y Y) (Z Z))) (ENABLE COMMUTATIVITY-OF-TIMES) (DO-NOT-INDUCT T) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . DISTRIBUTIVITY-OF-TIMES-OVER-GCD) (IMMEDIATE-DEPENDENTS0 DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF . DISTRIBUTIVITY-OF-TIMES-OVER-GCD) (IMMEDIATE-DEPENDENTS0 GCD . DISTRIBUTIVITY-OF-TIMES-OVER-GCD) (LEMMAS GCD . DISTRIBUTIVITY-OF-TIMES-OVER-GCD) (LEMMAS GCD . DISTRIBUTIVITY-OF-TIMES-OVER-GCD) (LEMMAS GCD . DISTRIBUTIVITY-OF-TIMES-OVER-GCD) (LEMMAS GCD . DISTRIBUTIVITY-OF-TIMES-OVER-GCD))))) (PUT1-LST (QUOTE DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF) (QUOTE (IDATE 1000404112441 IMMEDIATE-DEPENDENTS0 (DISTRIBUTIVITY-OF-TIMES-OVER-GCD) EVENT (PROVE-LEMMA DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF NIL (EQUAL (GCD (TIMES X Z) (TIMES Y Z)) (TIMES Z (GCD X Y))) ((ENABLE GCD COMMUTATIVITY-OF-GCD GCD-0 GCD-PLUS) (ENABLE-THEORY ADDITION MULTIPLICATION REMAINDERS GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF) (IMMEDIATE-DEPENDENTS0 EQUAL-PLUS-0 . DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-LESSP-PLUS . DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF) (IMMEDIATE-DEPENDENTS0 TIMES-DISTRIBUTES-OVER-PLUS . DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-DIFFERENCE-PLUS . DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF) (IMMEDIATE-DEPENDENTS0 REMAINDER-X-X . DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF) (IMMEDIATE-DEPENDENTS0 GCD-PLUS . DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-ELIM . DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-GCD . DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO . DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF) (IMMEDIATE-DEPENDENTS0 TIMES-DISTRIBUTES-OVER-DIFFERENCE . DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-LEQ-ARG1 . DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES-CANCELLATION1 . DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF) (IMMEDIATE-DEPENDENTS0 GCD-0 . DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF) (IMMEDIATE-DEPENDENTS0 LESSP-DIFFERENCE . DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF) (IMMEDIATE-DEPENDENTS0 ADDITION . DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF) (IMMEDIATE-DEPENDENTS0 MULTIPLICATION . DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF) (IMMEDIATE-DEPENDENTS0 REMAINDERS . DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF) (IMMEDIATE-DEPENDENTS0 GCD . DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF))))) (PUT1-LST (QUOTE REMAINDER-GCD) (QUOTE (IDATE 1000404112441 IMMEDIATE-DEPENDENTS0 (REQUAL-REDUCE1 EQUAL-TIMES-GCD-BRIDGE1 QUOTIENT-GCD-TIMES-FACT GCD-QUOTIENT-QUOTIENT GCDS GCD-IDEMPOTENCE COMMUTATIVITY2-OF-GCD ASSOCIATIVITY-OF-GCD) EVENT (PROVE-LEMMA REMAINDER-GCD (REWRITE) (AND (EQUAL (REMAINDER A (GCD A B)) (QUOTE 0)) (EQUAL (REMAINDER B (GCD A B)) (QUOTE 0))) ((ENABLE GCD) (ENABLE-THEORY ADDITION REMAINDERS GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REMAINDER-NOOP . REMAINDER-GCD) (IMMEDIATE-DEPENDENTS0 REMAINDER-ZERO . REMAINDER-GCD) (IMMEDIATE-DEPENDENTS0 EQUAL-PLUS-0 . REMAINDER-GCD) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-LESSP-PLUS . REMAINDER-GCD) (IMMEDIATE-DEPENDENTS0 REMAINDER-PLUS . REMAINDER-GCD) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-ELIM . REMAINDER-GCD) (IMMEDIATE-DEPENDENTS0 REMAINDER-X-X . REMAINDER-GCD) (IMMEDIATE-DEPENDENTS0 REMAINDER-OF-NON-NUMBER . REMAINDER-GCD) (IMMEDIATE-DEPENDENTS0 LESSP-DIFFERENCE . REMAINDER-GCD) (IMMEDIATE-DEPENDENTS0 ADDITION . REMAINDER-GCD) (IMMEDIATE-DEPENDENTS0 REMAINDERS . REMAINDER-GCD) (IMMEDIATE-DEPENDENTS0 GCD . REMAINDER-GCD) (LEMMAS REMAINDER . REMAINDER-GCD) (LEMMAS REMAINDER . REMAINDER-GCD))))) (PUT1-LST (QUOTE GCD-PLUS-INSTANCE) (QUOTE (IDATE 1000404112440 IMMEDIATE-DEPENDENTS0 (GCD-QUOTIENT-QUOTIENT GCDS) EVENT (PROVE-LEMMA GCD-PLUS-INSTANCE (REWRITE) (AND (EQUAL (GCD A (PLUS A B)) (GCD A B)) (EQUAL (GCD A (PLUS B A)) (GCD A B))) ((ENABLE GCD-PLUS-INSTANCE-TEMP) (DO-NOT-INDUCT T) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 GCD-PLUS-INSTANCE-TEMP . GCD-PLUS-INSTANCE) (IMMEDIATE-DEPENDENTS0 GCD . GCD-PLUS-INSTANCE) (LEMMAS GCD . GCD-PLUS-INSTANCE) (LEMMAS GCD . GCD-PLUS-INSTANCE))))) (PUT1-LST (QUOTE GCD-PLUS) (QUOTE (IDATE 1000404112440 IMMEDIATE-DEPENDENTS0 (GCD-QUOTIENT-QUOTIENT GCDS GCD-IDEMPOTENCE DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF) EVENT (PROVE-LEMMA GCD-PLUS (REWRITE) (IMPLIES (EQUAL (REMAINDER B A) (QUOTE 0)) (AND (EQUAL (GCD A (PLUS B C)) (GCD A C)) (AND (EQUAL (GCD A (PLUS C B)) (GCD A C)) (AND (EQUAL (GCD (PLUS B C) A) (GCD A C)) (EQUAL (GCD (PLUS C B) A) (GCD A C)))))) ((ENABLE COMMUTATIVITY-OF-PLUS COMMUTATIVITY-OF-GCD) (USE (GCD-PLUS-PROOF (A A) (B B) (C C))) (DO-NOT-INDUCT T) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . GCD-PLUS) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-GCD . GCD-PLUS) (IMMEDIATE-DEPENDENTS0 GCD-PLUS-PROOF . GCD-PLUS) (IMMEDIATE-DEPENDENTS0 GCD . GCD-PLUS) (LEMMAS GCD . GCD-PLUS) (LEMMAS GCD . GCD-PLUS) (LEMMAS GCD . GCD-PLUS) (LEMMAS GCD . GCD-PLUS))))) (PUT1-LST (QUOTE GCD-PLUS-PROOF) (QUOTE (IDATE 1000404112440 IMMEDIATE-DEPENDENTS0 (GCD-PLUS) EVENT (PROVE-LEMMA GCD-PLUS-PROOF NIL (IMPLIES (EQUAL (REMAINDER B A) (QUOTE 0)) (EQUAL (GCD A (PLUS B C)) (GCD A C))) ((ENABLE GCD COMMUTATIVITY-OF-GCD GCD-1 GCD-PLUS-INSTANCE-TEMP) (ENABLE-THEORY ADDITION GROUND-ZERO) (INDUCT (REMAINDER B A)) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 GCD-PLUS-INSTANCE-TEMP . GCD-PLUS-PROOF) (IMMEDIATE-DEPENDENTS0 PLUS-DIFFERENCE-ARG1-CASESPLIT . GCD-PLUS-PROOF) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-LEQ-ARG1 . GCD-PLUS-PROOF) (IMMEDIATE-DEPENDENTS0 EQUAL-PLUS-0 . GCD-PLUS-PROOF) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-GCD . GCD-PLUS-PROOF) (IMMEDIATE-DEPENDENTS0 PLUS-STOPPER . GCD-PLUS-PROOF) (IMMEDIATE-DEPENDENTS0 ADDITION . GCD-PLUS-PROOF) (IMMEDIATE-DEPENDENTS0 GCD . GCD-PLUS-PROOF))))) (PUT1-LST (QUOTE GCD-PLUS-INSTANCE-TEMP) (QUOTE (IDATE 1000404112439 IMMEDIATE-DEPENDENTS0 (GCD-PLUS-INSTANCE GCD-PLUS-PROOF) EVENT (PROVE-LEMMA GCD-PLUS-INSTANCE-TEMP (REWRITE) (AND (EQUAL (GCD A (PLUS A B)) (GCD A B)) (EQUAL (GCD A (PLUS B A)) (GCD A B))) ((ENABLE COMMUTATIVITY-OF-PLUS) (USE (GCD-PLUS-INSTANCE-TEMP-PROOF (A A) (B B))) (DO-NOT-INDUCT T) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . GCD-PLUS-INSTANCE-TEMP) (IMMEDIATE-DEPENDENTS0 GCD-PLUS-INSTANCE-TEMP-PROOF . GCD-PLUS-INSTANCE-TEMP) (IMMEDIATE-DEPENDENTS0 GCD . GCD-PLUS-INSTANCE-TEMP) (LEMMAS GCD . GCD-PLUS-INSTANCE-TEMP) (LEMMAS GCD . 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GCD-PLUS-INSTANCE-TEMP-PROOF) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-GCD . GCD-PLUS-INSTANCE-TEMP-PROOF) (IMMEDIATE-DEPENDENTS0 PLUS-RIGHT-ID2 . GCD-PLUS-INSTANCE-TEMP-PROOF) (IMMEDIATE-DEPENDENTS0 PLUS-STOPPER . GCD-PLUS-INSTANCE-TEMP-PROOF) (IMMEDIATE-DEPENDENTS0 ADDITION . GCD-PLUS-INSTANCE-TEMP-PROOF) (IMMEDIATE-DEPENDENTS0 GCD . GCD-PLUS-INSTANCE-TEMP-PROOF))))) (PUT1-LST (QUOTE LESSP-GCD) (QUOTE (IDATE 1000404112439 IMMEDIATE-DEPENDENTS0 (RATIONAL-INEG-NUMERATOR-REDUCE-BRIDGE REDUCE-REDUCE REQUAL-REDUCE1 REQUAL-REDUCE-REDUCE-EQUAL QUOTIENT-GCD-TIMES-FACT GCD-FACTORS-GIVES-LINEAR-COMBINATION RATIONALP-REDUCE GCDS) EVENT (PROVE-LEMMA LESSP-GCD (REWRITE) (IMPLIES (NOT (ZEROP B)) (AND (EQUAL (LESSP B (GCD A B)) (QUOTE *1*FALSE)) (EQUAL (LESSP B (GCD B A)) (QUOTE *1*FALSE)))) ((ENABLE GCD COMMUTATIVITY-OF-GCD) (ENABLE-THEORY ADDITION GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LESSP-DIFFERENCE . LESSP-GCD) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-GCD . 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A))) (REWRITE-RULE ASSOCIATIVITY-OF-GCD NIL (EQUAL (GCD (GCD A B) C) (GCD A (GCD B C))) NIL) (REWRITE-RULE DISTRIBUTIVITY-OF-TIMES-OVER-GCD NIL (EQUAL (GCD (TIMES Z X) (TIMES Z Y)) (TIMES Z (GCD X Y))) NIL) (REWRITE-RULE DISTRIBUTIVITY-OF-TIMES-OVER-GCD NIL (EQUAL (GCD (TIMES X Z) (TIMES Z Y)) (TIMES Z (GCD X Y))) NIL) (REWRITE-RULE DISTRIBUTIVITY-OF-TIMES-OVER-GCD NIL (EQUAL (GCD (TIMES Z X) (TIMES Y Z)) (TIMES Z (GCD X Y))) 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 GCD-PLUS-INSTANCE NIL (EQUAL (GCD A (PLUS B A)) (GCD A B)) NIL) (REWRITE-RULE GCD-PLUS-INSTANCE NIL (EQUAL (GCD A (PLUS A B)) (GCD A B)) NIL) (REWRITE-RULE GCD-PLUS ((EQUAL (REMAINDER B A) (QUOTE 0))) (EQUAL (GCD (PLUS C B) A) (GCD A C)) NIL) (REWRITE-RULE GCD-PLUS ((EQUAL (REMAINDER B A) (QUOTE 0))) (EQUAL (GCD (PLUS B C) A) (GCD A C)) NIL) (REWRITE-RULE GCD-PLUS ((EQUAL (REMAINDER B A) (QUOTE 0))) (EQUAL (GCD A (PLUS C B)) (GCD A C)) NIL) (REWRITE-RULE GCD-PLUS ((EQUAL (REMAINDER B A) (QUOTE 0))) (EQUAL (GCD A (PLUS B C)) (GCD A C)) NIL) (REWRITE-RULE GCD-PLUS-INSTANCE-TEMP NIL (EQUAL (GCD A (PLUS B A)) (GCD A B)) NIL) (REWRITE-RULE GCD-PLUS-INSTANCE-TEMP NIL (EQUAL (GCD A (PLUS A B)) (GCD A B)) NIL) (REWRITE-RULE GCD-1 NIL (EQUAL (GCD X (QUOTE 1)) (QUOTE 1)) NIL) (REWRITE-RULE GCD-1 NIL (EQUAL (GCD (QUOTE 1) X) (QUOTE 1)) NIL) (REWRITE-RULE GCD-0 NIL (EQUAL (GCD X (QUOTE 0)) (IF (NUMBERP X) X (QUOTE 0))) NIL) (REWRITE-RULE GCD-0 NIL (EQUAL (GCD (QUOTE 0) X) (IF (NUMBERP X) X (QUOTE 0))) NIL) (REWRITE-RULE COMMUTATIVITY-OF-GCD NIL (EQUAL (GCD B A) (GCD A B)) ((B . A)))) TOTALP-LST ((GCD . T)) 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 *1*GCD SUBRP *1*FALSE 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 (ADD1 X) (FIX Y)) ORD-LESSP (ADD1-EQUAL ZEROP ORD-LESSP LESSP SUB1-ADD1 LESSP-DIFFERENCE FIX CDR-CONS CAR-CONS ORDINALP))) IDATE 1000404112439 CONTROLLER-POCKETS (3) SATELLITES (*1*GCD) IMMEDIATE-DEPENDENTS0 (NRATIONAL-RPLUS-ARG1 REDUCE-REDUCE EQUAL-TIMES-GCD-BRIDGE1 QUOTIENT-GCD-TIMES-FACT5 QUOTIENT-GCD-TIMES-FACT4 QUOTIENT-GCD-TIMES-FACT3 QUOTIENT-GCD-TIMES-FACT2 QUOTIENT-GCD-TIMES-FACT1 QUOTIENT-GCD-TIMES-FACT TIMES-GCD-FACT GCD-REMAINDER-TIMES-FACT1-PROOF DIVIDES-PRODUCT-REDUCTION GCD-FACTORS-GIVES-LINEAR-COMBINATION-REWRITE GCD-FACTORS-GIVES-LINEAR-COMBINATION GCD-QUOTIENT-QUOTIENT GCD-TIMES2 GCD-TIMES1 GCD-REMAINDER-FACT2 GCD-REMAINDER-FACT1 REDUCE GCD-IDEMPOTENCE GCD-X-X COMMUTATIVITY2-OF-GCD COMMUTATIVITY2-OF-GCD-ZERO-CASE ASSOCIATIVITY-OF-GCD ASSOCIATIVITY-OF-GCD-ZERO-CASE COMMON-DIVISOR-DIVIDES-GCD GCD-IS-THE-GREATEST DISTRIBUTIVITY-OF-TIMES-OVER-GCD DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF REMAINDER-GCD GCD-PLUS-INSTANCE GCD-PLUS GCD-PLUS-PROOF GCD-PLUS-INSTANCE-TEMP GCD-PLUS-INSTANCE-TEMP-PROOF LESSP-GCD EQUAL-GCD-0 GCD-1 GCD-0 COMMUTATIVITY-OF-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)))) ((ORD-LESSP (CONS (ADD1 X) (FIX Y))))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LESSP-DIFFERENCE . GCD) (DCELL . *1*GCD))))) (PUT1-LST (QUOTE LOGS) (QUOTE (IDATE 1000404112439 IMMEDIATE-DEPENDENTS0 (ARITHMETIC) EVENT (DEFTHEORY LOGS (LOG-EXP LOG-TIMES-EXP LOG-TIMES LOG-QUOTIENT-EXP LOG-QUOTIENT-TIMES LOG-QUOTIENT LOG-1 LOG-0 EQUAL-LOG-0 EXP-EXP)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 LOG-EXP . LOGS) (IMMEDIATE-DEPENDENTS0 LOG-TIMES-EXP . LOGS) (IMMEDIATE-DEPENDENTS0 LOG-TIMES . LOGS) (IMMEDIATE-DEPENDENTS0 LOG-QUOTIENT-EXP . LOGS) (IMMEDIATE-DEPENDENTS0 LOG-QUOTIENT-TIMES . LOGS) (IMMEDIATE-DEPENDENTS0 LOG-QUOTIENT . LOGS) (IMMEDIATE-DEPENDENTS0 LOG-1 . LOGS) (IMMEDIATE-DEPENDENTS0 LOG-0 . LOGS) (IMMEDIATE-DEPENDENTS0 EQUAL-LOG-0 . LOGS) (IMMEDIATE-DEPENDENTS0 EXP-EXP . LOGS))))) (PUT1-LST (QUOTE LOG-EXP) (QUOTE (IDATE 1000404112439 IMMEDIATE-DEPENDENTS0 (LOGS) EVENT (PROVE-LEMMA LOG-EXP (REWRITE) (IMPLIES (LESSP (QUOTE 1) C) (EQUAL (LOG C (EXP C N)) (ADD1 N))) ((ENABLE LOG EXP LOG-1) (ENABLE-THEORY ADDITION MULTIPLICATION REMAINDERS QUOTIENTS GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 QUOTIENT-TIMES-INSTANCE . LOG-EXP) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . LOG-EXP) (IMMEDIATE-DEPENDENTS0 LOG-1 . LOG-EXP) (IMMEDIATE-DEPENDENTS0 ADDITION . LOG-EXP) (IMMEDIATE-DEPENDENTS0 MULTIPLICATION . LOG-EXP) (IMMEDIATE-DEPENDENTS0 REMAINDERS . LOG-EXP) (IMMEDIATE-DEPENDENTS0 QUOTIENTS . LOG-EXP) (IMMEDIATE-DEPENDENTS0 EXP . LOG-EXP) (IMMEDIATE-DEPENDENTS0 LOG . LOG-EXP) (LEMMAS LOG . 