(UNIF-LEGAL-Q-IDENTIFY)
(UNIF-LEGAL-Q)
(UNIF-REDUCE-ONE-STEP-Q-IDENTIFY
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 (1 1 (:TYPE-PRESCRIPTION TRUE-LISTP))
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(UNIF-REDUCE-ONE-STEP-Q)
(INDUCT-PATH-SUBTERM
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(MAP-NFIX-NAT-TRUE-LISTP
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(UGLY-LEMMA-1
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 (3 3 (:REWRITE DEFAULT-<-2))
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(PATH-SUBTERM
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 (951 951 (:REWRITE DEFAULT-CDR))
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 (498 285 (:REWRITE DEFAULT-<-2))
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 (432 37 (:DEFINITION BOUNDED-NAT-TRUE-LISTP))
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 (293 293 (:REWRITE DEFAULT-+-1))
 (285 285 (:META CANCEL_PLUS-LESSP-CORRECT))
 (280 14 (:DEFINITION MAP-NFIX))
 (143 143 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (143 143 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (109 67 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (89 89 (:REWRITE BOUNDED-NAT-TRUE-LISTP-NAT-TRUE-LISTP))
 (88 88 (:REWRITE DAG-P-COMPLETENESS))
 (56 14 (:DEFINITION NFIX))
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(SIZE-SUBTERM
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 (5 5 (:META CANCEL_PLUS-EQUAL-CORRECT))
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(IDENTIFY-PRESERVES-DAG-P-MAIN-LEMMA
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 (60 3 (:DEFINITION MAP-NFIX))
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 (54 6 (:DEFINITION BOUNDED-NAT-TRUE-LISTP))
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 (41 41 (:META CANCEL_TIMES-EQUAL-CORRECT))
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(IDENTIFY-PRESERVES-DAG-P
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 (18 2 (:DEFINITION BOUNDED-NAT-TRUE-LISTP))
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 (11 1 (:DEFINITION LAST))
 (10 10 (:TYPE-PRESCRIPTION OCCUR-CHECK-D))
 (10 10 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (7 1 (:DEFINITION UPDATE-NTH))
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(UNIF-REDUCE-ONE-STEP-Q-PRESERVES-BOUNDED-WELL-FORMED-UPL
 (462 42 (:DEFINITION NTH))
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 (309 288 (:REWRITE DEFAULT-CDR))
 (290 260 (:REWRITE DEFAULT-CAR))
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 (168 6 (:DEFINITION DAG-AS-TERM))
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 (90 3 (:DEFINITION OCCUR-CHECK-D))
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 (82 5 (:DEFINITION LIST-OF-TERM-DAG-VARIABLES))
 (81 81 (:META CANCEL_PLUS-LESSP-CORRECT))
 (64 55 (:REWRITE DEFAULT-+-2))
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 (52 26 (:TYPE-PRESCRIPTION TRUE-LISTP-UPDATE-NTH))
 (49 5 (:DEFINITION BOUNDED-NAT-TRUE-LISTP))
 (45 9 (:DEFINITION LEN))
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 (28 28 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (28 28 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (26 26 (:TYPE-PRESCRIPTION UPDATE-NTH))
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 (24 4 (:DEFINITION MEMBER-EQUAL))
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(UNIF-REDUCE-ONE-STEP-Q-PRESERVES-LENGTH
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 (47 47 (:REWRITE DEFAULT-CDR))
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 (5 5 (:META CANCEL_TIMES-EQUAL-CORRECT))
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(UNIF-REDUCE-ONE-STEP-Q-PRESERVES-WELL-FORMED-UPL
 (20 4 (:DEFINITION LEN))
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 (4 4 (:REWRITE DEFAULT-+-1))
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(UNIF-LEGAL-Q-IMPLIES-UNIF-LEGAL-P-FOR-NON-IDENTIFICATIONS
 (2 2 (:REWRITE DEFAULT-CAR))
 (1 1 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (1 1 (:META CANCEL_PLUS-EQUAL-CORRECT))
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(UNIF-REDUCE-ONE-STEP-Q-UNIF-REDUCE-ONE-STEP-S-FOR-NON-IDENTIFICATIONS
 (3 3 (:REWRITE DEFAULT-CAR))
 (1 1 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (1 1 (:META CANCEL_PLUS-EQUAL-CORRECT))
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(IDENTIFY-ON-TERM-DAGS
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 (3599 509 (:DEFINITION NTH))
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 (1957 70 (:DEFINITION OCCUR-CHECK-D))
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 (567 27 (:DEFINITION NO-DUPLICATESP-EQUAL))
