(|2^N-1|
 (355 9 (:DEFINITION ALWAYS$))
 (215 2 (:REWRITE PLAIN-UQI-RATIONAL-LISTP))
 (178 13 (:REWRITE APPLY$-PRIMITIVE))
 (167 5 (:REWRITE APPLY$-SYMBOL-ARITY-1))
 (152 9 (:META APPLY$-PRIM-META-FN-CORRECT))
 (126 9 (:DEFINITION FROM-TO-BY-DOWN-OPENER))
 (115 2 (:REWRITE PLAIN-UQI-TRUE-LIST-LISTP))
 (97 6 (:REWRITE RATIONAL-LISTP-IMPLIES-ALWAYS$-RATIONALP))
 (91 8 (:DEFINITION RATIONAL-LISTP))
 (82 2 (:REWRITE PLAIN-UQI-SYMBOL-LISTP))
 (65 2 (:REWRITE PLAIN-UQI-RATIONAL-LIST-LISTP))
 (54 44 (:REWRITE DEFAULT-CAR))
 (51 3 (:REWRITE TRUE-LIST-LISTP-IMPLIES-ALWAYS$-TRUE-LISTP))
 (45 9 (:DEFINITION BINARY-APPEND))
 (43 3 (:DEFINITION TRUE-LIST-LISTP))
 (38 38 (:REWRITE DEFAULT-+-2))
 (38 38 (:REWRITE DEFAULT-+-1))
 (38 33 (:REWRITE DEFAULT-CDR))
 (37 37 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (36 2 (:REWRITE PLAIN-UQI-ACL2-NUMBER-LISTP))
 (34 34 (:TYPE-PRESCRIPTION ALWAYS$))
 (32 2 (:REWRITE PLAIN-UQI-INTEGER-LISTP))
 (30 3 (:DEFINITION TRUE-LISTP))
 (29 11 (:REWRITE FOLD-CONSTS-IN-+))
 (29 3 (:REWRITE SYMBOL-LISTP-IMPLIES-ALWAYS$-SYMBOLP))
 (28 28 (:REWRITE DEFAULT-<-2))
 (28 28 (:REWRITE DEFAULT-<-1))
 (23 23 (:TYPE-PRESCRIPTION APPLY$-PRIMP))
 (21 3 (:DEFINITION SYMBOL-LISTP))
 (20 10 (:REWRITE APPLY$-PRIMP-BADGE))
 (16 4 (:REWRITE O-P-O-INFP-CAR))
 (14 2 (:REWRITE INTEGER-LISTP-IMPLIES-ALWAYS$-INTEGERP))
 (14 2 (:REWRITE ACL2-NUMBER-LISTP-IMPLIES-ALWAYS$-ACL2-NUMBERP))
 (13 13 (:REWRITE ALWAYS$-P-LST-IMPLIES-P-ELEMENT))
 (12 12 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (11 11 (:TYPE-PRESCRIPTION TRUE-LIST-LISTP))
 (11 11 (:TYPE-PRESCRIPTION SYMBOL-LISTP))
 (11 11 (:REWRITE RATIONAL-LISTP-IMPLIES-RATIONALP))
 (9 1 (:DEFINITION INTEGER-LISTP))
 (9 1 (:DEFINITION ACL2-NUMBER-LISTP))
 (6 6 (:REWRITE TRUE-LIST-LISTP-IMPLIES-TRUE-LISTP))
 (6 6 (:REWRITE DEFAULT-*-2))
 (6 6 (:REWRITE DEFAULT-*-1))
 (6 2 (:REWRITE O<=-O-FINP-DEF))
 (6 1 (:REWRITE O-INFP->NEQ-0))
 (5 5 (:REWRITE APPLY$-CONSP-ARITY-1))
 (4 4 (:REWRITE INTEGER-LISTP-IMPLIES-INTEGERP))
 (4 3 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (4 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (4 1 (:REWRITE O-FIRST-EXPT-<))
 (3 3 (:TYPE-PRESCRIPTION O-FINP))
 (3 3 (:REWRITE SYMBOL-LISTP-IMPLIES-SYMBOLP))
 (3 1 (:REWRITE O-FIRST-EXPT-O-INFP))
 (2 2 (:TYPE-PRESCRIPTION INTEGER-LISTP))
 (2 2 (:TYPE-PRESCRIPTION ACL2-NUMBER-LISTP))
 (2 2 (:REWRITE |a < b & b < c  =>  a < c|))
 (2 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE SUBSETP-IMPLIES-MEMBER))
 (2 2 (:REWRITE PLAIN-UQI-ALWAYS$))
 (2 2 (:REWRITE O-INFP-O-FINP-O<=))
 (2 2 (:REWRITE INTEGER-LISTP-FROM-TO-BY))
 (2 2 (:REWRITE DEFAULT-UNARY-MINUS))
 (2 2 (:REWRITE ACL2-NUMBER-LISTP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:REWRITE ACL2-NUMBER-LISTP-FROM-TO-BY))
 (2 2 (:REWRITE AC-<))
 (1 1 (:REWRITE O-FIRST-COEFF-<))
 )
(APPLY$-WARRANT-2^N-1)
(APPLY$-WARRANT-2^N-1-DEFINITION)
(APPLY$-WARRANT-2^N-1-NECC)
(APPLY$-2^N-1
 (140 10 (:DEFINITION FROM-TO-BY-DOWN-OPENER))