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TRANSITIVITY-OF-DIVIDES) (IMMEDIATE-DEPENDENTS0 REMAINDER-PLUS . TRANSITIVITY-OF-DIVIDES) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-ELIM . TRANSITIVITY-OF-DIVIDES) (IMMEDIATE-DEPENDENTS0 REMAINDER-NOOP . TRANSITIVITY-OF-DIVIDES) (IMMEDIATE-DEPENDENTS0 ADDITION . TRANSITIVITY-OF-DIVIDES))))) (PUT1-LST (QUOTE REMAINDER-X-X) (QUOTE (IDATE 1000404112410 IMMEDIATE-DEPENDENTS0 (DIVIDES-EACH-EQUALITY GCD-QUOTIENT-QUOTIENT DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF REMAINDER-GCD REMAINDERS) EVENT (PROVE-LEMMA REMAINDER-X-X (REWRITE) (EQUAL (REMAINDER X X) (QUOTE 0)) ((ENABLE EQUAL-DIFFERENCE-0) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE-0 . REMAINDER-X-X) (LEMMAS REMAINDER . REMAINDER-X-X))))) (PUT1-LST (QUOTE REMAINDER-1-ARG2) (QUOTE (IDATE 1000404112410 IMMEDIATE-DEPENDENTS0 (TIMES-GCD-FACT GCD-REMAINDER-TIMES-FACT1-PROOF GCD-REMAINDER-FACT1 REMAINDERS REMAINDER-EXP-EXP) EVENT (PROVE-LEMMA REMAINDER-1-ARG2 (REWRITE) (EQUAL (REMAINDER Y (QUOTE 1)) (QUOTE 0)) ((ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((LEMMAS REMAINDER . REMAINDER-1-ARG2))))) (PUT1-LST (QUOTE REMAINDER-1-ARG1) (QUOTE (IDATE 1000404112410 IMMEDIATE-DEPENDENTS0 (DIVIDES-EACH-EQUALITY REMAINDERS) EVENT (PROVE-LEMMA REMAINDER-1-ARG1 (REWRITE) (EQUAL (REMAINDER (QUOTE 1) X) (IF (EQUAL X (QUOTE 1)) (QUOTE 0) (QUOTE 1))) ((ENABLE DIFFERENCE-LEQ-ARG1) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIFFERENCE-LEQ-ARG1 . REMAINDER-1-ARG1) (LEMMAS REMAINDER . REMAINDER-1-ARG1))))) (PUT1-LST (QUOTE REMAINDER-REMAINDER) (QUOTE (IDATE 1000404112410 IMMEDIATE-DEPENDENTS0 (REMAINDERS) EVENT (PROVE-LEMMA REMAINDER-REMAINDER (REWRITE) (IMPLIES (EQUAL (REMAINDER B A) (QUOTE 0)) (EQUAL (REMAINDER (REMAINDER N B) A) (REMAINDER N A))) ((INDUCT (REMAINDER N B)) (ENABLE REMAINDER-PLUS REMAINDER-QUOTIENT-ELIM REMAINDER-ZERO) (ENABLE-THEORY ADDITION MULTIPLICATION GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-PLUS . REMAINDER-REMAINDER) (IMMEDIATE-DEPENDENTS0 REMAINDER-PLUS . REMAINDER-REMAINDER) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-LESSP-PLUS . REMAINDER-REMAINDER) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-EQUAL-PLUS . REMAINDER-REMAINDER) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . REMAINDER-REMAINDER) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-ELIM . REMAINDER-REMAINDER) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . REMAINDER-REMAINDER) (IMMEDIATE-DEPENDENTS0 REMAINDER-ZERO . REMAINDER-REMAINDER) (IMMEDIATE-DEPENDENTS0 ADDITION . REMAINDER-REMAINDER) (IMMEDIATE-DEPENDENTS0 MULTIPLICATION . REMAINDER-REMAINDER) (LEMMAS REMAINDER . REMAINDER-REMAINDER))))) (PUT1-LST (QUOTE REMAINDER-EXP) (QUOTE (IDATE 1000404112409 IMMEDIATE-DEPENDENTS0 (REMAINDERS) EVENT (PROVE-LEMMA REMAINDER-EXP (REWRITE) (IMPLIES (NOT (ZEROP K)) (EQUAL (REMAINDER (EXP N K) N) (QUOTE 0))) ((ENABLE EXP REMAINDER-TIMES1-INSTANCE) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES1-INSTANCE . REMAINDER-EXP) (IMMEDIATE-DEPENDENTS0 EXP . REMAINDER-EXP) (LEMMAS REMAINDER . REMAINDER-EXP))))) (PUT1-LST (QUOTE REMAINDER-PLUS-TIMES-TIMES-INSTANCE) (QUOTE (IDATE 1000404112409 IMMEDIATE-DEPENDENTS0 (QUOTIENT-REMAINDER REMAINDERS) EVENT (PROVE-LEMMA REMAINDER-PLUS-TIMES-TIMES-INSTANCE (REWRITE) (IMPLIES (LESSP A B) (AND (EQUAL (REMAINDER (PLUS A (PLUS (TIMES B C) (TIMES B D))) (TIMES B E)) (PLUS A (TIMES B (REMAINDER (PLUS C D) E)))) (EQUAL (REMAINDER (PLUS A (PLUS (TIMES C B) (TIMES D B))) (TIMES E B)) (PLUS A (TIMES B (REMAINDER (PLUS C D) E)))))) ((ENABLE COMMUTATIVITY-OF-TIMES REMAINDER-TIMES-TIMES REMAINDER-PLUS-TIMES-TIMES) (USE (TIMES-DISTRIBUTES-OVER-PLUS (X B) (Y C) (Z D))) (DO-NOT-INDUCT T) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . REMAINDER-PLUS-TIMES-TIMES-INSTANCE) (IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES-TIMES . REMAINDER-PLUS-TIMES-TIMES-INSTANCE) (IMMEDIATE-DEPENDENTS0 REMAINDER-PLUS-TIMES-TIMES . REMAINDER-PLUS-TIMES-TIMES-INSTANCE) (IMMEDIATE-DEPENDENTS0 TIMES-DISTRIBUTES-OVER-PLUS . REMAINDER-PLUS-TIMES-TIMES-INSTANCE) (LEMMAS REMAINDER . REMAINDER-PLUS-TIMES-TIMES-INSTANCE) (LEMMAS REMAINDER . REMAINDER-PLUS-TIMES-TIMES-INSTANCE))))) (PUT1-LST (QUOTE REMAINDER-PLUS-TIMES-TIMES) (QUOTE (IDATE 1000404112409 IMMEDIATE-DEPENDENTS0 (REMAINDERS REMAINDER-PLUS-TIMES-TIMES-INSTANCE) EVENT (PROVE-LEMMA REMAINDER-PLUS-TIMES-TIMES (REWRITE) (IMPLIES (LESSP A B) (AND (EQUAL (REMAINDER (PLUS A (TIMES B C)) (TIMES B D)) (PLUS A (REMAINDER (TIMES B C) (TIMES B D)))) (EQUAL (REMAINDER (PLUS A (TIMES C B)) (TIMES D B)) (PLUS A (REMAINDER (TIMES C B) (TIMES D B)))))) ((USE (REMAINDER-PLUS-TIMES-TIMES-PROOF (A A) (B B) (C C) (D D))) (ENABLE COMMUTATIVITY-OF-TIMES) (DO-NOT-INDUCT T) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . REMAINDER-PLUS-TIMES-TIMES) (IMMEDIATE-DEPENDENTS0 REMAINDER-PLUS-TIMES-TIMES-PROOF . REMAINDER-PLUS-TIMES-TIMES) (LEMMAS REMAINDER . REMAINDER-PLUS-TIMES-TIMES) (LEMMAS REMAINDER . REMAINDER-PLUS-TIMES-TIMES))))) (PUT1-LST (QUOTE REMAINDER-PLUS-TIMES-TIMES-PROOF) (QUOTE (IDATE 1000404112409 IMMEDIATE-DEPENDENTS0 (REMAINDER-PLUS-TIMES-TIMES) EVENT (PROVE-LEMMA REMAINDER-PLUS-TIMES-TIMES-PROOF NIL (IMPLIES (LESSP A B) (EQUAL (REMAINDER (PLUS A (TIMES B C)) (TIMES B D)) (PLUS A (REMAINDER (TIMES B C) (TIMES B D))))) ((USE (REMAINDER-PLUS-FACT (A A) (X B) (B (TIMES B C)) (C (TIMES B D)))) (ENABLE REMAINDER-TIMES1-INSTANCE REMAINDER-TIMES2-INSTANCE) (DO-NOT-INDUCT T) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES2-INSTANCE . REMAINDER-PLUS-TIMES-TIMES-PROOF) (IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES1-INSTANCE . REMAINDER-PLUS-TIMES-TIMES-PROOF) (IMMEDIATE-DEPENDENTS0 REMAINDER-PLUS-FACT . REMAINDER-PLUS-TIMES-TIMES-PROOF))))) (PUT1-LST (QUOTE REMAINDER-PLUS-FACT) (QUOTE (IDATE 1000404112409 IMMEDIATE-DEPENDENTS0 (REMAINDER-PLUS-TIMES-TIMES-PROOF) EVENT (PROVE-LEMMA REMAINDER-PLUS-FACT NIL (IMPLIES (AND (EQUAL (REMAINDER B X) (QUOTE 0)) (AND (EQUAL (REMAINDER C X) (QUOTE 0)) (LESSP A X))) (EQUAL (REMAINDER (PLUS A B) C) (PLUS A (REMAINDER B C)))) ((ENABLE LESSP-PLUS-FACT REMAINDER-NOOP REMAINDER-DIFFERENCE1) (ENABLE-THEORY ADDITION MULTIPLICATION GROUND-ZERO) (INDUCT (REMAINDER B C)) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIFF-X-X . REMAINDER-PLUS-FACT) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-DIFFERENCE-PLUS . REMAINDER-PLUS-FACT) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-LESSP-PLUS . REMAINDER-PLUS-FACT) (IMMEDIATE-DEPENDENTS0 REMAINDER-DIFFERENCE1 . REMAINDER-PLUS-FACT) (IMMEDIATE-DEPENDENTS0 PLUS-DIFFERENCE-ARG2-CASESPLIT . REMAINDER-PLUS-FACT) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-LEQ-ARG1 . REMAINDER-PLUS-FACT) (IMMEDIATE-DEPENDENTS0 PLUS-STOPPER . REMAINDER-PLUS-FACT) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . REMAINDER-PLUS-FACT) (IMMEDIATE-DEPENDENTS0 PLUS-RIGHT-ID2 . REMAINDER-PLUS-FACT) (IMMEDIATE-DEPENDENTS0 LESSP-PLUS-FACT . REMAINDER-PLUS-FACT) (IMMEDIATE-DEPENDENTS0 REMAINDER-NOOP . REMAINDER-PLUS-FACT) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-EQUAL-PLUS . REMAINDER-PLUS-FACT) (IMMEDIATE-DEPENDENTS0 ADDITION . REMAINDER-PLUS-FACT) (IMMEDIATE-DEPENDENTS0 MULTIPLICATION . REMAINDER-PLUS-FACT))))) (PUT1-LST (QUOTE LESSP-PLUS-FACT) (QUOTE (IDATE 1000404112408 IMMEDIATE-DEPENDENTS0 (QUOTIENT-PLUS-FACT LESSP-PLUS-FACT-OFF REMAINDER-PLUS-FACT) EVENT (PROVE-LEMMA LESSP-PLUS-FACT (REWRITE) (IMPLIES (AND (EQUAL (REMAINDER B X) (QUOTE 0)) (AND (EQUAL (REMAINDER C X) (QUOTE 0)) (AND (LESSP B C) (LESSP A X)))) (EQUAL (LESSP (PLUS A B) C) (QUOTE *1*TRUE))) ((ENABLE-THEORY ADDITION GROUND-ZERO) (INDUCT (DOUBLE-REMAINDER-INDUCTION B C X)) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PLUS-DIFFERENCE-ARG2-CASESPLIT . LESSP-PLUS-FACT) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-LEQ-ARG1 . LESSP-PLUS-FACT) (IMMEDIATE-DEPENDENTS0 PLUS-STOPPER . LESSP-PLUS-FACT) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . LESSP-PLUS-FACT) (IMMEDIATE-DEPENDENTS0 PLUS-RIGHT-ID2 . LESSP-PLUS-FACT) (IMMEDIATE-DEPENDENTS0 DOUBLE-REMAINDER-INDUCTION . LESSP-PLUS-FACT) (IMMEDIATE-DEPENDENTS0 ADDITION . LESSP-PLUS-FACT) (LEMMAS LESSP . LESSP-PLUS-FACT))))) (PUT1-LST (QUOTE EQUAL-REMAINDER-DIFFERENCE-0) (QUOTE (IDATE 1000404112408 IMMEDIATE-DEPENDENTS0 (EQUAL-REMAINDER-DIFFERENCE-0-OFF) EVENT (PROVE-LEMMA EQUAL-REMAINDER-DIFFERENCE-0 (REWRITE) (EQUAL (EQUAL (REMAINDER (DIFFERENCE A B) C) (QUOTE 0)) (IF (IF (LESSP A B) (QUOTE *1*FALSE) (QUOTE *1*TRUE)) (EQUAL (REMAINDER A C) (REMAINDER B C)) (QUOTE *1*TRUE))) ((ENABLE LESSP-REMAINDER REMAINDER-DIFFERENCE1 REMAINDER-OF-NON-NUMBER REMAINDER-PLUS REMAINDER-QUOTIENT-ELIM REMAINDER-TIMES1-INSTANCE REMAINDER-ZERO) (ENABLE-THEORY ADDITION GROUND-ZERO) (DO-NOT-INDUCT T) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-LESSP-PLUS . EQUAL-REMAINDER-DIFFERENCE-0) (IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES1-INSTANCE . EQUAL-REMAINDER-DIFFERENCE-0) (IMMEDIATE-DEPENDENTS0 REMAINDER-PLUS . EQUAL-REMAINDER-DIFFERENCE-0) (IMMEDIATE-DEPENDENTS0 REMAINDER-ZERO . EQUAL-REMAINDER-DIFFERENCE-0) (IMMEDIATE-DEPENDENTS0 PLUS-STOPPER . EQUAL-REMAINDER-DIFFERENCE-0) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . EQUAL-REMAINDER-DIFFERENCE-0) (IMMEDIATE-DEPENDENTS0 PLUS-RIGHT-ID2 . EQUAL-REMAINDER-DIFFERENCE-0) (IMMEDIATE-DEPENDENTS0 REMAINDER-OF-NON-NUMBER . EQUAL-REMAINDER-DIFFERENCE-0) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-ELIM . EQUAL-REMAINDER-DIFFERENCE-0) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER . EQUAL-REMAINDER-DIFFERENCE-0) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . EQUAL-REMAINDER-DIFFERENCE-0) (IMMEDIATE-DEPENDENTS0 DIFF-X-X . EQUAL-REMAINDER-DIFFERENCE-0) (IMMEDIATE-DEPENDENTS0 REMAINDER-DIFFERENCE1 . EQUAL-REMAINDER-DIFFERENCE-0) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-LEQ-ARG1 . EQUAL-REMAINDER-DIFFERENCE-0) (IMMEDIATE-DEPENDENTS0 ADDITION . EQUAL-REMAINDER-DIFFERENCE-0) (LEMMAS EQUAL . EQUAL-REMAINDER-DIFFERENCE-0))))) (PUT1-LST (QUOTE REMAINDER-DIFFERENCE3) (QUOTE (IDATE 1000404112408 IMMEDIATE-DEPENDENTS0 (REMAINDER-DIFFERENCE3-OFF) EVENT (PROVE-LEMMA REMAINDER-DIFFERENCE3 (REWRITE) (IMPLIES (AND (EQUAL (REMAINDER B C) (QUOTE 0)) (NOT (EQUAL (REMAINDER A C) (QUOTE 0)))) (EQUAL (REMAINDER (DIFFERENCE A B) C) (IF (LESSP B A) (REMAINDER A C) (QUOTE 0)))) ((ENABLE REMAINDER-NOOP REMAINDER-OF-NON-NUMBER REMAINDER-ZERO) (ENABLE-THEORY ADDITION GROUND-ZERO) (INDUCT (DOUBLE-REMAINDER-INDUCTION A B C)) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . REMAINDER-DIFFERENCE3) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-DIFFERENCE-PLUS . REMAINDER-DIFFERENCE3) (IMMEDIATE-DEPENDENTS0 PLUS-DIFFERENCE-ARG2-CASESPLIT . REMAINDER-DIFFERENCE3) (IMMEDIATE-DEPENDENTS0 REMAINDER-OF-NON-NUMBER . REMAINDER-DIFFERENCE3) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-LEQ-ARG1 . REMAINDER-DIFFERENCE3) (IMMEDIATE-DEPENDENTS0 REMAINDER-NOOP . REMAINDER-DIFFERENCE3) (IMMEDIATE-DEPENDENTS0 REMAINDER-ZERO . REMAINDER-DIFFERENCE3) (IMMEDIATE-DEPENDENTS0 DIFF-DIFF-ARG1 . REMAINDER-DIFFERENCE3) (IMMEDIATE-DEPENDENTS0 DOUBLE-REMAINDER-INDUCTION . REMAINDER-DIFFERENCE3) (IMMEDIATE-DEPENDENTS0 ADDITION . REMAINDER-DIFFERENCE3) (LEMMAS REMAINDER . REMAINDER-DIFFERENCE3))))) (PUT1-LST (QUOTE REMAINDER-DIFFERENCE2) (QUOTE (IDATE 1000404112407 IMMEDIATE-DEPENDENTS0 (IDIV-IMOD-UNIQUENESS IQUOTIENT-IREMAINDER-UNIQUENESS REMAINDERS) EVENT (PROVE-LEMMA REMAINDER-DIFFERENCE2 (REWRITE) (IMPLIES (AND (EQUAL (REMAINDER A C) (QUOTE 0)) (NOT (EQUAL (REMAINDER B C) (QUOTE 0)))) (EQUAL (REMAINDER (DIFFERENCE A B) C) (IF (LESSP B A) (DIFFERENCE C (REMAINDER B C)) (QUOTE 0)))) ((ENABLE EQUAL-REMAINDER-PLUS-0 LESSP-REMAINDER REMAINDER-NOOP REMAINDER-OF-NON-NUMBER REMAINDER-QUOTIENT-ELIM REMAINDER-TIMES1-INSTANCE REMAINDER-ZERO) (DISABLE TIMES-DISTRIBUTES-OVER-PLUS) (ENABLE-THEORY ADDITION MULTIPLICATION GROUND-ZERO) (INDUCT (DOUBLE-REMAINDER-INDUCTION A B C)) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . REMAINDER-DIFFERENCE2) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-DIFFERENCE-PLUS . REMAINDER-DIFFERENCE2) (IMMEDIATE-DEPENDENTS0 PLUS-DIFFERENCE-ARG2-CASESPLIT . REMAINDER-DIFFERENCE2) (IMMEDIATE-DEPENDENTS0 REMAINDER-OF-NON-NUMBER . REMAINDER-DIFFERENCE2) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-LESSP-PLUS . REMAINDER-DIFFERENCE2) (IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES1-INSTANCE . REMAINDER-DIFFERENCE2) (IMMEDIATE-DEPENDENTS0 EQUAL-REMAINDER-PLUS-0 . REMAINDER-DIFFERENCE2) (IMMEDIATE-DEPENDENTS0 EQUAL-PLUS-0 . REMAINDER-DIFFERENCE2) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . REMAINDER-DIFFERENCE2) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-ELIM . REMAINDER-DIFFERENCE2) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER . REMAINDER-DIFFERENCE2) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . REMAINDER-DIFFERENCE2) (IMMEDIATE-DEPENDENTS0 REMAINDER-NOOP . REMAINDER-DIFFERENCE2) (IMMEDIATE-DEPENDENTS0 REMAINDER-ZERO . REMAINDER-DIFFERENCE2) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-LEQ-ARG1 . REMAINDER-DIFFERENCE2) (IMMEDIATE-DEPENDENTS0 DIFF-DIFF-ARG1 . REMAINDER-DIFFERENCE2) (IMMEDIATE-DEPENDENTS0 DOUBLE-REMAINDER-INDUCTION . REMAINDER-DIFFERENCE2) (IMMEDIATE-DEPENDENTS0 ADDITION . REMAINDER-DIFFERENCE2) (IMMEDIATE-DEPENDENTS0 MULTIPLICATION . REMAINDER-DIFFERENCE2) (LEMMAS REMAINDER . REMAINDER-DIFFERENCE2))))) (PUT1-LST (QUOTE *1*DOUBLE-REMAINDER-INDUCTION) (QUOTE (MAIN-EVENT DOUBLE-REMAINDER-INDUCTION))) (PUT1-LST (QUOTE DOUBLE-REMAINDER-INDUCTION) (QUOTE (TYPE-PRESCRIPTION-LST ((DOUBLE-REMAINDER-INDUCTION 4 NIL NIL NIL)) TOTALP-LST ((DOUBLE-REMAINDER-INDUCTION . T)) QUICK-BLOCK-INFO (SELF-REFLEXIVE SELF-REFLEXIVE UNCHANGING) SDEFN (LAMBDA (A B C) (IF (EQUAL C (QUOTE 0)) (QUOTE 0) (IF (NUMBERP C) (IF (LESSP A C) (QUOTE 0) (IF (LESSP B C) (QUOTE 0) (DOUBLE-REMAINDER-INDUCTION (DIFFERENCE A C) (DIFFERENCE B C) C))) (QUOTE 0)))) LISP-CODE *1*DOUBLE-REMAINDER-INDUCTION SUBRP *1*FALSE INDUCTION-MACHINE ((TESTS-AND-CASES ((ZEROP C)) NIL) (TESTS-AND-CASES ((NOT (ZEROP C)) (LESSP A C)) NIL) (TESTS-AND-CASES ((NOT (ZEROP C)) (NOT (LESSP A C)) (LESSP B C)) NIL) (TESTS-AND-CASES ((NOT (ZEROP C)) (NOT (LESSP A C)) (NOT (LESSP B C))) (((DIFFERENCE A C) (DIFFERENCE B C) C)))) LEVEL-NO 2 JUSTIFICATIONS ((JUSTIFICATION (A) (COUNT A) LESSP (ZERO COUNT-NOT-LESSP ZEROP COUNT-NUMBERP)) (JUSTIFICATION (B) (COUNT B) LESSP (ZERO COUNT-NOT-LESSP ZEROP COUNT-NUMBERP))) IDATE 1000404112406 CONTROLLER-POCKETS (1 2) SATELLITES (*1*DOUBLE-REMAINDER-INDUCTION) IMMEDIATE-DEPENDENTS0 (LEQ-QUOTIENT QUOTIENT-DIFFERENCE3 QUOTIENT-DIFFERENCE2 LESSP-PLUS-FACT REMAINDER-DIFFERENCE3 REMAINDER-DIFFERENCE2) EVENT (DEFN DOUBLE-REMAINDER-INDUCTION (A B C) (IF (ZEROP C) (QUOTE 0) (IF (LESSP A C) (QUOTE 0) (IF (LESSP B C) (QUOTE 0) (DOUBLE-REMAINDER-INDUCTION (DIFFERENCE A C) (DIFFERENCE B C) C))))) LOCAL-UNDO-TUPLES ((DCELL . *1*DOUBLE-REMAINDER-INDUCTION))))) (PUT1-LST (QUOTE REMAINDER-DIFFERENCE1) (QUOTE (IDATE 1000404112406 IMMEDIATE-DEPENDENTS0 (QUOTIENT-PLUS-FACT REMAINDERS REMAINDER-PLUS-FACT EQUAL-REMAINDER-DIFFERENCE-0) EVENT (PROVE-LEMMA REMAINDER-DIFFERENCE1 (REWRITE) (IMPLIES (EQUAL (REMAINDER A C) (REMAINDER B C)) (EQUAL (REMAINDER (DIFFERENCE A B) C) (DIFFERENCE (REMAINDER A C) (REMAINDER B C)))) ((ENABLE LESSP-REMAINDER EQUAL-REMAINDER-PLUS-REMAINDER REMAINDER-PLUS REMAINDER-QUOTIENT-ELIM REMAINDER-TIMES1-INSTANCE) (ENABLE-THEORY ADDITION GROUND-ZERO) (DO-NOT-INDUCT T) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES1-INSTANCE . REMAINDER-DIFFERENCE1) (IMMEDIATE-DEPENDENTS0 REMAINDER-PLUS . REMAINDER-DIFFERENCE1) (IMMEDIATE-DEPENDENTS0 EQUAL-REMAINDER-PLUS-REMAINDER . REMAINDER-DIFFERENCE1) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-LESSP-PLUS . REMAINDER-DIFFERENCE1) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-LEQ-ARG1 . REMAINDER-DIFFERENCE1) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-ELIM . REMAINDER-DIFFERENCE1) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER . REMAINDER-DIFFERENCE1) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . REMAINDER-DIFFERENCE1) (IMMEDIATE-DEPENDENTS0 DIFF-X-X . REMAINDER-DIFFERENCE1) (IMMEDIATE-DEPENDENTS0 ADDITION . REMAINDER-DIFFERENCE1) (LEMMAS REMAINDER . REMAINDER-DIFFERENCE1))))) (PUT1-LST (QUOTE REMAINDER-TIMES2-INSTANCE) (QUOTE (IDATE 1000404112406 IMMEDIATE-DEPENDENTS0 (TIMES-GCD-FACT REMAINDERS REMAINDER-EXP-EXP REMAINDER-PLUS-TIMES-TIMES-PROOF) EVENT (PROVE-LEMMA REMAINDER-TIMES2-INSTANCE (REWRITE) (AND (EQUAL (REMAINDER (TIMES X Y) (TIMES X Z)) (TIMES X (REMAINDER Y Z))) (EQUAL (REMAINDER (TIMES X Z) (TIMES Y Z)) (TIMES (REMAINDER X Y) Z))) ((ENABLE REMAINDER-TIMES-TIMES) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES-TIMES . REMAINDER-TIMES2-INSTANCE) (LEMMAS REMAINDER . REMAINDER-TIMES2-INSTANCE) (LEMMAS REMAINDER . REMAINDER-TIMES2-INSTANCE))))) (PUT1-LST (QUOTE REMAINDER-TIMES2) (QUOTE (IDATE 1000404112406 IMMEDIATE-DEPENDENTS0 (TIMES-GCD-FACT DIVIDES-EACH-EQUALITY QUOTIENT-REMAINDER-TIMES REMAINDERS) EVENT (PROVE-LEMMA REMAINDER-TIMES2 (REWRITE) (IMPLIES (EQUAL (REMAINDER A Z) (QUOTE 0)) (AND (EQUAL (REMAINDER A (TIMES Y Z)) (TIMES Z (REMAINDER (QUOTIENT A Z) Y))) (EQUAL (REMAINDER A (TIMES Z Y)) (TIMES Z (REMAINDER (QUOTIENT A Z) Y))))) ((USE (REMAINDER-TIMES2-PROOF (A A) (Y Y) (Z Z))) (ENABLE COMMUTATIVITY-OF-TIMES) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . REMAINDER-TIMES2) (IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES2-PROOF . REMAINDER-TIMES2) (LEMMAS REMAINDER . REMAINDER-TIMES2) (LEMMAS REMAINDER . REMAINDER-TIMES2))))) (PUT1-LST (QUOTE REMAINDER-TIMES2-PROOF) (QUOTE (IDATE 1000404112406 IMMEDIATE-DEPENDENTS0 (REMAINDER-TIMES2) EVENT (PROVE-LEMMA REMAINDER-TIMES2-PROOF NIL (IMPLIES (EQUAL (REMAINDER A Z) (QUOTE 0)) (EQUAL (REMAINDER A (TIMES Z Y)) (TIMES Z (REMAINDER (QUOTIENT A Z) Y)))) ((ENABLE-THEORY ADDITION MULTIPLICATION GROUND-ZERO) (ENABLE LESSP-REMAINDER REMAINDER-NOOP REMAINDER-PLUS REMAINDER-QUOTIENT-ELIM REMAINDER-TIMES-TIMES REMAINDER-TIMES1-INSTANCE REMAINDER-ZERO) (DO-NOT-INDUCT T) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-TIMES . REMAINDER-TIMES2-PROOF) (IMMEDIATE-DEPENDENTS0 TIMES-DISTRIBUTES-OVER-PLUS . REMAINDER-TIMES2-PROOF) (IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES1-INSTANCE . REMAINDER-TIMES2-PROOF) (IMMEDIATE-DEPENDENTS0 REMAINDER-NOOP . REMAINDER-TIMES2-PROOF) (IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES-TIMES . REMAINDER-TIMES2-PROOF) (IMMEDIATE-DEPENDENTS0 REMAINDER-PLUS . REMAINDER-TIMES2-PROOF) (IMMEDIATE-DEPENDENTS0 PLUS-STOPPER . REMAINDER-TIMES2-PROOF) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO . REMAINDER-TIMES2-PROOF) (IMMEDIATE-DEPENDENTS0 REMAINDER-ZERO . REMAINDER-TIMES2-PROOF) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . REMAINDER-TIMES2-PROOF) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER . REMAINDER-TIMES2-PROOF) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . REMAINDER-TIMES2-PROOF) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . REMAINDER-TIMES2-PROOF) (IMMEDIATE-DEPENDENTS0 ADDITION . REMAINDER-TIMES2-PROOF) (IMMEDIATE-DEPENDENTS0 MULTIPLICATION . REMAINDER-TIMES2-PROOF))))) (PUT1-LST (QUOTE REMAINDER-TIMES-TIMES) (QUOTE (IDATE 1000404112406 IMMEDIATE-DEPENDENTS0 (REMAINDER-TIMES-TIMES-OFF REMAINDER-PLUS-TIMES-TIMES-INSTANCE REMAINDER-TIMES2-INSTANCE REMAINDER-TIMES2-PROOF) EVENT (PROVE-LEMMA REMAINDER-TIMES-TIMES (REWRITE) (AND (EQUAL (REMAINDER (TIMES X Y) (TIMES X Z)) (TIMES X (REMAINDER Y Z))) (EQUAL (REMAINDER (TIMES X Z) (TIMES Y Z)) (TIMES (REMAINDER X Y) Z))) ((USE (REMAINDER-TIMES-TIMES-PROOF (X X) (Y Y) (Z Z)) (REMAINDER-TIMES-TIMES-PROOF (X Z) (Y X) (Z Y))) (ENABLE COMMUTATIVITY-OF-TIMES) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . REMAINDER-TIMES-TIMES) (IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES-TIMES-PROOF . REMAINDER-TIMES-TIMES) (LEMMAS REMAINDER . REMAINDER-TIMES-TIMES) (LEMMAS REMAINDER . REMAINDER-TIMES-TIMES))))) (PUT1-LST (QUOTE REMAINDER-TIMES-TIMES-PROOF) (QUOTE (IDATE 1000404112406 IMMEDIATE-DEPENDENTS0 (REMAINDER-TIMES-TIMES) EVENT (PROVE-LEMMA REMAINDER-TIMES-TIMES-PROOF NIL (EQUAL (REMAINDER (TIMES X Y) (TIMES X Z)) (TIMES X (REMAINDER Y Z))) ((ENABLE-THEORY ADDITION MULTIPLICATION GROUND-ZERO) (ENABLE REMAINDER-ZERO) (INDUCT (REMAINDER Y Z)) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-DISTRIBUTES-OVER-DIFFERENCE . REMAINDER-TIMES-TIMES-PROOF) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-LEQ-ARG1 . REMAINDER-TIMES-TIMES-PROOF) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES-CANCELLATION1 . REMAINDER-TIMES-TIMES-PROOF) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . REMAINDER-TIMES-TIMES-PROOF) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . REMAINDER-TIMES-TIMES-PROOF) (IMMEDIATE-DEPENDENTS0 REMAINDER-ZERO . REMAINDER-TIMES-TIMES-PROOF) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO . REMAINDER-TIMES-TIMES-PROOF) (IMMEDIATE-DEPENDENTS0 ADDITION . REMAINDER-TIMES-TIMES-PROOF) (IMMEDIATE-DEPENDENTS0 MULTIPLICATION . REMAINDER-TIMES-TIMES-PROOF))))) (PUT1-LST (QUOTE REMAINDER-TIMES1-INSTANCE) (QUOTE (IDATE 1000404112405 IMMEDIATE-DEPENDENTS0 (TIMES-GCD-FACT REMAINDER-0-SUFFICIENCY IQUO-IREM-UNIQUENESS IDIV-IMOD-UNIQUENESS IQUOTIENT-IREMAINDER-UNIQUENESS QUOTIENT-REMAINDER-UNIQUENESS COMMON-DIVISOR-DIVIDES-GCD QUOTIENT-QUOTIENT QUOTIENT-PLUS-TIMES-TIMES-PROOF QUOTIENT-REMAINDER-INSTANCE QUOTIENT-REMAINDER QUOTIENT-REMAINDER-TIMES QUOTIENT-DIFFERENCE2 QUOTIENT-DIFFERENCE1 QUOTIENT-TIMES-PROOF REMAINDERS REMAINDER-EXP REMAINDER-PLUS-TIMES-TIMES-PROOF EQUAL-REMAINDER-DIFFERENCE-0 REMAINDER-DIFFERENCE2 REMAINDER-DIFFERENCE1 REMAINDER-TIMES2-PROOF) EVENT (PROVE-LEMMA REMAINDER-TIMES1-INSTANCE (REWRITE) (AND (EQUAL (REMAINDER (TIMES X Y) Y) (QUOTE 0)) (EQUAL (REMAINDER (TIMES X Y) X) (QUOTE 0))) ((USE (REMAINDER-TIMES1-INSTANCE-PROOF (X X) (Y Y)) (REMAINDER-TIMES1-INSTANCE-PROOF (X Y) (Y X))) (ENABLE COMMUTATIVITY-OF-TIMES) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . REMAINDER-TIMES1-INSTANCE) (IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES1-INSTANCE-PROOF . REMAINDER-TIMES1-INSTANCE) (LEMMAS REMAINDER . REMAINDER-TIMES1-INSTANCE) (LEMMAS REMAINDER . REMAINDER-TIMES1-INSTANCE))))) (PUT1-LST (QUOTE REMAINDER-TIMES1-INSTANCE-PROOF) (QUOTE (IDATE 1000404112405 IMMEDIATE-DEPENDENTS0 (REMAINDER-TIMES1-INSTANCE) EVENT (PROVE-LEMMA REMAINDER-TIMES1-INSTANCE-PROOF NIL (EQUAL (REMAINDER (TIMES X Y) Y) (QUOTE 0)) ((ENABLE COMMUTATIVITY-OF-TIMES DIFFERENCE-PLUS REMAINDER-ZERO) (INDUCT (TIMES