 (559 558 (:REWRITE DEFAULT-<-1))
 (558 558 (:META CANCEL_PLUS-LESSP-CORRECT))
 (501 50 (:DEFINITION BOUNDED-NAT-TRUE-LISTP))
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 (350 350 (:TYPE-PRESCRIPTION OCCUR-CHECK-D))
 (309 309 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (309 309 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (297 27 (:DEFINITION LIST-OF-TERM-DAG-VARIABLES))
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 (132 6 (:LINEAR BOUNDED-TERM-GRAPH-P-NTH-PROPERTY-1))
 (108 108 (:TYPE-PRESCRIPTION LIST-OF-TERM-DAG-VARIABLES))
 (83 83 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (13 13 (:REWRITE BOUNDED-NAT-TRUE-LISTP-NAT-TRUE-LISTP))
 (9 9 (:TYPE-PRESCRIPTION EQLABLEP))
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(IDENTIFY-ON-TERM-DAGS-TBS-AS-SYSTEM
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(IDENTIFY-ON-TERM-DAGS-SOLVED-AS-SYSTEM
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(UNIF-REDUCE-ONE-STEP-Q-FOR-IDENTIFICATIONS
 (224 8 (:DEFINITION DAG-AS-TERM))
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 (1 1 (:TYPE-PRESCRIPTION BOUNDED-NAT-TRUE-LISTP))
 )
(UNIF-SEQ-Q-P)
(UNIF-SEQ-Q-LAST)
(REMOVE-IDENTIFICATIONS)
(UNIF-SEQ-Q-P-UNIF-SEQ-P-P
 (73 73 (:REWRITE DEFAULT-CAR))
 (24 24 (:REWRITE DEFAULT-CDR))
 (13 7 (:REWRITE UNIF-LEGAL-D-IMPLIES-UNIF-LEGAL-P))
 (12 12 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (12 12 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (6 6 (:REWRITE UNIF-REDUCE-ONE-STEP-Q-PRESERVES-WELL-FORMED-UPL))
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(UNIF-SEQ-P-LAST-UNIF-SEQ-Q-LAST
 (79 79 (:REWRITE DEFAULT-CAR))
 (44 44 (:REWRITE DEFAULT-CDR))
 (18 18 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (18 18 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (2 2 (:REWRITE UNIF-REDUCE-ONE-STEP-Q-PRESERVES-WELL-FORMED-UPL))
 )
(MGS-SEQ-Q-P)
(MGS-SEQ-Q)
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(MGS-SEQ-Q-MGS-SEQ-FAILURE-SUCCESS
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 (3 1 (:DEFINITION UNIF-SEQ-P-LAST))
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(MGS-SEQ-Q-MGS-SEQ-COMPUTED-SUBSTITUTION
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(MGS-SEQ-Q-DAG-P
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 (144 12 (:DEFINITION BOUNDED-NAT-TRUE-LISTP))
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 (25 5 (:DEFINITION MEMBER-EQUAL))
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(MGS-SEQ-Q-COMPLETENESS
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 (6 6 (:META CANCEL_PLUS-LESSP-CORRECT))
 )
(MGS-SEQ-Q-SOUNDNESS
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 (56 7 (:DEFINITION REMOVE-IDENTIFICATIONS))
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 (54 54 (:META CANCEL_PLUS-EQUAL-CORRECT))
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 (29 29 (:META CANCEL_PLUS-LESSP-CORRECT))
 (9 3 (:REWRITE MGS-SEQ-Q-DAG-P))
 (3 1 (:REWRITE MGS-SEQ-D-P-MGS-SEQ-P))
 (3 1 (:REWRITE MGS-SEQ-D-MGS-SEQ-FAILURE-SUCCESS))
 )
(MGS-SEQ-Q-IDEMPOTENT
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 (44 1 (:DEFINITION TBS-AS-SYSTEM))
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 (35 3 (:DEFINITION NTH))
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 (8 1 (:DEFINITION REMOVE-IDENTIFICATIONS))
 (6 6 (:TYPE-PRESCRIPTION MGS-SEQ))
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 (4 4 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (4 4 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (3 3 (:TYPE-PRESCRIPTION DAG-P))
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 (3 3 (:REWRITE DEFAULT-+-1))
 (3 3 (:REWRITE DAG-P-COMPLETENESS))
 (3 3 (:META CANCEL_PLUS-LESSP-CORRECT))
 (3 1 (:REWRITE MGS-SEQ-Q-DAG-P))
 )
(MGS-SEQ-Q-MOST-GENERAL-SOLUTION
 (138 7 (:DEFINITION DAG-AS-TERM))
 (132 3 (:DEFINITION TBS-AS-SYSTEM))
 (79 7 (:DEFINITION NTH))
 (71 56 (:REWRITE DEFAULT-CAR))
 (62 47 (:REWRITE DEFAULT-CDR))
 (60 2 (:DEFINITION SOLUTION))
 (44 4 (:DEFINITION APPLY-SUBST))
 (35 7 (:REWRITE ZP-OPEN))
 (32 4 (:DEFINITION VAL))
 (32 1 (:DEFINITION SOLVED-AS-SYSTEM))
 (14 14 (:REWRITE TERM-GRAPH-P-MAIN-PROPERTY))
 (14 14 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (14 14 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (8 1 (:DEFINITION REMOVE-IDENTIFICATIONS))
 (7 7 (:TYPE-PRESCRIPTION DAG-P))
 (7 7 (:REWRITE DEFAULT-<-2))
 (7 7 (:REWRITE DEFAULT-<-1))
 (7 7 (:REWRITE DEFAULT-+-2))
 (7 7 (:REWRITE DEFAULT-+-1))
 (7 7 (:REWRITE DAG-P-COMPLETENESS))
 (7 7 (:META CANCEL_PLUS-LESSP-CORRECT))
 (6 6 (:TYPE-PRESCRIPTION MGS-SEQ))
 (3 1 (:REWRITE MGS-SEQ-Q-DAG-P))
 )