 (50 10 (:DEFINITION BINARY-APPEND))
 (38 38 (:REWRITE DEFAULT-CAR))
 (36 34 (:REWRITE DEFAULT-+-2))
 (36 34 (:REWRITE DEFAULT-+-1))
 (30 10 (:REWRITE FOLD-CONSTS-IN-+))
 (30 10 (:DEFINITION FROM-TO-BY))
 (21 21 (:REWRITE DEFAULT-<-2))
 (21 21 (:REWRITE DEFAULT-<-1))
 (18 18 (:REWRITE DEFAULT-CDR))
 (14 9 (:REWRITE APPLY$-PRIMP-BADGE))
 (13 7 (:REWRITE APPLY$-PRIMITIVE))
 (11 11 (:TYPE-PRESCRIPTION APPLY$-PRIMP))
 (6 6 (:REWRITE TAMEP-TRUE-CAR/CDR-NESTP))
 (4 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:REWRITE RATIONAL-LISTP-IMPLIES-RATIONALP))
 (2 2 (:REWRITE ACL2-NUMBER-LISTP-IMPLIES-ACL2-NUMBERP))
 (1 1 (:REWRITE INTEGER-LISTP-IMPLIES-INTEGERP))
 )
(|2^N-1|
 (710 18 (:DEFINITION ALWAYS$))
 (430 4 (:REWRITE PLAIN-UQI-RATIONAL-LISTP))
 (344 25 (:REWRITE APPLY$-PRIMITIVE))
 (334 10 (:REWRITE APPLY$-SYMBOL-ARITY-1))
 (322 23 (:DEFINITION FROM-TO-BY-DOWN-OPENER))
 (294 16 (:META APPLY$-PRIM-META-FN-CORRECT))
 (230 4 (:REWRITE PLAIN-UQI-TRUE-LIST-LISTP))
 (194 12 (:REWRITE RATIONAL-LISTP-IMPLIES-ALWAYS$-RATIONALP))
 (182 16 (:DEFINITION RATIONAL-LISTP))
 (164 4 (:REWRITE PLAIN-UQI-SYMBOL-LISTP))
 (132 1 (:DEFINITION SUM$))
 (131 11 (:REWRITE APPLY$-CONSP-ARITY-1))
 (130 4 (:REWRITE PLAIN-UQI-RATIONAL-LIST-LISTP))
 (125 105 (:REWRITE DEFAULT-CAR))
 (115 23 (:DEFINITION BINARY-APPEND))
 (102 6 (:REWRITE TRUE-LIST-LISTP-IMPLIES-ALWAYS$-TRUE-LISTP))
 (87 86 (:REWRITE DEFAULT-+-2))
 (87 86 (:REWRITE DEFAULT-+-1))
 (87 77 (:REWRITE DEFAULT-CDR))
 (86 6 (:DEFINITION TRUE-LIST-LISTP))
 (74 74 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (66 66 (:TYPE-PRESCRIPTION ALWAYS$))
 (60 6 (:DEFINITION TRUE-LISTP))
 (59 4 (:REWRITE PLAIN-UQI-ACL2-NUMBER-LISTP))
 (58 6 (:REWRITE SYMBOL-LISTP-IMPLIES-ALWAYS$-SYMBOLP))
 (53 4 (:REWRITE PLAIN-UQI-INTEGER-LISTP))
 (52 52 (:REWRITE DEFAULT-<-2))
 (52 52 (:REWRITE DEFAULT-<-1))
 (45 45 (:TYPE-PRESCRIPTION APPLY$-PRIMP))
 (42 6 (:DEFINITION SYMBOL-LISTP))
 (40 20 (:REWRITE APPLY$-PRIMP-BADGE))
 (32 8 (:REWRITE O-P-O-INFP-CAR))
 (25 3 (:REWRITE INTEGER-LISTP-IMPLIES-ALWAYS$-INTEGERP))
 (25 3 (:REWRITE ACL2-NUMBER-LISTP-IMPLIES-ALWAYS$-ACL2-NUMBERP))
 (24 24 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (24 24 (:REWRITE ALWAYS$-P-LST-IMPLIES-P-ELEMENT))
 (22 22 (:TYPE-PRESCRIPTION TRUE-LIST-LISTP))
 (22 22 (:TYPE-PRESCRIPTION SYMBOL-LISTP))
 (21 21 (:REWRITE RATIONAL-LISTP-IMPLIES-RATIONALP))
 (18 2 (:DEFINITION INTEGER-LISTP))
 (18 2 (:DEFINITION ACL2-NUMBER-LISTP))
 (16 16 (:TYPE-PRESCRIPTION O-P))
 (12 12 (:REWRITE TRUE-LIST-LISTP-IMPLIES-TRUE-LISTP))
 (9 9 (:REWRITE DEFAULT-*-2))
 (9 9 (:REWRITE DEFAULT-*-1))
 (8 8 (:REWRITE O-P-DEF-O-FINP-1))
 (6 6 (:REWRITE TAMEP-TRUE-CAR/CDR-NESTP))
 (6 6 (:REWRITE SYMBOL-LISTP-IMPLIES-SYMBOLP))
 (6 3 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (6 1 (:REWRITE O-INFP->NEQ-0))
 (5 5 (:REWRITE INTEGER-LISTP-IMPLIES-INTEGERP))
 (4 4 (:REWRITE SUBSETP-IMPLIES-MEMBER))
 (4 4 (:REWRITE PLAIN-UQI-ALWAYS$))
 (3 3 (:TYPE-PRESCRIPTION O-FINP))
 (3 3 (:TYPE-PRESCRIPTION INTEGER-LISTP))