X Y)) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REMAINDER-ZERO . REMAINDER-TIMES1-INSTANCE-PROOF) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . REMAINDER-TIMES1-INSTANCE-PROOF) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-PLUS . REMAINDER-TIMES1-INSTANCE-PROOF))))) (PUT1-LST (QUOTE REMAINDER-TIMES1) (QUOTE (IDATE 1000404112405 IMMEDIATE-DEPENDENTS0 (TIMES-GCD-FACT GCD-REMAINDER-TIMES-FACT1-PROOF QUOTIENT-TIMES-PROOF REMAINDERS) EVENT (PROVE-LEMMA REMAINDER-TIMES1 (REWRITE) (IMPLIES (EQUAL (REMAINDER B C) (QUOTE 0)) (AND (EQUAL (REMAINDER (TIMES A B) C) (QUOTE 0)) (EQUAL (REMAINDER (TIMES B A) C) (QUOTE 0)))) ((USE (REMAINDER-TIMES1-PROOF (A A) (B B) (C C)) (REMAINDER-TIMES1-PROOF (A B) (B A) (C C))) (ENABLE COMMUTATIVITY-OF-TIMES) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . REMAINDER-TIMES1) (IMMEDIATE-DEPENDENTS0 REMAINDER-TIMES1-PROOF . REMAINDER-TIMES1) (LEMMAS REMAINDER . REMAINDER-TIMES1) (LEMMAS REMAINDER . REMAINDER-TIMES1))))) (PUT1-LST (QUOTE REMAINDER-TIMES1-PROOF) (QUOTE (IDATE 1000404112405 IMMEDIATE-DEPENDENTS0 (REMAINDER-TIMES1) EVENT (PROVE-LEMMA REMAINDER-TIMES1-PROOF NIL (IMPLIES (EQUAL (REMAINDER B C) (QUOTE 0)) (EQUAL (REMAINDER (TIMES A B) C) (QUOTE 0))) ((ENABLE-THEORY MULTIPLICATION ADDITION GROUND-ZERO) (ENABLE REMAINDER-PLUS REMAINDER-NOOP REMAINDER-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REMAINDER-PLUS . REMAINDER-TIMES1-PROOF) (IMMEDIATE-DEPENDENTS0 MULTIPLICATION . REMAINDER-TIMES1-PROOF) (IMMEDIATE-DEPENDENTS0 ADDITION . REMAINDER-TIMES1-PROOF))))) (PUT1-LST (QUOTE EQUAL-REMAINDER-PLUS-REMAINDER) (QUOTE (IDATE 1000404112405 IMMEDIATE-DEPENDENTS0 (QUOTIENT-DIFFERENCE1 EQUAL-REMAINDER-PLUS-REMAINDER-OFF REMAINDER-DIFFERENCE1) EVENT (PROVE-LEMMA EQUAL-REMAINDER-PLUS-REMAINDER (REWRITE) (IMPLIES (LESSP A C) (AND (EQUAL (EQUAL (REMAINDER (PLUS A B) C) (REMAINDER B C)) (ZEROP A)) (EQUAL (EQUAL (REMAINDER (PLUS B A) C) (REMAINDER B C)) (ZEROP A)))) ((USE (EQUAL-REMAINDER-PLUS-REMAINDER-PROOF (A A) (B B) (C C))) (ENABLE COMMUTATIVITY-OF-PLUS) (DO-NOT-INDUCT T) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . EQUAL-REMAINDER-PLUS-REMAINDER) (IMMEDIATE-DEPENDENTS0 EQUAL-REMAINDER-PLUS-REMAINDER-PROOF . EQUAL-REMAINDER-PLUS-REMAINDER) (LEMMAS EQUAL . EQUAL-REMAINDER-PLUS-REMAINDER) (LEMMAS EQUAL . EQUAL-REMAINDER-PLUS-REMAINDER))))) (PUT1-LST (QUOTE EQUAL-REMAINDER-PLUS-REMAINDER-PROOF) (QUOTE (IDATE 1000404112405 IMMEDIATE-DEPENDENTS0 (EQUAL-REMAINDER-PLUS-REMAINDER) EVENT (PROVE-LEMMA EQUAL-REMAINDER-PLUS-REMAINDER-PROOF NIL (IMPLIES (LESSP A C) (EQUAL (EQUAL (REMAINDER (PLUS A B) C) (REMAINDER B C)) (ZEROP A))) ((ENABLE REMAINDER-NOOP) (ENABLE-THEORY ADDITION GROUND-ZERO) (INDUCT (REMAINDER B C)) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIFF-X-X . EQUAL-REMAINDER-PLUS-REMAINDER-PROOF) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-DIFFERENCE-PLUS . EQUAL-REMAINDER-PLUS-REMAINDER-PROOF) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-LESSP-PLUS . EQUAL-REMAINDER-PLUS-REMAINDER-PROOF) (IMMEDIATE-DEPENDENTS0 PLUS-DIFFERENCE-ARG2-CASESPLIT . EQUAL-REMAINDER-PLUS-REMAINDER-PROOF) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-LEQ-ARG1 . EQUAL-REMAINDER-PLUS-REMAINDER-PROOF) (IMMEDIATE-DEPENDENTS0 PLUS-RIGHT-ID2 . EQUAL-REMAINDER-PLUS-REMAINDER-PROOF) (IMMEDIATE-DEPENDENTS0 PLUS-STOPPER . EQUAL-REMAINDER-PLUS-REMAINDER-PROOF) (IMMEDIATE-DEPENDENTS0 REMAINDER-NOOP . EQUAL-REMAINDER-PLUS-REMAINDER-PROOF) (IMMEDIATE-DEPENDENTS0 ADDITION . EQUAL-REMAINDER-PLUS-REMAINDER-PROOF))))) (PUT1-LST (QUOTE EQUAL-REMAINDER-PLUS-0) (QUOTE (IDATE 1000404112404 IMMEDIATE-DEPENDENTS0 (REMAINDERS REMAINDER-DIFFERENCE2) EVENT (PROVE-LEMMA EQUAL-REMAINDER-PLUS-0 (REWRITE) (IMPLIES (EQUAL (REMAINDER A C) (QUOTE 0)) (AND (EQUAL (EQUAL (REMAINDER (PLUS A B) C) (QUOTE 0)) (EQUAL (REMAINDER B C) (QUOTE 0))) (AND (EQUAL (EQUAL (REMAINDER (PLUS B A) C) (QUOTE 0)) (EQUAL (REMAINDER B C) (QUOTE 0))) (EQUAL (EQUAL (REMAINDER (PLUS X (PLUS Y A)) C) (QUOTE 0)) (EQUAL (REMAINDER (PLUS X Y) C) (QUOTE 0)))))) ((USE (EQUAL-REMAINDER-PLUS-0-PROOF (A A) (B B) (C C)) (EQUAL-REMAINDER-PLUS-0-PROOF (A B) (B A) (C C)) (EQUAL-REMAINDER-PLUS-0-PROOF (A A) (B (PLUS X Y)) (C C))) (ENABLE ASSOCIATIVITY-OF-PLUS COMMUTATIVITY-OF-PLUS COMMUTATIVITY2-OF-PLUS) (DO-NOT-INDUCT T) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . EQUAL-REMAINDER-PLUS-0) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-PLUS . EQUAL-REMAINDER-PLUS-0) (IMMEDIATE-DEPENDENTS0 EQUAL-REMAINDER-PLUS-0-PROOF . EQUAL-REMAINDER-PLUS-0) (LEMMAS EQUAL . EQUAL-REMAINDER-PLUS-0) (LEMMAS EQUAL . EQUAL-REMAINDER-PLUS-0) (LEMMAS EQUAL . EQUAL-REMAINDER-PLUS-0))))) (PUT1-LST (QUOTE EQUAL-REMAINDER-PLUS-0-PROOF) (QUOTE (IDATE 1000404112404 IMMEDIATE-DEPENDENTS0 (EQUAL-REMAINDER-PLUS-0) EVENT (PROVE-LEMMA EQUAL-REMAINDER-PLUS-0-PROOF NIL (IMPLIES (EQUAL (REMAINDER A C) (QUOTE 0)) (EQUAL (EQUAL (REMAINDER (PLUS A B) C) (QUOTE 0)) (EQUAL (REMAINDER B C) (QUOTE 0)))) ((ENABLE REMAINDER-PLUS) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 REMAINDER-PLUS . EQUAL-REMAINDER-PLUS-0-PROOF))))) (PUT1-LST (QUOTE REMAINDER-PLUS) (QUOTE (IDATE 1000404112404 IMMEDIATE-DEPENDENTS0 (QUOTIENT-REMAINDER-UNIQUENESS REMAINDER-GCD QUOTIENT-REMAINDER QUOTIENT-REMAINDER-TIMES QUOTIENT-DIFFERENCE2 QUOTIENT-DIFFERENCE1 REMAINDERS TRANSITIVITY-OF-DIVIDES REMAINDER-REMAINDER EQUAL-REMAINDER-DIFFERENCE-0 REMAINDER-DIFFERENCE1 REMAINDER-TIMES2-PROOF REMAINDER-TIMES1-PROOF EQUAL-REMAINDER-PLUS-0-PROOF) EVENT (PROVE-LEMMA REMAINDER-PLUS (REWRITE) (IMPLIES (EQUAL (REMAINDER A C) (QUOTE 0)) (AND (EQUAL (REMAINDER (PLUS A B) C) (REMAINDER B C)) (AND (EQUAL (REMAINDER (PLUS B A) C) (REMAINDER B C)) (EQUAL (REMAINDER (PLUS X (PLUS Y A)) C) (REMAINDER (PLUS X Y) C))))) ((USE (REMAINDER-PLUS-PROOF (A B) (B A) (C C)) (REMAINDER-PLUS-PROOF (A A) (B B) (C C)) (REMAINDER-PLUS-PROOF (B A) (A (PLUS X Y)) (C C))) (ENABLE COMMUTATIVITY-OF-PLUS COMMUTATIVITY2-OF-PLUS ASSOCIATIVITY-OF-PLUS) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . REMAINDER-PLUS) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-PLUS . REMAINDER-PLUS) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-PLUS . REMAINDER-PLUS) (IMMEDIATE-DEPENDENTS0 REMAINDER-PLUS-PROOF . REMAINDER-PLUS) (LEMMAS REMAINDER . REMAINDER-PLUS) (LEMMAS REMAINDER . REMAINDER-PLUS) (LEMMAS REMAINDER . REMAINDER-PLUS))))) (PUT1-LST (QUOTE REMAINDER-PLUS-PROOF) (QUOTE (IDATE 1000404112404 IMMEDIATE-DEPENDENTS0 (REMAINDER-PLUS) EVENT (PROVE-LEMMA REMAINDER-PLUS-PROOF NIL (IMPLIES (EQUAL (REMAINDER B C) (QUOTE 0)) (EQUAL (REMAINDER (PLUS A B) C) (REMAINDER A C))) ((ENABLE REMAINDER-NOOP) (ENABLE-THEORY ADDITION GROUND-ZERO) (INDUCT (REMAINDER B C)) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-DIFFERENCE-PLUS . REMAINDER-PLUS-PROOF) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-LESSP-PLUS . REMAINDER-PLUS-PROOF) (IMMEDIATE-DEPENDENTS0 PLUS-DIFFERENCE-ARG2-CASESPLIT . REMAINDER-PLUS-PROOF) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-LEQ-ARG1 . REMAINDER-PLUS-PROOF) (IMMEDIATE-DEPENDENTS0 REMAINDER-NOOP . REMAINDER-PLUS-PROOF) (IMMEDIATE-DEPENDENTS0 PLUS-STOPPER . REMAINDER-PLUS-PROOF) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . REMAINDER-PLUS-PROOF) (IMMEDIATE-DEPENDENTS0 PLUS-RIGHT-ID2 . REMAINDER-PLUS-PROOF) (IMMEDIATE-DEPENDENTS0 ADDITION . REMAINDER-PLUS-PROOF))))) (PUT1-LST (QUOTE REMAINDER-ADD1) (QUOTE (IDATE 1000404112404 IMMEDIATE-DEPENDENTS0 (REMAINDERS) EVENT (PROVE-LEMMA REMAINDER-ADD1 (REWRITE) (IMPLIES (EQUAL (REMAINDER A B) (QUOTE 0)) (EQUAL (REMAINDER (ADD1 A) B) (REMAINDER (QUOTE 1) B))) ((ENABLE REMAINDER-NOOP) (ENABLE-THEORY ADDITION GROUND-ZERO) (INDUCT (REMAINDER A B)) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-LESSP-PLUS . REMAINDER-ADD1) (IMMEDIATE-DEPENDENTS0 DIFF-SUB1-ARG2 . REMAINDER-ADD1) (IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-DIFFERENCE-PLUS . REMAINDER-ADD1) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-ELIM . REMAINDER-ADD1) (IMMEDIATE-DEPENDENTS0 DIFF-ADD1-ARG2 . REMAINDER-ADD1) (IMMEDIATE-DEPENDENTS0 DIFF-SUB1-ARG2-CASESPLIT . REMAINDER-ADD1) (IMMEDIATE-DEPENDENTS0 REMAINDER-NOOP . REMAINDER-ADD1) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-LEQ-ARG1 . REMAINDER-ADD1) (IMMEDIATE-DEPENDENTS0 ADDITION . REMAINDER-ADD1) (LEMMAS REMAINDER . REMAINDER-ADD1))))) (PUT1-LST (QUOTE REMAINDER-SUB1) (QUOTE (IDATE 1000404112404 IMMEDIATE-DEPENDENTS0 (REMAINDERS) EVENT (PROVE-LEMMA REMAINDER-SUB1 (REWRITE) (IMPLIES (AND (NOT (ZEROP A)) (NOT (ZEROP B))) (EQUAL (REMAINDER (SUB1 A) B) (IF (EQUAL (REMAINDER A B) (QUOTE 0)) (SUB1 B) (SUB1 (REMAINDER A B))))) ((ENABLE LESSP-REMAINDER REMAINDER-NOOP REMAINDER-QUOTIENT-ELIM) (ENABLE-THEORY ADDITION GROUND-ZERO) (INDUCT (REMAINDER A B)) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIFF-ADD1-ARG2 . REMAINDER-SUB1) (IMMEDIATE-DEPENDENTS0 PLUS-STOPPER . REMAINDER-SUB1) (IMMEDIATE-DEPENDENTS0 LESSP-REMAINDER . REMAINDER-SUB1) (IMMEDIATE-DEPENDENTS0 REMAINDER-QUOTIENT-ELIM . REMAINDER-SUB1) (IMMEDIATE-DEPENDENTS0 DIFF-X-X . REMAINDER-SUB1) (IMMEDIATE-DEPENDENTS0 DIFF-SUB1-ARG2 . REMAINDER-SUB1) (IMMEDIATE-DEPENDENTS0 DIFF-SUB1-ARG2-CASESPLIT . REMAINDER-SUB1) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-LEQ-ARG1 . REMAINDER-SUB1) (IMMEDIATE-DEPENDENTS0 REMAINDER-NOOP . REMAINDER-SUB1) (IMMEDIATE-DEPENDENTS0 ADDITION . REMAINDER-SUB1) (LEMMAS REMAINDER . REMAINDER-SUB1))))) (PUT1-LST (QUOTE REMAINDER-QUOTIENT-ELIM) (QUOTE (IDATE 1000404112401 IMMEDIATE-DEPENDENTS0 (EQUAL-TIMES-TIMES-QUOTIENT-ARG2 TIMES-GCD-FACT DIVIDES-EACH-EQUALITY GCD-REMAINDER-FACT1 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2 DIVISION-THEOREM-PART3 DIVISION-THEOREM-PART2 COMMON-DIVISOR-DIVIDES-GCD GCD-IS-THE-GREATEST LOG-QUOTIENT-EXP LOG-QUOTIENT-TIMES-PROOF QUOTIENT-QUOTIENT QUOTIENT-REMAINDER QUOTIENT-REMAINDER-TIMES QUOTIENT-DIFFERENCE3 QUOTIENT-DIFFERENCE2 QUOTIENT-DIFFERENCE1 QUOTIENT-TIMES-PROOF REMAINDERS REMAINDER-REMAINDER EQUAL-REMAINDER-DIFFERENCE-0 REMAINDER-DIFFERENCE2 REMAINDER-DIFFERENCE1 REMAINDER-TIMES2-PROOF REMAINDER-SUB1) 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)) ((ENABLE PLUS-REMAINDER-TIMES-QUOTIENT) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PLUS-REMAINDER-TIMES-QUOTIENT . REMAINDER-QUOTIENT-ELIM) (ELIMINATE-DESTRUCTORS-DESTS . REMAINDER) (ELIMINATE-DESTRUCTORS-SEQ . REMAINDER) (ELIMINATE-DESTRUCTORS-DESTS . QUOTIENT) (ELIMINATE-DESTRUCTORS-SEQ . QUOTIENT))))) (PUT1-LST (QUOTE PLUS-REMAINDER-TIMES-QUOTIENT) (QUOTE (IDATE 1000404112401 IMMEDIATE-DEPENDENTS0 (PLUS-REMAINDER-TIMES-QUOTIENT-OFF REMAINDER-QUOTIENT-ELIM) EVENT (PROVE-LEMMA PLUS-REMAINDER-TIMES-QUOTIENT (REWRITE) (EQUAL (PLUS (REMAINDER X Y) (TIMES Y (QUOTIENT X Y))) (FIX X)) ((ENABLE COMMUTATIVITY2-OF-PLUS COMMUTATIVITY-OF-PLUS TIMES-ZERO TIMES-ADD1 COMMUTATIVITY-OF-TIMES) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-ADD1 . PLUS-REMAINDER-TIMES-QUOTIENT) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-PLUS . PLUS-REMAINDER-TIMES-QUOTIENT) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . PLUS-REMAINDER-TIMES-QUOTIENT) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO . PLUS-REMAINDER-TIMES-QUOTIENT) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . PLUS-REMAINDER-TIMES-QUOTIENT) (LEMMAS PLUS . PLUS-REMAINDER-TIMES-QUOTIENT))))) (PUT1-LST (QUOTE REMAINDER-ZERO) (QUOTE (IDATE 1000404112401 IMMEDIATE-DEPENDENTS0 (EQUAL-TIMES-TIMES-QUOTIENT-ARG2 TIMES-GCD-FACT GCD-REMAINDER-TIMES-FACT1-PROOF DIVIDES-PRODUCT-REDUCTION DIVIDES-EACH-EQUALITY QUOTIENT-DIFFERENCE-LESSP-ARG2 COMMON-DIVISOR-DIVIDES-GCD GCD-IS-THE-GREATEST REMAINDER-GCD QUOTIENT-REMAINDER QUOTIENT-REMAINDER-TIMES REMAINDER-EQUALS-ITS-FIRST-ARGUMENT QUOTIENT-DIFFERENCE3 QUOTIENT-DIFFERENCE2 QUOTIENT-DIFFERENCE1 QUOTIENT-TIMES-PROOF REMAINDERS REMAINDER-REMAINDER EQUAL-REMAINDER-DIFFERENCE-0 REMAINDER-DIFFERENCE3 REMAINDER-DIFFERENCE2 REMAINDER-TIMES2-PROOF REMAINDER-TIMES-TIMES-PROOF REMAINDER-TIMES1-INSTANCE-PROOF) EVENT (PROVE-LEMMA REMAINDER-ZERO (REWRITE) (IMPLIES (ZEROP X) (EQUAL (REMAINDER Y X) (FIX Y))) ((ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((LEMMAS REMAINDER . REMAINDER-ZERO))))) (PUT1-LST (QUOTE REMAINDER-OF-NON-NUMBER) (QUOTE (IDATE 1000404112401 IMMEDIATE-DEPENDENTS0 (EQUAL-TIMES-TIMES-QUOTIENT-ARG2 TIMES-GCD-FACT GCD-REMAINDER-TIMES-FACT1-PROOF DIVIDES-EACH-EQUALITY DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3 QUOTIENT-DIFFERENCE-LESSP-ARG2 COMMON-DIVISOR-DIVIDES-GCD REMAINDER-GCD QUOTIENT-PLUS-FACT QUOTIENT-REMAINDER QUOTIENT-REMAINDER-TIMES QUOTIENT-DIFFERENCE3 QUOTIENT-DIFFERENCE2 QUOTIENT-DIFFERENCE1 REMAINDERS EQUAL-REMAINDER-DIFFERENCE-0 REMAINDER-DIFFERENCE3 REMAINDER-DIFFERENCE2) EVENT (PROVE-LEMMA REMAINDER-OF-NON-NUMBER (REWRITE) (IMPLIES (NOT (NUMBERP A)) (EQUAL (REMAINDER A N) (REMAINDER (QUOTE 0) N))) ((ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((LEMMAS REMAINDER . 