 (3 3 (:TYPE-PRESCRIPTION ACL2-NUMBER-LISTP))
 (3 3 (:REWRITE ZP-OPEN))
 (3 3 (:REWRITE INTEGER-LISTP-FROM-TO-BY))
 (3 3 (:REWRITE ACL2-NUMBER-LISTP-IMPLIES-ACL2-NUMBERP))
 (3 3 (:REWRITE ACL2-NUMBER-LISTP-FROM-TO-BY))
 (3 1 (:REWRITE O-FIRST-EXPT-O-INFP))
 (2 2 (:REWRITE DEFAULT-UNARY-MINUS))
 (2 2 (:REWRITE APPLY$-WARRANT-2^N-1-NECC))
 (2 1 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (1 1 (:TYPE-PRESCRIPTION LEN))
 )
(2^N-1-LOOP-LEMMA
 (2446 17 (:REWRITE APPLY$-CONSP-ARITY-1))
 (610 122 (:DEFINITION BINARY-APPEND))
 (515 429 (:REWRITE DEFAULT-+-2))
 (469 429 (:REWRITE DEFAULT-+-1))
 (317 317 (:REWRITE DEFAULT-<-2))
 (317 317 (:REWRITE DEFAULT-<-1))
 (297 287 (:REWRITE DEFAULT-CAR))
 (213 199 (:REWRITE DEFAULT-CDR))
 (80 16 (:REWRITE ZP-OPEN))
 (57 20 (:REWRITE DEFAULT-*-2))
 (54 54 (:REWRITE TAMEP-TRUE-CAR/CDR-NESTP))
 (48 25 (:REWRITE APPLY$-PRIMITIVE))
 (26 26 (:REWRITE INTEGER-LISTP-IMPLIES-INTEGERP))
 (23 23 (:TYPE-PRESCRIPTION APPLY$-PRIMP))
 (20 20 (:REWRITE DEFAULT-*-1))
 (17 17 (:TYPE-PRESCRIPTION LEN))
 (10 10 (:REWRITE APPLY$-WARRANT-2^N-1-NECC))
 (9 5 (:REWRITE ZIP-OPEN))
 (4 4 (:REWRITE O-INFP->NEQ-0))
 (4 2 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (2 2 (:TYPE-PRESCRIPTION BINARY-APPEND))
 )
(2^N-1-IS-EXPT-2-N-1
 (34 2 (:DEFINITION EXPT))
 (14 1 (:DEFINITION FROM-TO-BY-DOWN-OPENER))
 (12 2 (:REWRITE COMMUTATIVITY-OF-+))
 (10 10 (:REWRITE DEFAULT-+-2))
 (10 10 (:REWRITE DEFAULT-+-1))
 (9 3 (:REWRITE FOLD-CONSTS-IN-+))
 (6 2 (:REWRITE DEFAULT-*-2))
 (5 5 (:REWRITE DEFAULT-<-2))
 (5 5 (:REWRITE DEFAULT-<-1))
 (5 1 (:DEFINITION BINARY-APPEND))
 (4 2 (:REWRITE ZIP-OPEN))
 (3 1 (:DEFINITION FROM-TO-BY))
 (2 2 (:TYPE-PRESCRIPTION FROM-TO-BY))
 (2 2 (:REWRITE O-INFP->NEQ-0))
 (2 2 (:REWRITE DEFAULT-*-1))
 (1 1 (:REWRITE INTEGER-LISTP-IMPLIES-INTEGERP))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE APPLY$-WARRANT-2^N-1-NECC))
 )
(PSTERMP
 (18853 77 (:DEFINITION APPLY$-BADGEP))
 (18226 17 (:DEFINITION ALWAYS$))
 (16130 17 (:REWRITE APPLY$-CONSP-ARITY-1))
 (16098 5 (:REWRITE BETA-REDUCTION))
 (16057 10 (:REWRITE EV$-OPENER))
 (16037 15 (:DEFINITION TAMEP))
 (15872 20 (:DEFINITION SUITABLY-TAMEP-LISTP))
 (14733 138 (:DEFINITION SUBSETP-EQUAL))
 (13182 879 (:DEFINITION MEMBER-EQUAL))
 (9523 123 (:LINEAR APPLY$-BADGEP-PROPERTIES . 1))
 (8511 132 (:REWRITE APPLY$-BADGEP-PROPERTIES . 1))
 (8129 349 (:REWRITE SUBSETP-REFLEXIVE-LEMMA))
 (7453 498 (:REWRITE MEMBER-EQUAL-NEWVAR-COMPONENTS-1))
 (5499 5499 (:REWRITE DEFAULT-CDR))
 (3105 20 (:REWRITE ZP-OPEN))
 (2703 2 (:REWRITE PLAIN-UQI-INTEGER-LISTP))
 (2615 7 (:DEFINITION INTEGER-LISTP))
 (1718 4 (:REWRITE INTEGER-LISTP-IMPLIES-ALWAYS$-INTEGERP))
 (1564 1564 (:REWRITE SUBSETP-IMPLIES-MEMBER))
 (1554 1554 (:REWRITE DEFAULT-CAR))
 (1494 1494 (:REWRITE MEMBER-EQUAL-NEWVAR-COMPONENTS-3))
 (1301 80 (:REWRITE APPLY$-BADGEP-PROPERTIES . 2))
 (1126 12 (:REWRITE APPLY$-SYMBOL-ARITY-1))
 (1076 17 (:REWRITE APPLY$-PRIMITIVE))
 (1044 138 (:REWRITE INTEGER-LISTP-IMPLIES-INTEGERP))