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REMAINDER-NOOP))))) (PUT1-LST (QUOTE LESSP-REMAINDER) (QUOTE (IDATE 1000404112401 IMMEDIATE-DEPENDENTS0 (EQUAL-TIMES-TIMES-QUOTIENT-ARG2 TIMES-GCD-FACT DIVIDES-EACH-EQUALITY GCD-REMAINDER-FACT1 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2 DIVISION-THEOREM-PART3 DIVISION-THEOREM-PART2 COMMON-DIVISOR-DIVIDES-GCD GCD-IS-THE-GREATEST LOG-QUOTIENT-EXP LOG-QUOTIENT-TIMES-PROOF QUOTIENT-QUOTIENT QUOTIENT-REMAINDER QUOTIENT-REMAINDER-TIMES REMAINDER-EQUALS-ITS-FIRST-ARGUMENT QUOTIENT-DIFFERENCE3 QUOTIENT-DIFFERENCE2 QUOTIENT-DIFFERENCE1 QUOTIENT-TIMES-PROOF REMAINDERS EQUAL-REMAINDER-DIFFERENCE-0 REMAINDER-DIFFERENCE2 REMAINDER-DIFFERENCE1 REMAINDER-TIMES2-PROOF REMAINDER-SUB1) EVENT (PROVE-LEMMA LESSP-REMAINDER (REWRITE GENERALIZE) (EQUAL (LESSP (REMAINDER X Y) Y) (NOT (ZEROP Y))) ((ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((GENERALIZE-LEMMAS NIL . LESSP-REMAINDER) (LEMMAS LESSP . LESSP-REMAINDER))))) (PUT1-LST (QUOTE MULTIPLICATION) (QUOTE (IDATE 1000404112401 IMMEDIATE-DEPENDENTS0 (ITIMES-1-ARG1 EQUAL-ITIMES-MINUS-1 EQUAL-ITIMES-1 EQUAL-ITIMES-0 ITIMES-DISTRIBUTES-OVER-IDIFFERENCE-PROOF ASSOCIATIVITY-OF-ITIMES COMMUTATIVITY2-OF-ITIMES ITIMES-DISTRIBUTES-OVER-IPLUS-PROOF COMMUTATIVITY-OF-ITIMES ARITHMETIC COMMON-DIVISOR-DIVIDES-GCD GCD-IS-THE-GREATEST DISTRIBUTIVITY-OF-TIMES-OVER-GCD-PROOF LOG-EXP LOG-TIMES-EXP-PROOF LOG-TIMES-PROOF LOG-QUOTIENT-EXP LOG-QUOTIENT-TIMES-PROOF EXP-DIFFERENCE QUOTIENT-QUOTIENT QUOTIENT-PLUS-FACT QUOTIENT-REMAINDER QUOTIENT-REMAINDER-TIMES QUOTIENT-DIFFERENCE3 QUOTIENT-DIFFERENCE2 QUOTIENT-DIFFERENCE1 QUOTIENT-TIMES-TIMES-PROOF QUOTIENT-TIMES-PROOF REMAINDER-EXP-EXP REMAINDER-REMAINDER REMAINDER-PLUS-FACT REMAINDER-DIFFERENCE2 REMAINDER-TIMES2-PROOF REMAINDER-TIMES-TIMES-PROOF REMAINDER-TIMES1-PROOF) EVENT (DEFTHEORY MULTIPLICATION (EQUAL-SUB1-TIMES-0 LESSP-1-TIMES LESSP-PLUS-TIMES2 LESSP-PLUS-TIMES1 LESSP-TIMES-CANCELLATION2 LESSP-TIMES-CANCELLATION1 LESSP-TIMES3 LESSP-TIMES2 LESSP-TIMES1 TIMES-1-ARG1 EQUAL-TIMES-1 EQUAL-TIMES-0 TIMES-QUOTIENT TIMES-DISTRIBUTES-OVER-DIFFERENCE ASSOCIATIVITY-OF-TIMES COMMUTATIVITY2-OF-TIMES TIMES-DISTRIBUTES-OVER-PLUS COMMUTATIVITY-OF-TIMES TIMES-SUB1 TIMES-ADD1 TIMES-ZERO)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQUAL-SUB1-TIMES-0 . MULTIPLICATION) (IMMEDIATE-DEPENDENTS0 LESSP-1-TIMES . MULTIPLICATION) (IMMEDIATE-DEPENDENTS0 LESSP-PLUS-TIMES2 . MULTIPLICATION) (IMMEDIATE-DEPENDENTS0 LESSP-PLUS-TIMES1 . MULTIPLICATION) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES-CANCELLATION2 . MULTIPLICATION) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES-CANCELLATION1 . MULTIPLICATION) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES3 . MULTIPLICATION) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES2 . MULTIPLICATION) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES1 . MULTIPLICATION) (IMMEDIATE-DEPENDENTS0 TIMES-1-ARG1 . MULTIPLICATION) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-1 . MULTIPLICATION) (IMMEDIATE-DEPENDENTS0 EQUAL-TIMES-0 . MULTIPLICATION) (IMMEDIATE-DEPENDENTS0 TIMES-QUOTIENT . MULTIPLICATION) (IMMEDIATE-DEPENDENTS0 TIMES-DISTRIBUTES-OVER-DIFFERENCE . MULTIPLICATION) (IMMEDIATE-DEPENDENTS0 ASSOCIATIVITY-OF-TIMES . MULTIPLICATION) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-TIMES . MULTIPLICATION) (IMMEDIATE-DEPENDENTS0 TIMES-DISTRIBUTES-OVER-PLUS . MULTIPLICATION) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . MULTIPLICATION) (IMMEDIATE-DEPENDENTS0 TIMES-SUB1 . MULTIPLICATION) (IMMEDIATE-DEPENDENTS0 TIMES-ADD1 . MULTIPLICATION) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO . MULTIPLICATION))))) (PUT1-LST (QUOTE EQUAL-SUB1-TIMES-0) (QUOTE (IDATE 1000404112401 IMMEDIATE-DEPENDENTS0 (MULTIPLICATION) EVENT (PROVE-LEMMA EQUAL-SUB1-TIMES-0 (REWRITE) (EQUAL (EQUAL (SUB1 (TIMES A B)) (QUOTE 0)) (OR (ZEROP A) (OR (ZEROP B) (AND (EQUAL A (QUOTE 1)) (EQUAL B (QUOTE 1)))))) ((ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((LEMMAS EQUAL . EQUAL-SUB1-TIMES-0))))) (PUT1-LST (QUOTE LESSP-1-TIMES) (QUOTE (IDATE 1000404112400 IMMEDIATE-DEPENDENTS0 (MULTIPLICATION) EVENT (PROVE-LEMMA LESSP-1-TIMES (REWRITE) (EQUAL (LESSP (QUOTE 1) (TIMES A B)) (NOT (OR (ZEROP A) (OR (ZEROP B) (AND (EQUAL A (QUOTE 1)) (EQUAL B (QUOTE 1))))))) ((ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((LEMMAS LESSP . 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LESSP-PLUS-TIMES2))))) (PUT1-LST (QUOTE LESSP-PLUS-TIMES1) (QUOTE (IDATE 1000404112400 IMMEDIATE-DEPENDENTS0 (IQUO-IREM-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART3 DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2 DIVISION-THEOREM-PART3 QUOTIENT-DIFFERENCE3 QUOTIENT-DIFFERENCE2 QUOTIENT-TIMES-PROOF MULTIPLICATION) EVENT (PROVE-LEMMA LESSP-PLUS-TIMES1 (REWRITE) (AND (EQUAL (LESSP (PLUS A (TIMES B C)) B) (AND (LESSP A B) (ZEROP C))) (AND (EQUAL (LESSP (PLUS A (TIMES C B)) B) (AND (LESSP A B) (ZEROP C))) (AND (EQUAL (LESSP (PLUS (TIMES C B) A) B) (AND (LESSP A B) (ZEROP C))) (EQUAL (LESSP (PLUS (TIMES B C) A) B) (AND (LESSP A B) (ZEROP C)))))) ((USE (LESSP-PLUS-TIMES-PROOF (A B) (B C) (C (QUOTE 1)) (X A))) (ENABLE COMMUTATIVITY-OF-PLUS COMMUTATIVITY-OF-TIMES TIMES-1-ARG1) (DO-NOT-INDUCT T) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 TIMES-1-ARG1 . LESSP-PLUS-TIMES1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . LESSP-PLUS-TIMES1) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . LESSP-PLUS-TIMES1) (IMMEDIATE-DEPENDENTS0 LESSP-PLUS-TIMES-PROOF . LESSP-PLUS-TIMES1) (LEMMAS LESSP . LESSP-PLUS-TIMES1) (LEMMAS LESSP . LESSP-PLUS-TIMES1) (LEMMAS LESSP . LESSP-PLUS-TIMES1) (LEMMAS LESSP . LESSP-PLUS-TIMES1))))) (PUT1-LST (QUOTE LESSP-PLUS-TIMES-PROOF) (QUOTE (IDATE 1000404112400 IMMEDIATE-DEPENDENTS0 (LESSP-PLUS-TIMES2 LESSP-PLUS-TIMES1) EVENT (PROVE-LEMMA LESSP-PLUS-TIMES-PROOF NIL (IMPLIES (LESSP X A) (EQUAL (LESSP (PLUS X (TIMES A B)) (TIMES A C)) (LESSP B C))) ((ENABLE-THEORY ADDITION GROUND-ZERO) (ENABLE COMMUTATIVITY-OF-TIMES LESSP-TIMES-CANCELLATION1 LESSP-TIMES1 LESSP-TIMES2 LESSP-TIMES3 TIMES-ADD1 TIMES-ZERO) (INDUCT (LESSP B C)) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 CORRECTNESS-OF-CANCEL-LESSP-PLUS . LESSP-PLUS-TIMES-PROOF) (IMMEDIATE-DEPENDENTS0 TIMES-ADD1 . LESSP-PLUS-TIMES-PROOF) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-PLUS . LESSP-PLUS-TIMES-PROOF) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES1 . LESSP-PLUS-TIMES-PROOF) (IMMEDIATE-DEPENDENTS0 PLUS-STOPPER . LESSP-PLUS-TIMES-PROOF) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . LESSP-PLUS-TIMES-PROOF) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-TIMES . LESSP-PLUS-TIMES-PROOF) (IMMEDIATE-DEPENDENTS0 TIMES-ZERO . LESSP-PLUS-TIMES-PROOF) (IMMEDIATE-DEPENDENTS0 ADDITION . 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LESSP-TIMES-CANCELLATION2) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-TIMES . LESSP-TIMES-CANCELLATION2) (IMMEDIATE-DEPENDENTS0 LESSP-TIMES-CANCELLATION-PROOF . LESSP-TIMES-CANCELLATION2) (LEMMAS LESSP . LESSP-TIMES-CANCELLATION2) (LEMMAS LESSP . LESSP-TIMES-CANCELLATION2) (LEMMAS LESSP . LESSP-TIMES-CANCELLATION2) (LEMMAS LESSP . LESSP-TIMES-CANCELLATION2) (LEMMAS LESSP . LESSP-TIMES-CANCELLATION2) (LEMMAS LESSP . LESSP-TIMES-CANCELLATION2) (LEMMAS LESSP . LESSP-TIMES-CANCELLATION2) (LEMMAS LESSP . 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MEMBER-IMPLIES-NUMBERP) (IMMEDIATE-DEPENDENTS0 PLUS-FRINGE . MEMBER-IMPLIES-NUMBERP) (LEMMAS NUMBERP . MEMBER-IMPLIES-NUMBERP))))) (PUT1-LST (QUOTE PLUS-TREE-PLUS-FRINGE) (QUOTE (IDATE 1000404112357 IMMEDIATE-DEPENDENTS0 (PLUS-TREE-PLUS-FRINGE-OFF CORRECTNESS-OF-CANCEL-LESSP-PLUS CORRECTNESS-OF-CANCEL-DIFFERENCE-PLUS CORRECTNESS-OF-CANCEL-EQUAL-PLUS) EVENT (PROVE-LEMMA PLUS-TREE-PLUS-FRINGE (REWRITE) (EQUAL (EVAL$ (QUOTE *1*TRUE) (PLUS-TREE (PLUS-FRINGE X)) A) (FIX (EVAL$ (QUOTE *1*TRUE) X A))) ((ENABLE PLUS-RIGHT-ID2 COMMUTATIVITY-OF-PLUS PLUS-FRINGE PLUS-TREE NUMBERP-EVAL$-PLUS NUMBERP-EVAL$-BRIDGE EVAL$-PLUS-TREE-APPEND) (INDUCT (PLUS-FRINGE X)) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 NUMBERP-EVAL$-BRIDGE . PLUS-TREE-PLUS-FRINGE) (IMMEDIATE-DEPENDENTS0 PLUS-RIGHT-ID2 . PLUS-TREE-PLUS-FRINGE) (IMMEDIATE-DEPENDENTS0 EVAL$-PLUS-TREE-APPEND . PLUS-TREE-PLUS-FRINGE) (IMMEDIATE-DEPENDENTS0 NUMBERP-EVAL$-PLUS . PLUS-TREE-PLUS-FRINGE) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . PLUS-TREE-PLUS-FRINGE) (IMMEDIATE-DEPENDENTS0 PLUS-FRINGE . PLUS-TREE-PLUS-FRINGE) (IMMEDIATE-DEPENDENTS0 PLUS-TREE . PLUS-TREE-PLUS-FRINGE) (LEMMAS EVAL$ . PLUS-TREE-PLUS-FRINGE))))) (PUT1-LST (QUOTE EVAL$-PLUS-TREE-APPEND) (QUOTE (IDATE 1000404112354 IMMEDIATE-DEPENDENTS0 (EVAL$-PLUS-TREE-APPEND-OFF PLUS-TREE-PLUS-FRINGE) EVENT (PROVE-LEMMA EVAL$-PLUS-TREE-APPEND (REWRITE) (EQUAL (EVAL$ (QUOTE *1*TRUE) (PLUS-TREE (APPEND X Y)) A) (PLUS (EVAL$ (QUOTE *1*TRUE) (PLUS-TREE X) A) (EVAL$ (QUOTE *1*TRUE) (PLUS-TREE Y) A))) ((ENABLE PLUS-RIGHT-ID2 COMMUTATIVITY2-OF-PLUS COMMUTATIVITY-OF-PLUS EQUAL-PLUS-0 PLUS-CANCELLATION PLUS-TREE NUMBERP-EVAL$-PLUS-TREE NUMBERP-EVAL$-BRIDGE) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-PLUS . EVAL$-PLUS-TREE-APPEND) (IMMEDIATE-DEPENDENTS0 NUMBERP-EVAL$-BRIDGE . EVAL$-PLUS-TREE-APPEND) (IMMEDIATE-DEPENDENTS0 PLUS-RIGHT-ID2 . EVAL$-PLUS-TREE-APPEND) (IMMEDIATE-DEPENDENTS0 PLUS-CANCELLATION . EVAL$-PLUS-TREE-APPEND) (IMMEDIATE-DEPENDENTS0 NUMBERP-EVAL$-PLUS-TREE . EVAL$-PLUS-TREE-APPEND) (IMMEDIATE-DEPENDENTS0 EQUAL-PLUS-0 . EVAL$-PLUS-TREE-APPEND) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . EVAL$-PLUS-TREE-APPEND) (IMMEDIATE-DEPENDENTS0 PLUS-TREE . EVAL$-PLUS-TREE-APPEND) (LEMMAS EVAL$ . EVAL$-PLUS-TREE-APPEND))))) (PUT1-LST (QUOTE BRIDGE-TO-SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP) (QUOTE (IDATE 1000404112347 IMMEDIATE-DEPENDENTS0 (BRIDGE-TO-SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP-OFF CORRECTNESS-OF-CANCEL-LESSP-PLUS CORRECTNESS-OF-CANCEL-DIFFERENCE-PLUS CORRECTNESS-OF-CANCEL-EQUAL-PLUS) EVENT (PROVE-LEMMA BRIDGE-TO-SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP (REWRITE) (IMPLIES (AND (SUBBAGP Y (PLUS-FRINGE Z)) (EQUAL (EVAL$ (QUOTE *1*TRUE) Z A) (EVAL$ (QUOTE *1*TRUE) (PLUS-TREE (PLUS-FRINGE Z)) A))) (EQUAL (LESSP (EVAL$ (QUOTE *1*TRUE) Z A) (EVAL$ (QUOTE *1*TRUE) (PLUS-TREE Y) A)) (QUOTE *1*FALSE))) ((ENABLE SUBBAGP PLUS-FRINGE PLUS-TREE SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) 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-EVAL$-BRIDGE) (QUOTE (IDATE 1000404112347 IMMEDIATE-DEPENDENTS0 (NUMBERP-EVAL$-BRIDGE-OFF PLUS-TREE-PLUS-FRINGE EVAL$-PLUS-TREE-APPEND) EVENT (PROVE-LEMMA NUMBERP-EVAL$-BRIDGE (REWRITE) (IMPLIES (EQUAL (EVAL$ (QUOTE *1*TRUE) Z A) (EVAL$ (QUOTE *1*TRUE) (PLUS-TREE X) A)) (NUMBERP (EVAL$ (QUOTE *1*TRUE) Z A))) ((ENABLE PLUS-TREE NUMBERP-EVAL$-PLUS-TREE) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 NUMBERP-EVAL$-PLUS-TREE . NUMBERP-EVAL$-BRIDGE) (IMMEDIATE-DEPENDENTS0 PLUS-TREE . NUMBERP-EVAL$-BRIDGE) (LEMMAS NUMBERP . NUMBERP-EVAL$-BRIDGE))))) (PUT1-LST (QUOTE PLUS-TREE-BAGDIFF) (QUOTE (IDATE 1000404112341 IMMEDIATE-DEPENDENTS0 (PLUS-TREE-BAGDIFF-OFF CORRECTNESS-OF-CANCEL-LESSP-PLUS CORRECTNESS-OF-CANCEL-DIFFERENCE-PLUS CORRECTNESS-OF-CANCEL-EQUAL-PLUS) EVENT (PROVE-LEMMA PLUS-TREE-BAGDIFF (REWRITE) (IMPLIES (SUBBAGP X Y) (EQUAL (EVAL$ (QUOTE *1*TRUE) (PLUS-TREE (BAGDIFF Y X)) A) (DIFFERENCE (EVAL$ (QUOTE *1*TRUE) (PLUS-TREE Y) A) (EVAL$ (QUOTE *1*TRUE) (PLUS-TREE X) A)))) ((ENABLE SUBBAGP BAGDIFF PLUS-TREE PLUS-RIGHT-ID2 COMMUTATIVITY-OF-PLUS DIFFERENCE-DIFFERENCE-ARG1 DIFFERENCE-LEQ-ARG1 NUMBERP-EVAL$-PLUS-TREE MEMBER-IMPLIES-PLUS-TREE-GREATEREQP PLUS-TREE-DELETE SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP) (ENABLE-THEORY SETS-AND-BAGS GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 MEMBER-IMPLIES-PLUS-TREE-GREATEREQP . PLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 PLUS-RIGHT-ID2 . PLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . PLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP . PLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-LEQ-ARG1 . PLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 SUBBAGP-CDR2 . PLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 NUMBERP-EVAL$-PLUS-TREE . PLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 PLUS-TREE-DELETE . PLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-DIFFERENCE-ARG1 . PLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 SETS-AND-BAGS . PLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 BAGDIFF . PLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 PLUS-TREE . PLUS-TREE-BAGDIFF) (IMMEDIATE-DEPENDENTS0 SUBBAGP . PLUS-TREE-BAGDIFF) (LEMMAS EVAL$ . PLUS-TREE-BAGDIFF))))) (PUT1-LST (QUOTE SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP) (QUOTE (IDATE 1000404112332 IMMEDIATE-DEPENDENTS0 (SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP-OFF 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 (EVAL$ (QUOTE *1*TRUE) (PLUS-TREE Y) A) (EVAL$ (QUOTE *1*TRUE) (PLUS-TREE X) A)))) ((ENABLE PLUS-TREE PLUS-RIGHT-ID2 SUBBAGP SUBBAGP-CDR2 MEMBER-IMPLIES-PLUS-TREE-GREATEREQP PLUS-TREE-DELETE) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) 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 EVAL$ . SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP) (LINEAR-LEMMAS EVAL$ . SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP))))) (PUT1-LST (QUOTE PLUS-TREE-DELETE) (QUOTE (IDATE 1000404112331 IMMEDIATE-DEPENDENTS0 (PLUS-TREE-DELETE-OFF CORRECTNESS-OF-CANCEL-LESSP-PLUS CORRECTNESS-OF-CANCEL-DIFFERENCE-PLUS CORRECTNESS-OF-CANCEL-EQUAL-PLUS PLUS-TREE-BAGDIFF SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP) EVENT (PROVE-LEMMA PLUS-TREE-DELETE (REWRITE) (EQUAL (EVAL$ (QUOTE *1*TRUE) (PLUS-TREE (DELETE X Y)) A) (IF (MEMBER X Y) (DIFFERENCE (EVAL$ (QUOTE *1*TRUE) (PLUS-TREE Y) A) (EVAL$ (QUOTE *1*TRUE) X A)) (EVAL$ (QUOTE *1*TRUE) (PLUS-TREE Y) A))) ((ENABLE DELETE PLUS-TREE PLUS-RIGHT-ID2 COMMUTATIVITY-OF-PLUS EQUAL-PLUS-0 DIFFERENCE-PLUS DIFFERENCE-LEQ-ARG1 EQUAL-DIFFERENCE-0 DIFFERENCE-CANCELLATION-0 NUMBERP-EVAL$-PLUS-TREE MEMBER-IMPLIES-PLUS-TREE-GREATEREQP) (ENABLE-THEORY SETS-AND-BAGS GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 EQUAL-PLUS-0 . PLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 PLUS-RIGHT-ID2 . PLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 MEMBER-IMPLIES-PLUS-TREE-GREATEREQP . PLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE-0 . PLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-CANCELLATION-0 . PLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 LISTP-DELETE . PLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 NUMBERP-EVAL$-PLUS-TREE . PLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-PLUS . PLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-LEQ-ARG1 . PLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 MEMBER-NON-LIST . PLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE-NON-MEMBER . PLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 SETS-AND-BAGS . PLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE . PLUS-TREE-DELETE) (IMMEDIATE-DEPENDENTS0 PLUS-TREE . PLUS-TREE-DELETE) (LEMMAS EVAL$ . PLUS-TREE-DELETE))))) (PUT1-LST (QUOTE MEMBER-IMPLIES-PLUS-TREE-GREATEREQP) (QUOTE (IDATE 1000404112315 IMMEDIATE-DEPENDENTS0 (MEMBER-IMPLIES-PLUS-TREE-GREATEREQP-OFF CORRECTNESS-OF-CANCEL-LESSP-PLUS CORRECTNESS-OF-CANCEL-DIFFERENCE-PLUS CORRECTNESS-OF-CANCEL-EQUAL-PLUS 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 (EVAL$ (QUOTE *1*TRUE) (PLUS-TREE Y) A) (EVAL$ (QUOTE *1*TRUE) X A)))) ((ENABLE PLUS-RIGHT-ID2 PLUS-TREE) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PLUS-RIGHT-ID2 . MEMBER-IMPLIES-PLUS-TREE-GREATEREQP) (IMMEDIATE-DEPENDENTS0 PLUS-TREE . MEMBER-IMPLIES-PLUS-TREE-GREATEREQP) (LINEAR-LEMMAS EVAL$ . MEMBER-IMPLIES-PLUS-TREE-GREATEREQP) (LINEAR-LEMMAS EVAL$ . MEMBER-IMPLIES-PLUS-TREE-GREATEREQP))))) (PUT1-LST (QUOTE NUMBERP-EVAL$-PLUS-TREE) (QUOTE (IDATE 1000404112314 IMMEDIATE-DEPENDENTS0 (NUMBERP-EVAL$-PLUS-TREE-OFF EVAL$-PLUS-TREE-APPEND NUMBERP-EVAL$-BRIDGE PLUS-TREE-BAGDIFF PLUS-TREE-DELETE) EVENT (PROVE-LEMMA NUMBERP-EVAL$-PLUS-TREE (REWRITE) (NUMBERP (EVAL$ (QUOTE *1*TRUE) (PLUS-TREE L) A)) ((ENABLE PLUS-TREE) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 PLUS-TREE . NUMBERP-EVAL$-PLUS-TREE) (LEMMAS NUMBERP . NUMBERP-EVAL$-PLUS-TREE))))) (PUT1-LST (QUOTE NUMBERP-EVAL$-PLUS) (QUOTE (IDATE 1000404112313 IMMEDIATE-DEPENDENTS0 (NUMBERP-EVAL$-PLUS-OFF CORRECTNESS-OF-CANCEL-LESSP-PLUS CORRECTNESS-OF-CANCEL-DIFFERENCE-PLUS CORRECTNESS-OF-CANCEL-EQUAL-PLUS MEMBER-IMPLIES-NUMBERP PLUS-TREE-PLUS-FRINGE) EVENT (PROVE-LEMMA NUMBERP-EVAL$-PLUS (REWRITE) (IMPLIES (AND (LISTP X) (EQUAL (CAR X) (QUOTE PLUS))) (NUMBERP (EVAL$ (QUOTE *1*TRUE) X A))) ((ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((LEMMAS NUMBERP . NUMBERP-EVAL$-PLUS))))) (PUT1-LST (QUOTE *1*PLUS-TREE) (QUOTE (MAIN-EVENT PLUS-TREE))) (PUT1-LST (QUOTE PLUS-TREE) (QUOTE (TYPE-PRESCRIPTION-LST ((PLUS-TREE 16 NIL)) TOTALP-LST ((PLUS-TREE . T)) QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (L) (IF (LISTP L) (IF (LISTP (CDR L)) (IF (LISTP (CDR (CDR L))) (CONS (QUOTE PLUS) (CONS (CAR L) (CONS (PLUS-TREE (CDR L)) (QUOTE NIL)))) (CONS (QUOTE PLUS) (CONS (CAR L) (CONS (CAR (CDR L)) (QUOTE NIL))))) (CONS (QUOTE FIX) (CONS (CAR L) (QUOTE NIL)))) (QUOTE (QUOTE 0)))) LISP-CODE *1*PLUS-TREE SUBRP *1*FALSE INDUCTION-MACHINE ((TESTS-AND-CASES ((NLISTP L)) NIL) (TESTS-AND-CASES ((NOT (NLISTP L)) (NLISTP (CDR L))) NIL) (TESTS-AND-CASES ((NOT (NLISTP L)) (NOT (NLISTP (CDR L))) (NLISTP (CDR (CDR L)))) NIL) (TESTS-AND-CASES ((NOT (NLISTP L)) (NOT (NLISTP (CDR L))) (NOT (NLISTP (CDR (CDR L))))) (((CDR L))))) LEVEL-NO 1 JUSTIFICATIONS ((JUSTIFICATION (L) (COUNT L) LESSP (CDR-LESSP NLISTP ZERO CDR-LESSEQP))) IDATE 1000404112313 CONTROLLER-POCKETS (1) SATELLITES (*1*PLUS-TREE) IMMEDIATE-DEPENDENTS0 (CANCEL-LESSP-PLUS CANCEL-DIFFERENCE-PLUS CANCEL-EQUAL-PLUS PLUS-TREE-PLUS-FRINGE EVAL$-PLUS-TREE-APPEND BRIDGE-TO-SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP NUMBERP-EVAL$-BRIDGE PLUS-TREE-BAGDIFF SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP PLUS-TREE-DELETE MEMBER-IMPLIES-PLUS-TREE-GREATEREQP NUMBERP-EVAL$-PLUS-TREE) EVENT (DEFN PLUS-TREE (L) (IF (NLISTP L) (QUOTE (QUOTE 0)) (IF (NLISTP (CDR L)) (CONS (QUOTE FIX) (CONS (CAR L) (QUOTE NIL))) (IF (NLISTP (CDR (CDR L))) (CONS (QUOTE PLUS) (CONS (CAR L) (CONS (CAR (CDR L)) (QUOTE NIL)))) (CONS (QUOTE PLUS) (CONS (CAR L) (CONS (PLUS-TREE (CDR L)) (QUOTE NIL)))))))) LOCAL-UNDO-TUPLES ((DCELL . *1*PLUS-TREE))))) (PUT1-LST (QUOTE *1*PLUS-FRINGE) (QUOTE (MAIN-EVENT PLUS-FRINGE))) (PUT1-LST (QUOTE PLUS-FRINGE) (QUOTE (TYPE-PRESCRIPTION-LST ((PLUS-FRINGE 16 NIL)) TOTALP-LST ((PLUS-FRINGE . T)) 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 *1*PLUS-FRINGE SUBRP *1*FALSE 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 1000404112313 CONTROLLER-POCKETS (1) SATELLITES (*1*PLUS-FRINGE) IMMEDIATE-DEPENDENTS0 (CANCEL-LESSP-PLUS CANCEL-DIFFERENCE-PLUS CANCEL-EQUAL-PLUS MEMBER-IMPLIES-NUMBERP PLUS-TREE-PLUS-FRINGE BRIDGE-TO-SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP) EVENT (DEFN PLUS-FRINGE (X) (IF (AND (LISTP X) (EQUAL (CAR X) (QUOTE PLUS))) (APPEND (PLUS-FRINGE (CAR (CDR X))) (PLUS-FRINGE (CAR (CDR (CDR X))))) (CONS X (QUOTE NIL)))) LOCAL-UNDO-TUPLES ((DCELL . *1*PLUS-FRINGE))))) (PUT1-LST (QUOTE DIFFERENCE-PLUS-CANCELLATION3) (QUOTE (IDATE 1000404112313 IMMEDIATE-DEPENDENTS0 (DIFFERENCE-PLUS-CANCELLATION3-OFF CORRECTNESS-OF-CANCEL-DIFFERENCE-PLUS) EVENT (PROVE-LEMMA DIFFERENCE-PLUS-CANCELLATION3 (REWRITE) (EQUAL (DIFFERENCE (PLUS W (PLUS X A)) (PLUS Y (PLUS Z A))) (DIFFERENCE (PLUS W X) (PLUS Y Z))) ((ENABLE COMMUTATIVITY2-OF-PLUS COMMUTATIVITY-OF-PLUS DIFFERENCE-PLUS-CANCELLATION1) (DO-NOT-INDUCT T) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . DIFFERENCE-PLUS-CANCELLATION3) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY2-OF-PLUS . DIFFERENCE-PLUS-CANCELLATION3) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-PLUS-CANCELLATION1 . DIFFERENCE-PLUS-CANCELLATION3) (LEMMAS DIFFERENCE . DIFFERENCE-PLUS-CANCELLATION3))))) (PUT1-LST (QUOTE DIFFERENCE-DIFFERENCE-DIFFERENCE) (QUOTE (IDATE 1000404112313 IMMEDIATE-DEPENDENTS0 (DIFFERENCE-DIFFERENCE-DIFFERENCE-OFF DIFF-DIFF-DIFF-CASESPLIT CORRECTNESS-OF-CANCEL-DIFFERENCE-PLUS) EVENT (PROVE-LEMMA DIFFERENCE-DIFFERENCE-DIFFERENCE (REWRITE) (IMPLIES (AND (IF (LESSP A B) (QUOTE *1*FALSE) (QUOTE *1*TRUE)) (IF (LESSP C D) (QUOTE *1*FALSE) (QUOTE *1*TRUE))) (EQUAL (DIFFERENCE (DIFFERENCE A B) (DIFFERENCE C D)) (DIFFERENCE (PLUS A D) (PLUS B C)))) ((ENABLE COMMUTATIVITY-OF-PLUS DIFFERENCE-SUB1-ARG2 DIFFERENCE-DIFFERENCE-ARG2 EQUAL-DIFFERENCE-0 PLUS-RIGHT-ID2) (INDUCT (DIFFERENCE A B)) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DIFFERENCE-SUB1-ARG2 . DIFFERENCE-DIFFERENCE-DIFFERENCE) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PLUS . DIFFERENCE-DIFFERENCE-DIFFERENCE) (IMMEDIATE-DEPENDENTS0 EQUAL-DIFFERENCE-0 . DIFFERENCE-DIFFERENCE-DIFFERENCE) (IMMEDIATE-DEPENDENTS0 PLUS-RIGHT-ID2 . DIFFERENCE-DIFFERENCE-DIFFERENCE) (IMMEDIATE-DEPENDENTS0 DIFFERENCE-DIFFERENCE-ARG2 . DIFFERENCE-DIFFERENCE-DIFFERENCE) (LEMMAS DIFFERENCE . 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COMMUTATIVITY-OF-PLUS))))) (PUT1-LST (QUOTE COMMUTATIVITY2-OF-PLUS) (QUOTE (IDATE 1000404112312 IMMEDIATE-DEPENDENTS0 (COMMUTATIVITY2-OF-IPLUS QUOTIENT-PLUS EQUAL-REMAINDER-PLUS-0 REMAINDER-PLUS PLUS-REMAINDER-TIMES-QUOTIENT LESSP-PLUS-TIMES-PROOF TIMES-DISTRIBUTES-OVER-PLUS-PROOF ADDITION EVAL$-PLUS-TREE-APPEND DIFFERENCE-PLUS-CANCELLATION3) EVENT (PROVE-LEMMA COMMUTATIVITY2-OF-PLUS (REWRITE) (EQUAL (PLUS X (PLUS Y Z)) (PLUS Y (PLUS X Z))) ((ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((LEMMAS PLUS . COMMUTATIVITY2-OF-PLUS))))) (PUT1-LST (QUOTE PLUS-ADD1) (QUOTE (IDATE 1000404112312 IMMEDIATE-DEPENDENTS0 (QUOTIENT-PLUS-PROOF QUOTIENT-SUB1 ADDITION) EVENT (PROVE-LEMMA PLUS-ADD1 (REWRITE) (EQUAL (PLUS X (ADD1 Y)) (IF (NUMBERP Y) (ADD1 (PLUS X Y)) (ADD1 X))) ((ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((LEMMAS PLUS . PLUS-ADD1))))) (PUT1-LST (QUOTE PLUS-RIGHT-ID2) (QUOTE (IDATE 1000404112312 IMMEDIATE-DEPENDENTS0 (EQUAL-PLUS-DIFFERENCE-REWRITE REQUAL-RNEG-SIMPLE-RPLUS ITIMES-DISTRIBUTES-OVER-IDIFFERENCE-PROOF ITIMES-DISTRIBUTES-OVER-IPLUS-PROOF IDIFFERENCE-IDIFFERENCE IDIFFERENCE-IPLUS IPLUS-FIX-INT2 IPLUS-CANCELLATION ASSOCIATIVITY-OF-IPLUS IPLUS-RIGHT-ID INEG-IDIFFERENCE INEG-IPLUS GCD-PLUS-INSTANCE-TEMP-PROOF LOG-QUOTIENT-TIMES-PROOF QUOTIENT-PLUS-PROOF REMAINDER-PLUS-FACT LESSP-PLUS-FACT EQUAL-REMAINDER-DIFFERENCE-0 EQUAL-REMAINDER-PLUS-REMAINDER-PROOF REMAINDER-PLUS-PROOF TIMES-DISTRIBUTES-OVER-DIFFERENCE-PROOF TIMES-ADD1 TIMES-ZERO ADDITION PLUS-TREE-PLUS-FRINGE EVAL$-PLUS-TREE-APPEND PLUS-TREE-BAGDIFF SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP PLUS-TREE-DELETE MEMBER-IMPLIES-PLUS-TREE-GREATEREQP DIFFERENCE-DIFFERENCE-DIFFERENCE DIFFERENCE-DIFFERENCE-ARG2 DIFFERENCE-PLUS PLUS-DIFFERENCE-DIFFERENCE-CASESPLIT PLUS-CANCELLATION EQUAL-PLUS-0) EVENT (PROVE-LEMMA PLUS-RIGHT-ID2 (REWRITE) (IMPLIES (ZEROP Y) (EQUAL (PLUS X Y) (FIX X))) ((INDUCT (PLUS X Y)) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((LEMMAS PLUS . PLUS-RIGHT-ID2))))) (PUT1-LST (QUOTE PLUS-STOPPER) (QUOTE (IDATE 1000404112312 IMMEDIATE-DEPENDENTS0 (REQUAL-SIMPLE-RPLUS-X-X-REWRITE EQUAL-PLUS-DIFFERENCE-REWRITE EQUAL-DIFFERENCE-REWRITE OCCURRENCES-APPEND REQUAL-RZEROP-SIMPLE-RPLUS SIMPLE-RPLUS-RZEROP REQUAL-RNEG-SIMPLE-RPLUS RPLUS-OPEN-UP EQUAL-TIMES-TIMES-QUOTIENT-ARG2 TIMES-GCD-FACT DIVIDES-PRODUCT-REDUCTION DPR-HACK2 GCD-FACTORS-GIVES-LINEAR-COMBINATION DIVIDES-EACH-EQUALITY GCD-REMAINDER-FACT1 IQUO-IREM-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-ZERO-PART2 IDIV-IMOD-UNIQUENESS DIVISION-THEOREM-FOR-TRUNCATE-TO-NEGINF-PART2 IQUOTIENT-IREMAINDER-UNIQUENESS DIVISION-THEOREM-PART3 DIVISION-THEOREM-PART2 QUOTIENT-REMAINDER-UNIQUENESS ITIMES-DISTRIBUTES-OVER-IDIFFERENCE-PROOF ITIMES-DISTRIBUTES-OVER-IPLUS-PROOF IPLUS-CANCELLATION ASSOCIATIVITY-OF-IPLUS COMMON-DIVISOR-DIVIDES-GCD GCD-IS-THE-GREATEST GCD-PLUS-PROOF GCD-PLUS-INSTANCE-TEMP-PROOF LOG-TIMES-EXP-PROOF LOG-QUOTIENT-EXP QUOTIENT-QUOTIENT QUOTIENT-PLUS-FACT QUOTIENT-REMAINDER QUOTIENT-REMAINDER-TIMES QUOTIENT-DIFFERENCE3 QUOTIENT-DIFFERENCE2 QUOTIENT-DIFFERENCE1 QUOTIENT-TIMES-PROOF QUOTIENT-PLUS-PROOF QUOTIENT-SUB1 REMAINDER-PLUS-FACT LESSP-PLUS-FACT EQUAL-REMAINDER-DIFFERENCE-0 REMAINDER-TIMES2-PROOF EQUAL-REMAINDER-PLUS-REMAINDER-PROOF REMAINDER-PLUS-PROOF REMAINDER-SUB1 LESSP-PLUS-TIMES-PROOF ADDITION) EVENT (PROVE-LEMMA PLUS-STOPPER (REWRITE) (IMPLIES (ZEROP A) (EQUAL (PLUS A B) (FIX B))) ((ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((LEMMAS PLUS . PLUS-STOPPER))))) (PUT1-LST (QUOTE OPEN-PLUS) (QUOTE (IDATE 1000404112312 IMMEDIATE-DEPENDENTS0 (OPEN-PLUS-OFF) EVENT (PROVE-LEMMA OPEN-PLUS (REWRITE) (EQUAL (PLUS (ADD1 A) B) (ADD1 (PLUS A B))) ((ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((LEMMAS PLUS . OPEN-PLUS))))) (PUT1-LST (QUOTE SETS-AND-BAGS) (QUOTE (IDATE 1000404112312 IMMEDIATE-DEPENDENTS0 (MEMBER-SUBBAGP2 SUBBAGP-TRANSITIVE SUBBAGP-NECC SUBBAGP-APPEND OCCURRENCES-APPEND SUBBAGP-WIT-LEMMA OCCURRENCES-DELETE2 CORRECTNESS-OF-CANCEL-IDIFFERENCE CORRECTNESS-OF-CANCEL-IPLUS IPLUS-TREE-BAGDIFF IPLUS-TREE-DELETE CORRECTNESS-OF-CANCEL-LESSP-PLUS CORRECTNESS-OF-CANCEL-DIFFERENCE-PLUS CORRECTNESS-OF-CANCEL-EQUAL-PLUS PLUS-TREE-BAGDIFF PLUS-TREE-DELETE) EVENT (DEFTHEORY SETS-AND-BAGS (SUBBAGP-BAGINT2 SUBBAGP-BAGINT1 SUBBAGP-CDR2 SUBBAGP-CDR1 SUBBAGP-DELETE SETP-DELETE PERMUTATION-DELETE-DELETE PERMUTATION-REFLEXIVITY COMMUTATIVITY-OF-PERMUTATION PERMUTATION-RIGHT-CONS PERMUTATION-RIGHT-CONS1 NOT-PERMUTATION MEMBER-BAGINT MEMBER-BAGDIFF MEMBER-DELETE MEMBER-DELETE-IMPLIES-MEMBERSHIP MEMBER-CONS MEMBER-NON-LIST OCCURRENCES-BAGINT OCCURRENCES-BAGDIFF OCCURRENCES-DELETE OCCURRENCES-CONS OCCURRENCES-IN-A-SET EQUAL-OCCURRENCES-ZERO DELETE-DELETE DELETE-NON-MEMBER LISTP-DELETE)) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SUBBAGP-BAGINT2 . SETS-AND-BAGS) (IMMEDIATE-DEPENDENTS0 SUBBAGP-BAGINT1 . SETS-AND-BAGS) (IMMEDIATE-DEPENDENTS0 SUBBAGP-CDR2 . SETS-AND-BAGS) (IMMEDIATE-DEPENDENTS0 SUBBAGP-CDR1 . SETS-AND-BAGS) (IMMEDIATE-DEPENDENTS0 SUBBAGP-DELETE . SETS-AND-BAGS) (IMMEDIATE-DEPENDENTS0 SETP-DELETE . SETS-AND-BAGS) (IMMEDIATE-DEPENDENTS0 PERMUTATION-DELETE-DELETE . SETS-AND-BAGS) (IMMEDIATE-DEPENDENTS0 PERMUTATION-REFLEXIVITY . SETS-AND-BAGS) (IMMEDIATE-DEPENDENTS0 COMMUTATIVITY-OF-PERMUTATION . SETS-AND-BAGS) (IMMEDIATE-DEPENDENTS0 PERMUTATION-RIGHT-CONS . SETS-AND-BAGS) (IMMEDIATE-DEPENDENTS0 PERMUTATION-RIGHT-CONS1 . SETS-AND-BAGS) (IMMEDIATE-DEPENDENTS0 NOT-PERMUTATION . SETS-AND-BAGS) (IMMEDIATE-DEPENDENTS0 MEMBER-BAGINT . SETS-AND-BAGS) (IMMEDIATE-DEPENDENTS0 MEMBER-BAGDIFF . SETS-AND-BAGS) (IMMEDIATE-DEPENDENTS0 MEMBER-DELETE . SETS-AND-BAGS) (IMMEDIATE-DEPENDENTS0 MEMBER-DELETE-IMPLIES-MEMBERSHIP . SETS-AND-BAGS) (IMMEDIATE-DEPENDENTS0 MEMBER-CONS . SETS-AND-BAGS) (IMMEDIATE-DEPENDENTS0 MEMBER-NON-LIST . SETS-AND-BAGS) (IMMEDIATE-DEPENDENTS0 OCCURRENCES-BAGINT . SETS-AND-BAGS) (IMMEDIATE-DEPENDENTS0 OCCURRENCES-BAGDIFF . SETS-AND-BAGS) (IMMEDIATE-DEPENDENTS0 OCCURRENCES-DELETE . SETS-AND-BAGS) (IMMEDIATE-DEPENDENTS0 OCCURRENCES-CONS . SETS-AND-BAGS) (IMMEDIATE-DEPENDENTS0 OCCURRENCES-IN-A-SET . SETS-AND-BAGS) (IMMEDIATE-DEPENDENTS0 EQUAL-OCCURRENCES-ZERO . SETS-AND-BAGS) (IMMEDIATE-DEPENDENTS0 DELETE-DELETE . SETS-AND-BAGS) (IMMEDIATE-DEPENDENTS0 DELETE-NON-MEMBER . SETS-AND-BAGS) (IMMEDIATE-DEPENDENTS0 LISTP-DELETE . SETS-AND-BAGS))))) (PUT1-LST (QUOTE SUBBAGP-BAGINT2) (QUOTE (IDATE 1000404112312 IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-CANCEL-RPLUS CORRECTNESS-OF-CANCEL-EQUAL-TIMES CANCEL-EQUAL-TIMES-PRESERVES-INEQUALITY-BRIDGE ZEROP-MAKES-EQUAL-TRUE-BRIDGE CORRECTNESS-OF-CANCEL-QUOTIENT-TIMES ZEROP-MAKES-QUOTIENT-ZERO-BRIDGE CORRECTNESS-OF-CANCEL-LESSP-TIMES ZEROP-MAKES-LESSP-FALSE-BRIDGE CORRECTNESS-OF-CANCEL-IDIFFERENCE CORRECTNESS-OF-CANCEL-IPLUS CORRECTNESS-OF-CANCEL-LESSP-PLUS CORRECTNESS-OF-CANCEL-DIFFERENCE-PLUS CORRECTNESS-OF-CANCEL-EQUAL-PLUS SETS-AND-BAGS) EVENT (PROVE-LEMMA SUBBAGP-BAGINT2 (REWRITE) (SUBBAGP (BAGINT X Y) Y) ((ENABLE SUBBAGP BAGINT SUBBAGP-CDR2) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) 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 (IDATE 1000404112312 IMMEDIATE-DEPENDENTS0 (CORRECTNESS-OF-CANCEL-RPLUS CORRECTNESS-OF-CANCEL-EQUAL-TIMES CANCEL-EQUAL-TIMES-PRESERVES-INEQUALITY-BRIDGE ZEROP-MAKES-EQUAL-TRUE-BRIDGE CORRECTNESS-OF-CANCEL-QUOTIENT-TIMES ZEROP-MAKES-QUOTIENT-ZERO-BRIDGE CORRECTNESS-OF-CANCEL-LESSP-TIMES ZEROP-MAKES-LESSP-FALSE-BRIDGE CORRECTNESS-OF-CANCEL-IDIFFERENCE CORRECTNESS-OF-CANCEL-IPLUS CORRECTNESS-OF-CANCEL-LESSP-PLUS CORRECTNESS-OF-CANCEL-DIFFERENCE-PLUS CORRECTNESS-OF-CANCEL-EQUAL-PLUS SETS-AND-BAGS) EVENT (PROVE-LEMMA SUBBAGP-BAGINT1 (REWRITE) (SUBBAGP (BAGINT X Y) X) ((ENABLE DELETE SUBBAGP BAGINT SUBBAGP-CDR2) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) 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 (IDATE 1000404112312 IMMEDIATE-DEPENDENTS0 (SUBBAGP-X-X SUBBAGP-APPEND-BRIDGE SUBBAGP-APPEND-SIMPLIFY1 MEMBER-SUBBAGP-DELETE SUBBAGP-MAKE-NEGS APPEND-BAGDIFF-ARG1 PERMUTATION-AS-SUBBAGP NOT-SUBBAGP-NOT-PERMUTATION SUBBAGP-PERMUTATION SUBBAGP-DELETE-CAR2 SUBBAGP-DELETE-CAR SUBBAGP-DELETE-SAME-MEANS SUBBAGP-DELETE-SAME CANCEL-EQUAL-TIMES-PRESERVES-INEQUALITY EVAL$-EQUAL-TIMES-TREE-BAGDIFF EVAL$-QUOTIENT-TIMES-TREE-BAGDIFF EVAL$-LESSP-TIMES-TREE-BAGDIFF IPLUS-TREE-BAGDIFF PLUS-TREE-BAGDIFF SUBBAGP-IMPLIES-PLUS-TREE-GREATEREQP SETS-AND-BAGS SUBBAGP-BAGINT2 SUBBAGP-BAGINT1) EVENT (PROVE-LEMMA SUBBAGP-CDR2 (REWRITE) (IMPLIES (SUBBAGP X (CDR Y)) (SUBBAGP X Y)) ((ENABLE DELETE SUBBAGP DELETE-NON-MEMBER SUBBAGP-CDR1) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DELETE . SUBBAGP-CDR2) (IMMEDIATE-DEPENDENTS0 DELETE-NON-MEMBER . SUBBAGP-CDR2) (IMMEDIATE-DEPENDENTS0 SUBBAGP-CDR1 . SUBBAGP-CDR2) (IMMEDIATE-DEPENDENTS0 SUBBAGP . SUBBAGP-CDR2) (LEMMAS SUBBAGP . SUBBAGP-CDR2))))) (PUT1-LST (QUOTE SUBBAGP-CDR1) (QUOTE (IDATE 1000404112312 IMMEDIATE-DEPENDENTS0 (EVAL$-EQUAL-TIMES-TREE-BAGDIFF EVAL$-QUOTIENT-TIMES-TREE-BAGDIFF EVAL$-LESSP-TIMES-TREE-BAGDIFF SETS-AND-BAGS SUBBAGP-CDR2) EVENT (PROVE-LEMMA SUBBAGP-CDR1 (REWRITE) (IMPLIES (SUBBAGP X Y) (SUBBAGP (CDR X) Y)) ((ENABLE SUBBAGP SUBBAGP-DELETE) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SUBBAGP-DELETE . SUBBAGP-CDR1) (IMMEDIATE-DEPENDENTS0 SUBBAGP . SUBBAGP-CDR1) (LEMMAS SUBBAGP . SUBBAGP-CDR1))))) (PUT1-LST (QUOTE SUBBAGP-DELETE) (QUOTE (IDATE 1000404112312 IMMEDIATE-DEPENDENTS0 (SETS-AND-BAGS SUBBAGP-CDR1) EVENT (PROVE-LEMMA SUBBAGP-DELETE (REWRITE) (IMPLIES (SUBBAGP X (DELETE U Y)) (SUBBAGP X Y)) ((ENABLE DELETE SUBBAGP MEMBER-DELETE-IMPLIES-MEMBERSHIP DELETE-DELETE) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 MEMBER-DELETE-IMPLIES-MEMBERSHIP . SUBBAGP-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE-DELETE . SUBBAGP-DELETE) (IMMEDIATE-DEPENDENTS0 DELETE . SUBBAGP-DELETE) (IMMEDIATE-DEPENDENTS0 SUBBAGP . SUBBAGP-DELETE) (LEMMAS SUBBAGP . SUBBAGP-DELETE))))) (PUT1-LST (QUOTE SETP-PERMUTATION) (QUOTE (IDATE 1000404112312 EVENT (PROVE-LEMMA SETP-PERMUTATION NIL (IMPLIES (AND (SETP B) (PERMUTATION A B)) (SETP A)) ((INDUCT (SETP-PERMUTATION-INDUCTION A B)) (USE (SETP-PERMUTATION-BASE-CASE (A A)) (SETP-PERMUTATION-INDUCTION-STEP (A A) (B B))) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SETP-PERMUTATION-BASE-CASE . SETP-PERMUTATION) (IMMEDIATE-DEPENDENTS0 SETP-PERMUTATION-INDUCTION-STEP . SETP-PERMUTATION) (IMMEDIATE-DEPENDENTS0 SETP-PERMUTATION-INDUCTION . SETP-PERMUTATION) (IMMEDIATE-DEPENDENTS0 PERMUTATION . SETP-PERMUTATION) (IMMEDIATE-DEPENDENTS0 SETP . SETP-PERMUTATION))))) (PUT1-LST (QUOTE SETP-PERMUTATION-INDUCTION-STEP) (QUOTE (IDATE 1000404112312 IMMEDIATE-DEPENDENTS0 (SETP-PERMUTATION) EVENT (PROVE-LEMMA SETP-PERMUTATION-INDUCTION-STEP NIL (IMPLIES (AND (LISTP A) (AND (SETP B) (AND (PERMUTATION A B) (IMPLIES (AND (SETP (DELETE (CAR A) B)) (PERMUTATION (CDR A) (DELETE (CAR A) B))) (SETP (CDR A)))))) (SETP A)) ((ENABLE SETP PERMUTATION DELETE MEMBER MEMBER-DELETE OCCURRENCES-IN-A-SET SETP-DELETE) (USE (PERMUTATION-IMPLIES-MEMBERSHIP-EQUIVALENCE (X (CAR A)) (A (CDR A)) (B (DELETE (CAR A) B)))) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 OCCURRENCES-IN-A-SET . SETP-PERMUTATION-INDUCTION-STEP) (IMMEDIATE-DEPENDENTS0 MEMBER-DELETE . SETP-PERMUTATION-INDUCTION-STEP) (IMMEDIATE-DEPENDENTS0 SETP-DELETE . SETP-PERMUTATION-INDUCTION-STEP) (IMMEDIATE-DEPENDENTS0 PERMUTATION-IMPLIES-MEMBERSHIP-EQUIVALENCE . SETP-PERMUTATION-INDUCTION-STEP) (IMMEDIATE-DEPENDENTS0 DELETE . SETP-PERMUTATION-INDUCTION-STEP) (IMMEDIATE-DEPENDENTS0 PERMUTATION . SETP-PERMUTATION-INDUCTION-STEP) (IMMEDIATE-DEPENDENTS0 SETP . SETP-PERMUTATION-INDUCTION-STEP))))) (PUT1-LST (QUOTE SETP-PERMUTATION-BASE-CASE) (QUOTE (IDATE 1000404112312 IMMEDIATE-DEPENDENTS0 (SETP-PERMUTATION) EVENT (PROVE-LEMMA SETP-PERMUTATION-BASE-CASE NIL (IMPLIES (NOT (LISTP A)) (SETP A)) ((ENABLE SETP) (ENABLE-THEORY GROUND-ZERO) (DISABLE-THEORY T))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 SETP . SETP-PERMUTATION-BASE-CASE))))) (PUT1-LST (QUOTE *1*SETP-PERMUTATION-INDUCTION) (QUOTE (MAIN-EVENT SETP-PERMUTATION-INDUCTION))) (PUT1-LST (QUOTE SETP-PERMUTATION-INDUCTION) (QUOTE (TYPE-PRESCRIPTION-LST ((SETP-PERMUTATION-INDUCTION 4 NIL NIL)) TOTALP-LST ((SETP-PERMUTATION-INDUCTION . T)) QUICK-BLOCK-INFO (SELF-REFLEXIVE SELF-REFLEXIVE) SDEFN (LAMBDA (A B) (IF (LISTP A) (SETP-PERMUTATION-INDUCTION (CDR A) (DELETE (CAR A) B)) (QUOTE 0))) LISP-CODE *1*SETP-PERMUTATION-INDUCTION SUBRP *1*FALSE INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP A)) (((CDR A) (DELETE (CAR A) B)))) (TESTS-AND-CASES ((NOT (LISTP A))) NIL)) LEVEL-NO 2 JUSTIFICATIONS ((JUSTIFICATION (A) (COUNT A) LESSP (ZERO CDR-LESSP))) IDATE 1000404112312 CONTROLLER-POCKETS (1) SATELLITES (*1*SETP-PERMUTATION-INDUCTION) IMMEDIATE-DEPENDENTS0 (SETP-PERMUTATION) EVENT (DEFN SETP-PERMUTATION-INDUCTION (A B) (IF (LISTP A) (SETP-PERMUTATION-INDUCTION (CDR A) (DELETE (CAR A) B)) (QUOTE 0))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DELETE . 