 (1042 12 (:META APPLY$-PRIM-META-FN-CORRECT))
 (1026 102 (:DEFINITION NATP))
 (1023 899 (:REWRITE APPLY$-PRIMP-BADGE))
 (996 996 (:REWRITE MEMBER-EQUAL-NEWVAR-COMPONENTS-2))
 (989 989 (:TYPE-PRESCRIPTION SUBSETP-EQUAL))
 (552 552 (:TYPE-PRESCRIPTION APPLY$-BADGEP))
 (476 5 (:REWRITE O<=-O-FINP-DEF))
 (473 219 (:REWRITE DEFAULT-+-2))
 (349 349 (:REWRITE TRANSITIVITY-OF-SUBSETP-EQUAL))
 (280 219 (:REWRITE DEFAULT-+-1))
 (274 128 (:REWRITE APPLY$-BADGEP-PROPERTIES . 3))
 (256 77 (:DEFINITION WEAK-APPLY$-BADGE-P))
 (216 36 (:DEFINITION ALL-NILS))
 (180 180 (:TYPE-PRESCRIPTION ALL-NILS))
 (176 67 (:LINEAR APPLY$-BADGEP-PROPERTIES . 2))
 (172 148 (:REWRITE DEFAULT-<-2))
 (156 148 (:REWRITE DEFAULT-<-1))
 (151 2 (:REWRITE PLAIN-UQI-TRUE-LIST-LISTP))
 (141 141 (:TYPE-PRESCRIPTION APPLY$-PRIMP))
 (106 25 (:REWRITE O-P-O-INFP-CAR))
 (97 2 (:REWRITE PLAIN-UQI-ACL2-NUMBER-LISTP))
 (89 89 (:REWRITE TRUE-LIST-LISTP-IMPLIES-TRUE-LISTP))
 (85 2 (:REWRITE PLAIN-UQI-SYMBOL-LISTP))
 (85 2 (:REWRITE PLAIN-UQI-RATIONAL-LISTP))
 (84 4 (:REWRITE TRUE-LIST-LISTP-IMPLIES-ALWAYS$-TRUE-LISTP))
 (72 18 (:DEFINITION INTEGER-ABS))
 (72 4 (:DEFINITION TRUE-LIST-LISTP))
 (71 9 (:DEFINITION RATIONAL-LISTP))
 (69 69 (:LINEAR BOUNDS-POSITION-EQUAL-AC))
 (69 69 (:LINEAR BOUNDS-POSITION-EQUAL))
 (69 2 (:REWRITE PLAIN-UQI-RATIONAL-LIST-LISTP))
 (61 61 (:REWRITE LEN-MEMBER-EQUAL-LOOP$-AS))
 (56 8 (:DEFINITION SYMBOL-LISTP))
 (54 54 (:LINEAR MEMBER-EQUAL-ACL2-COUNT-SMALLER-3))
 (50 26 (:REWRITE RATIONAL-LISTP-IMPLIES-RATIONALP))
 (48 4 (:REWRITE ACL2-NUMBER-LISTP-IMPLIES-ALWAYS$-ACL2-NUMBERP))
 (45 45 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (40 40 (:TYPE-PRESCRIPTION SUITABLY-TAMEP-LISTP))
 (40 4 (:REWRITE SYMBOL-LISTP-IMPLIES-ALWAYS$-SYMBOLP))
 (40 4 (:REWRITE RATIONAL-LISTP-IMPLIES-ALWAYS$-RATIONALP))
 (36 36 (:LINEAR MEMBER-EQUAL-ACL2-COUNT-SMALLER-2))
 (36 10 (:DEFINITION PAIRLIS$))
 (36 4 (:DEFINITION ACL2-NUMBER-LISTP))
 (35 35 (:TYPE-PRESCRIPTION TAMEP))
 (35 35 (:TYPE-PRESCRIPTION INTEGER-LISTP))
 (31 25 (:REWRITE O-P-DEF-O-FINP-1))
 (25 25 (:REWRITE TAMEP-TRUE-CAR/CDR-NESTP))
 (25 5 (:REWRITE AC-<))
 (24 3 (:REWRITE O-FIRST-EXPT-<))
 (20 20 (:TYPE-PRESCRIPTION TRUE-LIST-LISTP))
 (20 20 (:TYPE-PRESCRIPTION ACL2-NUMBER-LISTP))
 (18 18 (:REWRITE DEFAULT-UNARY-MINUS))
 (18 18 (:LINEAR MEMBER-EQUAL-ACL2-COUNT-SMALLER-1))
 (18 6 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (17 17 (:REWRITE ALWAYS$-P-LST-IMPLIES-P-ELEMENT))
 (12 6 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (12 3 (:REWRITE O-FIRST-COEFF-<))
 (11 11 (:REWRITE SYMBOL-LISTP-IMPLIES-SYMBOLP))
 (10 5 (:REWRITE O-INFP-O-FINP-O<=))
 (9 9 (:REWRITE INTEGERP==>NUMERATOR-=-X))
 (9 9 (:REWRITE INTEGERP==>DENOMINATOR-=-1))
 (9 9 (:REWRITE DEFAULT-REALPART))
 (9 9 (:REWRITE DEFAULT-NUMERATOR))
 (9 9 (:REWRITE DEFAULT-IMAGPART))
 (9 9 (:REWRITE DEFAULT-DENOMINATOR))
 (9 9 (:REWRITE DEFAULT-COERCE-2))
 (9 9 (:REWRITE DEFAULT-COERCE-1))
 (6 6 (:TYPE-PRESCRIPTION O-FINP))