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T)) 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 *1*FALSE)) (QUOTE *1*TRUE))) LISP-CODE *1*SUBBAGP SUBRP *1*FALSE 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 1000404112311 CONTROLLER-POCKETS (1) SATELLITES (*1*SUBBAGP) IMMEDIATE-DEPENDENTS0 (PERMUTATION-APPEND-SPLIT-BY-PARITY-BRIDGE SUBBAGP-X-X CANCELLING-FROM-RPLUS SUBBAGP-APPEND-BRIDGE2 SUBBAGP-APPEND-BRIDGE SUBBAGP-APPEND-SIMPLIFY2 SUBBAGP-PERMUTATION-EQUIV SUBBAGP-APPEND-SIMPLIFY1 CANCEL-ZERO-FACT-BRIDGE SUBBAGP-TRANSITIVE-BRIDGE SUBBAGP-TRANSITIVE-BRIDGE-HELPER SUBBAGP-BAGDIFF MEMBER-SUBBAGP-DELETE MEMBER-SUBBAGP2 PERMUTATION-DOES-NOT-EFFECT-RPLUS SUBBAGP-MAKE-NEGS APPEND-BAGDIFF-ARG1 SUBBAGP-TRANSITIVE SUBBAGP-NECC PERMUTATION-AS-SUBBAGP PERMUTATION-AS-SUBBAGP-HELPER NOT-SUBBAGP-NOT-PERMUTATION SUBBAGP-PERMUTATION SUBBAGP-DELETE-CAR2 SUBBAGP-DELETE-CAR SUBBAGP-DELETE-SAME-MEANS SUBBAGP-DELETE-SAME SUBBAGP-APPEND SUBBAGP-WIT-LEMMA MEMBER-SUBBAGP CANCEL-EQUAL-TIMES-PRESERVES-INEQUALITY EVAL$-EQUAL-TIMES-TREE-BAGDIFF EVAL$-QUOTIENT-TIMES-TREE-BAGDIFF EVAL$-LESSP-TIMES-TREE-BAGDIFF ZEROP-MAKES-TIMES-TREE-ZERO2 ZEROP-MAKES-TIMES-TREE-ZERO IPLUS-TREE-BAGDIFF 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)) (QUOTE *1*FALSE)) (QUOTE *1*TRUE))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DELETE . SUBBAGP) (DCELL . *1*SUBBAGP))))) (PUT1-LST (QUOTE *1*SETP) (QUOTE (MAIN-EVENT SETP))) (PUT1-LST (QUOTE SETP) (QUOTE (TYPE-PRESCRIPTION-LST ((SETP 3 NIL)) LEMMAS ((REWRITE-RULE SETP-DELETE ((SETP A)) (SETP (DELETE X A)) NIL)) TOTALP-LST ((SETP . T)) QUICK-BLOCK-INFO (SELF-REFLEXIVE) SDEFN (LAMBDA (L) (IF (LISTP L) (IF (MEMBER (CAR L) (CDR L)) (QUOTE *1*FALSE) (IF (SETP (CDR L)) (QUOTE *1*TRUE) (QUOTE *1*FALSE))) (QUOTE *1*TRUE))) LISP-CODE *1*SETP SUBRP *1*FALSE 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 1000404112311 CONTROLLER-POCKETS (1) SATELLITES (*1*SETP) IMMEDIATE-DEPENDENTS0 (SETP-PERMUTATION SETP-PERMUTATION-INDUCTION-STEP SETP-PERMUTATION-BASE-CASE SETP-DELETE OCCURRENCES-IN-A-SET) EVENT (DEFN SETP (L) (IF (LISTP L) (AND (NOT (MEMBER (CAR L) (CDR L))) (SETP (CDR L))) (QUOTE *1*TRUE))) LOCAL-UNDO-TUPLES ((DCELL . *1*SETP))))) (PUT1-LST (QUOTE *1*PERMUTATION) (QUOTE (MAIN-EVENT PERMUTATION))) (PUT1-LST (QUOTE PERMUTATION) (QUOTE (TYPE-PRESCRIPTION-LST ((PERMUTATION 3 NIL NIL)) LEMMAS ((REWRITE-RULE PERMUTATION-APPEND-SPLIT-BY-PARITY-BRIDGE NIL (PERMUTATION (APPEND (CAR (SPLIT-BY-PARITY X)) (MAKE-NEGS (CDR (SPLIT-BY-PARITY X)))) X) NIL) (REWRITE-RULE PERMUTATION-BAGDIFF-APPEND NIL (PERMUTATION X (BAGDIFF (APPEND X Z) Z)) NIL) (REWRITE-RULE PERMUTATION-BAGDIFF-APPEND-HELPER NIL (EQUAL (PERMUTATION Y (BAGDIFF (APPEND Z X) X)) (PERMUTATION Y (BAGDIFF (APPEND X Z) X))) NIL) (REWRITE-RULE PERMUTATION-BAGDIFF-APPEND-HELPER NIL (EQUAL (PERMUTATION (BAGDIFF (APPEND Z X) X) Y) (PERMUTATION (BAGDIFF (APPEND X Z) X) Y)) NIL) (REWRITE-RULE PERMUTATION-APPEND-ARG1-ARG2-BRIDGE NIL (PERMUTATION (BAGDIFF (APPEND X Z) Z) (BAGDIFF (APPEND Z X) Z)) NIL) (REWRITE-RULE PERMUTATION-BAGDIFF ((PERMUTATION X Y)) (PERMUTATION (BAGDIFF X Z) (BAGDIFF Y Z)) NIL) (REWRITE-RULE PERMUTATION-TRANSITIVE ((PERMUTATION X Y) (PERMUTATION Y Z)) (PERMUTATION X Z) NIL) (REWRITE-RULE PERMUTATION-AS-SUBBAGP NIL (EQUAL (PERMUTATION X Y) (IF (SUBBAGP X Y) (SUBBAGP Y X) (QUOTE *1*FALSE))) NIL) (REWRITE-RULE PERMUTATION-AS-SUBBAGP-HELPER NIL (IFF (PERMUTATION X Y) (IF (SUBBAGP X Y) (SUBBAGP Y X) (QUOTE *1*FALSE))) NIL) (REWRITE-RULE NOT-SUBBAGP-NOT-PERMUTATION ((NOT (SUBBAGP X Y))) (NOT (PERMUTATION Y X)) NIL) (REWRITE-RULE NOT-SUBBAGP-NOT-PERMUTATION ((NOT (SUBBAGP X Y))) (NOT (PERMUTATION X Y)) NIL) (REWRITE-RULE PERMUTATION-A-B NIL (PERMUTATION (APPEND A B) (APPEND B A)) NIL) (REWRITE-RULE SUBBAGP-PERMUTATION ((SUBBAGP X Y) (SUBBAGP Y X)) (PERMUTATION X Y) NIL) (REWRITE-RULE PERMUTATION-DELETE-DELETE ((PERMUTATION A B) (MEMBER X A) (MEMBER X B)) (PERMUTATION (DELETE X A) (DELETE X B)) NIL) (REWRITE-RULE PERMUTATION-REFLEXIVITY NIL (PERMUTATION L L) NIL) (REWRITE-RULE COMMUTATIVITY-OF-PERMUTATION NIL (EQUAL (PERMUTATION B A) (PERMUTATION A B)) ((B . A))) (REWRITE-RULE PERMUTATION-RIGHT-CONS NIL (EQUAL (PERMUTATION A (CONS X B)) (IF (MEMBER X A) (PERMUTATION (DELETE X A) B) (QUOTE *1*FALSE))) NIL) (REWRITE-RULE PERMUTATION-RIGHT-CONS1 ((LISTP B) (MEMBER (CAR B) A)) (EQUAL (PERMUTATION A B) (PERMUTATION (DELETE (CAR B) A) (CDR B))) NIL) (REWRITE-RULE NOT-PERMUTATION ((LISTP B) (NOT (MEMBER (CAR B) A))) (NOT (PERMUTATION A B)) NIL)) TOTALP-LST ((PERMUTATION . T)) QUICK-BLOCK-INFO (SELF-REFLEXIVE SELF-REFLEXIVE) SDEFN (LAMBDA (A B) (IF (LISTP A) (IF (MEMBER (CAR A) B) (IF (PERMUTATION (CDR A) (DELETE (CAR A) B)) (QUOTE *1*TRUE) (QUOTE *1*FALSE)) (QUOTE *1*FALSE)) (IF (LISTP B) (QUOTE *1*FALSE) (QUOTE *1*TRUE)))) LISP-CODE *1*PERMUTATION SUBRP *1*FALSE INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP A)) (((CDR A) (DELETE (CAR A) B)))) (TESTS-AND-CASES ((NOT (LISTP A))) NIL)) LEVEL-NO 2 JUSTIFICATIONS ((JUSTIFICATION (A) (COUNT A) LESSP (ZERO CDR-LESSP))) IDATE 1000404112311 CONTROLLER-POCKETS (1) SATELLITES (*1*PERMUTATION) IMMEDIATE-DEPENDENTS0 (PERMUTATION-APPEND-SPLIT-BY-PARITY-BRIDGE SUBBAGP-PERMUTATION-EQUIV PERMUTATION-BAGDIFF-APPEND PERMUTATION-BAGDIFF-APPEND-HELPER EQUAL-PERMUTATION PERMUTATION-APPEND-ARG1-ARG2-BRIDGE PERMUTATION-BAGDIFF PERMUTATION-TRANSITIVE PERMUTATION-DOES-NOT-EFFECT-RPLUS PERMUTATION-AS-SUBBAGP PERMUTATION-AS-SUBBAGP-HELPER NOT-SUBBAGP-NOT-PERMUTATION PERMUTATION-A-B SUBBAGP-PERMUTATION SETP-PERMUTATION SETP-PERMUTATION-INDUCTION-STEP TRANSITIVITY-OF-PERMUTATION TRANSITIVITY-OF-PERMUTATION-INDUCTION-STEP TRANSITIVITY-OF-PERMUTATION-BASE-CASE PERMUTATION-DELETE-DELETE PERMUTATION-REFLEXIVITY COMMUTATIVITY-OF-PERMUTATION PERMUTATION-RIGHT-CONS PERMUTATION-RIGHT-CONS1 NOT-PERMUTATION PERMUTATION-IMPLIES-MEMBERSHIP-EQUIVALENCE) EVENT (DEFN PERMUTATION (A B) (IF (LISTP A) (AND (MEMBER (CAR A) B) (PERMUTATION (CDR A) (DELETE (CAR A) B))) (NOT (LISTP B)))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DELETE . PERMUTATION) (DCELL . *1*PERMUTATION))))) (PUT1-LST (QUOTE *1*OCCURRENCES) (QUOTE (MAIN-EVENT OCCURRENCES))) (PUT1-LST (QUOTE OCCURRENCES) (QUOTE (TYPE-PRESCRIPTION-LST ((OCCURRENCES 4 NIL NIL)) LEMMAS ((REWRITE-RULE OCCURRENCES-APPEND NIL (EQUAL (OCCURRENCES A (APPEND X Y)) (PLUS (OCCURRENCES A X) (OCCURRENCES A Y))) NIL) (REWRITE-RULE OCCURRENCES-DELETE2 NIL (EQUAL (OCCURRENCES A (DELETE B X)) (IF (EQUAL A B) (SUB1 (OCCURRENCES A X)) (OCCURRENCES A X))) NIL) (REWRITE-RULE OCCURRENCES-BAGINT NIL (EQUAL (OCCURRENCES X (BAGINT A B)) (IF (LESSP (OCCURRENCES X A) (OCCURRENCES X B)) (OCCURRENCES X A) (OCCURRENCES X B))) NIL) (REWRITE-RULE OCCURRENCES-BAGDIFF NIL (EQUAL (OCCURRENCES X (BAGDIFF A B)) (DIFFERENCE (OCCURRENCES X A) (OCCURRENCES X B))) NIL) (REWRITE-RULE OCCURRENCES-DELETE NIL (EQUAL (OCCURRENCES X (DELETE Y L)) (IF (EQUAL X Y) (IF (MEMBER X L) (SUB1 (OCCURRENCES X L)) (QUOTE 0)) (OCCURRENCES X L))) NIL) (REWRITE-RULE OCCURRENCES-CONS NIL (EQUAL (OCCURRENCES X (CONS Y L)) (IF (EQUAL X Y) (ADD1 (OCCURRENCES X L)) (OCCURRENCES X L))) NIL) (REWRITE-RULE OCCURRENCES-IN-A-SET ((SETP L)) (EQUAL (OCCURRENCES X L) (IF (MEMBER X L) (QUOTE 1) (QUOTE 0))) NIL)) TOTALP-LST ((OCCURRENCES . T)) LINEAR-LEMMAS ((LINEAR-LEMMA SUBBAGP-NECC ((SUBBAGP X Y)) (NOT (LESSP (OCCURRENCES A Y) (OCCURRENCES A X))) (OCCURRENCES A X)) (LINEAR-LEMMA SUBBAGP-NECC ((SUBBAGP X Y)) (NOT (LESSP (OCCURRENCES A Y) (OCCURRENCES A X))) (OCCURRENCES A Y))) QUICK-BLOCK-INFO (UNCHANGING SELF-REFLEXIVE) SDEFN (LAMBDA (X L) (IF (LISTP L) (IF (EQUAL X (CAR L)) (ADD1 (OCCURRENCES X (CDR L))) (OCCURRENCES X (CDR L))) (QUOTE 0))) LISP-CODE *1*OCCURRENCES SUBRP *1*FALSE INDUCTION-MACHINE ((TESTS-AND-CASES ((LISTP L) (EQUAL X (CAR L))) ((X (CDR L)))) (TESTS-AND-CASES ((LISTP L) (NOT (EQUAL 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 1000404112311 CONTROLLER-POCKETS (2) SATELLITES (*1*OCCURRENCES) IMMEDIATE-DEPENDENTS0 (MEMBER-SUBBAGP2 SUBBAGP-TRANSITIVE SUBBAGP-NECC OCCURRENCES-APPEND SUBBAGP-WIT-LEMMA OCCURRENCES-DELETE2 MEMBER-OCCUR MEMBER-BAGDIFF MEMBER-DELETE OCCURRENCES-BAGINT OCCURRENCES-BAGDIFF OCCURRENCES-DELETE OCCURRENCES-CONS OCCURRENCES-IN-A-SET EQUAL-OCCURRENCES-ZERO) EVENT (DEFN OCCURRENCES (X L) (IF (LISTP L) (IF (EQUAL X (CAR L)) (ADD1 (OCCURRENCES X (CDR L))) (OCCURRENCES X (CDR L))) (QUOTE 0))) LOCAL-UNDO-TUPLES ((DCELL . *1*OCCURRENCES))))) (PUT1-LST (QUOTE *1*BAGINT) (QUOTE (MAIN-EVENT BAGINT))) (PUT1-LST (QUOTE BAGINT) (QUOTE (TYPE-PRESCRIPTION-LST ((BAGINT 24 NIL NIL)) LEMMAS ((REWRITE-RULE BAGINT-MAKE-NEGS-SPLIT-BY-PARITY NIL (EQUAL (BAGINT (MAKE-NEGS (BAGINT (CAR (SPLIT-BY-PARITY Y)) (CDR (SPLIT-BY-PARITY Y)))) (CAR (SPLIT-BY-PARITY Y))) (QUOTE NIL)) NIL) (REWRITE-RULE BAGINT-ALL-RNEGS-CAR-SPLIT-BY-PARITY ((ALL-RNEGS X)) (EQUAL (BAGINT X (CAR (SPLIT-BY-PARITY Y))) (QUOTE NIL)) NIL)) TOTALP-LST ((BAGINT . T)) 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 *1*BAGINT SUBRP *1*FALSE 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 1000404112311 CONTROLLER-POCKETS (1) SATELLITES (*1*BAGINT) IMMEDIATE-DEPENDENTS0 (CANCEL-RPLUS BAGINT-MAKE-NEGS-SPLIT-BY-PARITY BAGINT-ALL-RNEGS-CAR-SPLIT-BY-PARITY ALL-RNEGS-MAKE-NEGS-BAGINT ALL-RNEGS-MAKE-NEGS-BAGINT-FACT CANCELLING-FROM-RPLUS APPEND-BAGDIFF-ARG2 CANCEL-EQUAL-TIMES-PRESERVES-INEQUALITY-BRIDGE ZEROP-MAKES-EQUAL-TRUE-BRIDGE CANCEL-EQUAL-TIMES ZEROP-MAKES-QUOTIENT-ZERO-BRIDGE CANCEL-QUOTIENT-TIMES ZEROP-MAKES-LESSP-FALSE-BRIDGE CANCEL-LESSP-TIMES CANCEL-IDIFFERENCE CANCEL-IPLUS CANCEL-LESSP-PLUS CANCEL-DIFFERENCE-PLUS CANCEL-EQUAL-PLUS SUBBAGP-BAGINT2 SUBBAGP-BAGINT1 MEMBER-BAGINT OCCURRENCES-BAGINT) 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)) (QUOTE NIL))) LOCAL-UNDO-TUPLES ((IMMEDIATE-DEPENDENTS0 DELETE . BAGINT) (DCELL . *1*BAGINT))))) (PUT1-LST (QUOTE *1*BAGDIFF) (QUOTE (MAIN-EVENT BAGDIFF))) (PUT1-LST (QUOTE BAGDIFF) (QUOTE (TYPE-PRESCRIPTION-LST ((BAGDIFF -1 T NIL)) LEMMAS ((REWRITE-RULE BAGDIFF-CAR-IN ((LISTP X) (MEMBER (CAR X) Z)) (EQUAL (BAGDIFF X Z) (BAGDIFF (CDR X) (DELETE (CAR X) Z))) NIL) (REWRITE-RULE BAGDIFF-NOT-LISTP ((NOT (LISTP X))) (EQUAL (BAGDIFF X Z) X) NIL) (REWRITE-RULE BAGDIFF-CONS-Z-Z NIL (EQUAL (BAGDIFF (CONS X Z) Z) (CONS X (LAST-CDR Z))) NIL) (REWRITE-RULE BAGDIFF-APPEND-ARG1 NIL (EQUAL (BAGDIFF (APPEND Z X) Z) X) NIL) (REWRITE-RULE BAGDIFF-X-X NIL (EQUAL (BAGDIFF X X) (LAST-CDR X)) NIL) (REWRITE-RULE BAGDIFF-BAGDIFF NIL (EQUAL (BAGDIFF (BAGDIFF A B) C) (BAGDIFF A (APPEND B C))) NIL) (REWRITE-RULE BAGDIFF-DELETE NIL (EQUAL (BAGDIFF (DELETE E X) Y) (DELETE E (BAGDIFF X Y))) NIL)) TOTALP-LST ((BAGDIFF . 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