 (6 6 (:REWRITE ACL2-NUMBER-LISTP-IMPLIES-ACL2-NUMBERP))
 (5 5 (:REWRITE |a < b & b < c  =>  a < c|))
 (2 2 (:REWRITE PLAIN-UQI-ALWAYS$))
 )
(APPLY$-WARRANT-PSTERMP)
(APPLY$-WARRANT-PSTERMP-DEFINITION)
(APPLY$-WARRANT-PSTERMP-NECC)
(APPLY$-PSTERMP
 (131 2 (:DEFINITION ALWAYS$))
 (123 4 (:REWRITE APPLY$-CONSP-ARITY-1))
 (115 2 (:REWRITE BETA-REDUCTION))
 (93 4 (:REWRITE EV$-OPENER))
 (52 52 (:REWRITE DEFAULT-CAR))
 (52 8 (:DEFINITION LEN))
 (48 48 (:REWRITE DEFAULT-CDR))
 (44 8 (:REWRITE O-P-O-INFP-CAR))
 (36 4 (:DEFINITION EV$-LIST-DEF))
 (31 4 (:DEFINITION TAMEP))
 (20 8 (:REWRITE O-P-DEF-O-FINP-1))
 (20 4 (:DEFINITION TRUE-LISTP))
 (20 4 (:DEFINITION SUITABLY-TAMEP-LISTP))
 (20 4 (:DEFINITION PAIRLIS$))
 (20 2 (:DEFINITION SYMBOL-LISTP))
 (16 16 (:TYPE-PRESCRIPTION O-P))
 (16 8 (:REWRITE DEFAULT-+-2))
 (16 2 (:REWRITE APPLY$-SYMBOL-ARITY-1))
 (14 2 (:DEFINITION ASSOC-EQUAL))
 (12 12 (:TYPE-PRESCRIPTION O-FINP))
 (10 7 (:REWRITE APPLY$-PRIMP-BADGE))
 (9 5 (:REWRITE APPLY$-PRIMITIVE))
 (8 8 (:TYPE-PRESCRIPTION TAMEP))
 (8 8 (:TYPE-PRESCRIPTION SUITABLY-TAMEP-LISTP))
 (8 8 (:REWRITE TRUE-LIST-LISTP-IMPLIES-TRUE-LISTP))
 (8 8 (:REWRITE LEN-MEMBER-EQUAL-LOOP$-AS))
 (8 8 (:REWRITE DEFAULT-+-1))
 (7 7 (:TYPE-PRESCRIPTION APPLY$-PRIMP))
 (6 6 (:REWRITE TAMEP-TRUE-CAR/CDR-NESTP))
 (6 6 (:REWRITE SYMBOL-LISTP-IMPLIES-SYMBOLP))
 (6 6 (:REWRITE CAR-CONS))
 (4 4 (:REWRITE ALWAYS$-P-LST-IMPLIES-P-ELEMENT))
 (2 2 (:REWRITE DEFAULT-COERCE-2))
 (2 2 (:REWRITE DEFAULT-COERCE-1))
 (2 2 (:REWRITE CDR-CONS))
 )
(PSTERMP-INDUCTOR
 (292 121 (:REWRITE DEFAULT-+-2))
 (178 4 (:REWRITE O<=-O-FINP-DEF))
 (165 121 (:REWRITE DEFAULT-+-1))
 (106 106 (:REWRITE DEFAULT-CDR))
 (94 94 (:REWRITE DEFAULT-CAR))
 (70 16 (:REWRITE O-P-O-INFP-CAR))
 (48 48 (:LINEAR MEMBER-EQUAL-ACL2-COUNT-SMALLER-3))
 (40 10 (:DEFINITION INTEGER-ABS))
 (39 17 (:REWRITE DEFAULT-<-2))
 (36 12 (:DEFINITION APPLY$-BADGEP))
 (32 32 (:LINEAR MEMBER-EQUAL-ACL2-COUNT-SMALLER-2))
 (30 6 (:REWRITE APPLY$-BADGEP-PROPERTIES . 3))
 (28 4 (:DEFINITION SYMBOL-LISTP))
 (24 17 (:REWRITE DEFAULT-<-1))
 (24 12 (:DEFINITION WEAK-APPLY$-BADGE-P))
 (24 3 (:REWRITE O-FIRST-EXPT-<))
 (23 23 (:REWRITE TRUE-LIST-LISTP-IMPLIES-TRUE-LISTP))
 (22 16 (:REWRITE O-P-DEF-O-FINP-1))
 (21 21 (:REWRITE LEN-MEMBER-EQUAL-LOOP$-AS))
 (21 4 (:REWRITE AC-<))
 (20 20 (:LINEAR MEMBER-EQUAL-ACL2-COUNT-SMALLER-0))
 (18 6 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (16 16 (:LINEAR MEMBER-EQUAL-ACL2-COUNT-SMALLER-1))
 (15 3 (:REWRITE APPLY$-BADGEP-PROPERTIES . 2))
 (15 3 (:REWRITE APPLY$-BADGEP-PROPERTIES . 1))
 (12 12 (:TYPE-PRESCRIPTION APPLY$-BADGEP))
 (12 12 (:LINEAR BOUNDS-POSITION-EQUAL-AC))
 (12 12 (:LINEAR BOUNDS-POSITION-EQUAL))
 (12 3 (:REWRITE O-FIRST-COEFF-<))
 (10 10 (:REWRITE DEFAULT-UNARY-MINUS))
 (8 4 (:REWRITE O-INFP-O-FINP-O<=))
 (6 6 (:TYPE-PRESCRIPTION O-FINP))
 (5 5 (:REWRITE SYMBOL-LISTP-IMPLIES-SYMBOLP))
 (5 5 (:REWRITE RATIONAL-LISTP-IMPLIES-RATIONALP))
 (5 5 (:REWRITE INTEGERP==>NUMERATOR-=-X))
 (5 5 (:REWRITE INTEGERP==>DENOMINATOR-=-1))
 (5 5 (:REWRITE INTEGER-LISTP-IMPLIES-INTEGERP))
 (5 5 (:REWRITE DEFAULT-REALPART))
 (5 5 (:REWRITE DEFAULT-NUMERATOR))
 (5 5 (:REWRITE DEFAULT-IMAGPART))
 (5 5 (:REWRITE DEFAULT-DENOMINATOR))
 (5 5 (:REWRITE DEFAULT-COERCE-2))
 (5 5 (:REWRITE DEFAULT-COERCE-1))
 (4 4 (:REWRITE |a < b & b < c  =>  a < c|))
 )
(APPLY$-WARRANT-PSTERMP-INDUCTOR)
(APPLY$-WARRANT-PSTERMP-INDUCTOR-DEFINITION)
(APPLY$-WARRANT-PSTERMP-INDUCTOR-NECC)
(APPLY$-PSTERMP-INDUCTOR
 (52 8 (:DEFINITION LEN))
 (44 8 (:REWRITE O-P-O-INFP-CAR))
 (32 32 (:REWRITE DEFAULT-CDR))
 (28 28 (:REWRITE DEFAULT-CAR))
 (20 8 (:REWRITE O-P-DEF-O-FINP-1))
 (20 4 (:DEFINITION TRUE-LISTP))
 (20 2 (:DEFINITION SYMBOL-LISTP))
 (16 16 (:TYPE-PRESCRIPTION O-P))
 (16 8 (:REWRITE DEFAULT-+-2))
 (12 12 (:TYPE-PRESCRIPTION O-FINP))
 (8 8 (:REWRITE TRUE-LIST-LISTP-IMPLIES-TRUE-LISTP))
 (8 8 (:REWRITE LEN-MEMBER-EQUAL-LOOP$-AS))
 (8 8 (:REWRITE DEFAULT-+-1))
 (6 6 (:REWRITE SYMBOL-LISTP-IMPLIES-SYMBOLP))
 (2 2 (:TYPE-PRESCRIPTION APPLY$-PRIMP))
 (2 2 (:REWRITE DEFAULT-COERCE-2))
 (2 2 (:REWRITE DEFAULT-COERCE-1))
 (2 1 (:REWRITE APPLY$-PRIMP-BADGE))
 (2 1 (:REWRITE APPLY$-PRIMITIVE))
 )
(PSTERMP-INDUCTION-RULE)
(PSSUBST
 (1405 31 (:DEFINITION MEMBER-EQUAL))
 (1173 5 (:DEFINITION APPLY$-BADGEP))
 (992 3 (:DEFINITION INTEGER-LISTP))
 (977 11 (:REWRITE APPLY$-BADGEP-PROPERTIES . 1))
 (801 8 (:DEFINITION ALWAYS$))
 (751 16 (:DEFINITION SUBSETP-EQUAL))
 (713 2 (:REWRITE PLAIN-UQI-INTEGER-LISTP))
 (546 1 (:REWRITE FANCY-UQI-INTEGER-1))
 (539 43 (:REWRITE SUBSETP-REFLEXIVE-LEMMA))
 (455 2 (:REWRITE INTEGER-LISTP-IMPLIES-ALWAYS$-INTEGERP))
 (453 8 (:REWRITE APPLY$-SYMBOL-ARITY-1))
 (413 8 (:REWRITE APPLY$-PRIMITIVE))
 (397 8 (:META APPLY$-PRIM-META-FN-CORRECT))
 (317 317 (:REWRITE DEFAULT-CDR))
 (280 28 (:REWRITE MEMBER-EQUAL-NEWVAR-COMPONENTS-1))
 (221 5 (:REWRITE APPLY$-BADGEP-PROPERTIES . 2))
 (149 1 (:REWRITE O<=-O-FINP-DEF))
 (144 144 (:REWRITE DEFAULT-CAR))
 (132 65 (:REWRITE DEFAULT-+-2))
 (127 127 (:TYPE-PRESCRIPTION SUBSETP-EQUAL))
 (126 7 (:DEFINITION LOOP$-AS))
 (100 8 (:DEFINITION NATP))
 (95 2 (:REWRITE PLAIN-UQI-TRUE-LIST-LISTP))
 (88 65 (:REWRITE DEFAULT-+-1))
 (84 84 (:REWRITE MEMBER-EQUAL-NEWVAR-COMPONENTS-3))
 (78 78 (:REWRITE SUBSETP-IMPLIES-MEMBER))
 (74 13 (:DEFINITION LEN))
 (68 2 (:REWRITE PLAIN-UQI-ACL2-NUMBER-LISTP))
 (63 7 (:DEFINITION LENGTH))
 (62 2 (:REWRITE PLAIN-UQI-SYMBOL-LISTP))
 (62 2 (:REWRITE PLAIN-UQI-RATIONAL-LISTP))
 (56 56 (:REWRITE MEMBER-EQUAL-NEWVAR-COMPONENTS-2))
 (56 14 (:REWRITE COMMUTATIVITY-OF-+))
 (56 14 (:DEFINITION INTEGER-ABS))
 (54 6 (:DEFINITION TRUE-LISTP))
 (54 3 (:DEFINITION TRUE-LIST-LISTP))
 (54 2 (:REWRITE PLAIN-UQI-RATIONAL-LIST-LISTP))
 (46 10 (:REWRITE O-P-O-INFP-CAR))
 (43 43 (:REWRITE TRANSITIVITY-OF-SUBSETP-EQUAL))
 (43 5 (:DEFINITION RATIONAL-LISTP))
 (42 42 (:TYPE-PRESCRIPTION APPLY$-BADGEP))
 (42 7 (:DEFINITION CDR-LOOP$-AS-TUPLE))
 (42 7 (:DEFINITION CAR-LOOP$-AS-TUPLE))
 (42 2 (:REWRITE TRUE-LIST-LISTP-IMPLIES-ALWAYS$-TRUE-LISTP))
 (41 41 (:TYPE-PRESCRIPTION LEN))
 (40 40 (:TYPE-PRESCRIPTION ALWAYS$))
 (35 7 (:DEFINITION EMPTY-LOOP$-AS-TUPLEP))
 (34 1 (:REWRITE FANCY-UQI-RATIONAL-LISTP-1))
 (33 12 (:LINEAR APPLY$-BADGEP-PROPERTIES . 1))
 (32 16 (:REWRITE APPLY$-PRIMP-BADGE))
 (31 2 (:REWRITE STRUCTURE-OF-LOOP$-AS-ELEMENTS-BRIDGE))
 (27 3 (:DEFINITION ACL2-NUMBER-LISTP))
 (26 10 (:REWRITE APPLY$-BADGEP-PROPERTIES . 3))
 (25 25 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (25 25 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (25 23 (:REWRITE DEFAULT-<-2))
 (24 24 (:TYPE-PRESCRIPTION APPLY$-PRIMP))
 (24 23 (:REWRITE DEFAULT-<-1))
 (24 4 (:DEFINITION ALL-NILS))
 (24 2 (:REWRITE ACL2-NUMBER-LISTP-IMPLIES-ALWAYS$-ACL2-NUMBERP))
 (22 22 (:REWRITE CDR-CONS))
 (22 5 (:DEFINITION WEAK-APPLY$-BADGE-P))
 (22 1 (:REWRITE FANCY-UQI-IDENTITY-1))
 (21 21 (:REWRITE CAR-CONS))
 (21 3 (:DEFINITION SYMBOL-LISTP))
 (21 1 (:REWRITE FANCY-UQI-TRUE-LIST-1))
 (20 20 (:TYPE-PRESCRIPTION ALL-NILS))
 (20 2 (:REWRITE SYMBOL-LISTP-IMPLIES-ALWAYS$-SYMBOLP))
 (20 2 (:REWRITE RATIONAL-LISTP-IMPLIES-ALWAYS$-RATIONALP))
 (18 18 (:REWRITE INTEGER-LISTP-IMPLIES-INTEGERP))
 (17 17 (:REWRITE RATIONAL-LISTP-IMPLIES-RATIONALP))
 (16 16 (:REWRITE FOLD-CONSTS-IN-+))
 (16 10 (:REWRITE O-P-DEF-O-FINP-1))
 (15 15 (:TYPE-PRESCRIPTION TRUE-LIST-LISTP))
 (15 15 (:TYPE-PRESCRIPTION SYMBOL-LISTP))
 (15 15 (:TYPE-PRESCRIPTION INTEGER-LISTP))
 (15 15 (:TYPE-PRESCRIPTION ACL2-NUMBER-LISTP))
 (14 14 (:REWRITE DEFAULT-UNARY-MINUS))
 (13 13 (:REWRITE LEN-MEMBER-EQUAL-LOOP$-AS))
 (12 12 (:REWRITE TRUE-LIST-LISTP-IMPLIES-TRUE-LISTP))
 (12 1 (:REWRITE FANCY-UQI-ACL2-NUMBER-1))
 (11 4 (:LINEAR APPLY$-BADGEP-PROPERTIES . 2))
 (10 1 (:REWRITE FANCY-UQI-SYMBOL-1))
 (10 1 (:REWRITE FANCY-UQI-RATIONAL-1))
 (9 9 (:LINEAR BOUNDS-POSITION-EQUAL-AC))
 (9 9 (:LINEAR BOUNDS-POSITION-EQUAL))
 (8 8 (:REWRITE APPLY$-CONSP-ARITY-1))
 (8 8 (:REWRITE ALWAYS$-P-LST-IMPLIES-P-ELEMENT))
 (8 4 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (7 7 (:REWRITE INTEGERP==>NUMERATOR-=-X))
 (7 7 (:REWRITE INTEGERP==>DENOMINATOR-=-1))
 (7 7 (:REWRITE DEFAULT-REALPART))
 (7 7 (:REWRITE DEFAULT-NUMERATOR))
 (7 7 (:REWRITE DEFAULT-IMAGPART))
 (7 7 (:REWRITE DEFAULT-DENOMINATOR))
 (7 7 (:REWRITE DEFAULT-COERCE-2))
 (7 7 (:REWRITE DEFAULT-COERCE-1))
 (7 7 (:LINEAR MEMBER-EQUAL-ACL2-COUNT-SMALLER-3))
 (6 6 (:TYPE-PRESCRIPTION O-FINP))
 (5 5 (:LINEAR MEMBER-EQUAL-ACL2-COUNT-SMALLER-2))
 (4 4 (:REWRITE SYMBOL-LISTP-IMPLIES-SYMBOLP))
 (4 4 (:REWRITE ACL2-NUMBER-LISTP-IMPLIES-ACL2-NUMBERP))
 (4 1 (:REWRITE AC-<))
 (3 1 (:REWRITE EQUAL-LEN-1))
 (2 2 (:REWRITE PLAIN-UQI-ALWAYS$))
 (2 2 (:LINEAR MEMBER-EQUAL-ACL2-COUNT-SMALLER-0))
 (2 1 (:REWRITE O-INFP-O-FINP-O<=))
 (1 1 (:REWRITE |a < b & b < c  =>  a < c|))
 (1 1 (:REWRITE FANCY-UQI-ALWAYS$-1))
 (1 1 (:DEFINITION IDENTITY))
 )
(APPLY$-WARRANT-PSSUBST)
(APPLY$-WARRANT-PSSUBST-DEFINITION)
(APPLY$-WARRANT-PSSUBST-NECC)
(APPLY$-PSSUBST
 (1043 3 (:DEFINITION COLLECT$+))
 (1019 3 (:REWRITE BETA-REDUCTION))
 (911 12 (:REWRITE EV$-OPENER))
 (627 12 (:DEFINITION EV$-LIST-DEF))
 (378 21 (:DEFINITION LOOP$-AS))
 (322 39 (:DEFINITION TAMEP))
 (300 9 (:REWRITE EV$-CAR))
 (282 42 (:DEFINITION SUITABLY-TAMEP-LISTP))
 (254 229 (:REWRITE DEFAULT-CAR))
 (198 197 (:REWRITE DEFAULT-CDR))
 (150 12 (:DEFINITION ASSOC-EQUAL))
 (126 21 (:DEFINITION CDR-LOOP$-AS-TUPLE))
 (126 21 (:DEFINITION CAR-LOOP$-AS-TUPLE))
 (108 108 (:REWRITE CAR-CONS))
 (105 21 (:DEFINITION EMPTY-LOOP$-AS-TUPLEP))
 (105 6 (:DEFINITION PAIRLIS$))
 (87 87 (:TYPE-PRESCRIPTION TAMEP))
 (84 84 (:TYPE-PRESCRIPTION SUITABLY-TAMEP-LISTP))
 (84 84 (:REWRITE CDR-CONS))
 (63 63 (:REWRITE TAMEP-TRUE-CAR/CDR-NESTP))
 (48 3 (:REWRITE EV$-CDR))
 (42 22 (:REWRITE APPLY$-PRIMP-BADGE))
 (32 32 (:TYPE-PRESCRIPTION PSSUBST))
 (30 7 (:REWRITE O-P-O-INFP-CAR))
 (28 28 (:TYPE-PRESCRIPTION APPLY$-PRIMP))
 (25 2 (:DEFINITION APPLY$-BADGEP))
 (20 1 (:LINEAR APPLY$-BADGEP-PROPERTIES . 2))
 (18 10 (:REWRITE APPLY$-PRIMITIVE))
 (11 2 (:LINEAR APPLY$-BADGEP-PROPERTIES . 1))
 (9 7 (:REWRITE O-P-DEF-O-FINP-1))
 (8 2 (:DEFINITION WEAK-APPLY$-BADGE-P))
 (8 1 (:DEFINITION NATP))
 (6 6 (:TYPE-PRESCRIPTION LOOP$-AS))
 (6 6 (:META RELINK-FANCY-SCION-CORRECT))
 (4 4 (:TYPE-PRESCRIPTION APPLY$-BADGEP))
 (2 2 (:TYPE-PRESCRIPTION O-FINP))
 (2 1 (:REWRITE APPLY$-BADGEP-PROPERTIES . 1))
 (1 1 (:REWRITE INTEGER-LISTP-IMPLIES-INTEGERP))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 )
(PSSUBST-INDUCTOR)
(APPLY$-WARRANT-PSSUBST-INDUCTOR)
(APPLY$-WARRANT-PSSUBST-INDUCTOR-DEFINITION)
(APPLY$-WARRANT-PSSUBST-INDUCTOR-NECC)
(APPLY$-PSSUBST-INDUCTOR
 (138 3 (:DEFINITION COLLECT$+))
 (114 3 (:REWRITE BETA-REDUCTION))
 (108 6 (:DEFINITION LOOP$-AS))
 (105 6 (:DEFINITION PAIRLIS$))
 (76 75 (:REWRITE DEFAULT-CDR))
 (76 75 (:REWRITE DEFAULT-CAR))
 (36 6 (:DEFINITION CDR-LOOP$-AS-TUPLE))
 (36 6 (:DEFINITION CAR-LOOP$-AS-TUPLE))
 (32 32 (:TYPE-PRESCRIPTION PSSUBST-INDUCTOR))
 (30 6 (:DEFINITION EMPTY-LOOP$-AS-TUPLEP))
 (25 2 (:DEFINITION APPLY$-BADGEP))
 (24 24 (:REWRITE CDR-CONS))
 (24 24 (:REWRITE CAR-CONS))
 (20 1 (:LINEAR APPLY$-BADGEP-PROPERTIES . 2))
 (14 7 (:REWRITE APPLY$-PRIMITIVE))
 (11 11 (:TYPE-PRESCRIPTION APPLY$-PRIMP))
 (11 2 (:LINEAR APPLY$-BADGEP-PROPERTIES . 1))
 (8 4 (:REWRITE APPLY$-PRIMP-BADGE))
 (8 2 (:DEFINITION WEAK-APPLY$-BADGE-P))
 (8 1 (:DEFINITION NATP))
 (6 6 (:TYPE-PRESCRIPTION LOOP$-AS))
 (6 6 (:REWRITE EV$-OPENER))
 (6 6 (:META RELINK-FANCY-SCION-CORRECT))
 (6 1 (:REWRITE O-P-O-INFP-CAR))
 (4 4 (:TYPE-PRESCRIPTION APPLY$-BADGEP))
 (3 1 (:REWRITE O-P-DEF-O-FINP-1))
 (2 2 (:TYPE-PRESCRIPTION O-FINP))
 (2 1 (:REWRITE APPLY$-BADGEP-PROPERTIES . 1))
 (1 1 (:REWRITE INTEGER-LISTP-IMPLIES-INTEGERP))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 )
(PSSUBST-INDUCTION-RULE)
(PSTERMP-PSSUBST-[1]
 (745890 616609 (:REWRITE DEFAULT-CAR))
 (447641 436960 (:REWRITE DEFAULT-CDR))
 (166604 38237 (:REWRITE O-P-O-INFP-CAR))
 (135069 135069 (:REWRITE TAMEP-TRUE-CAR/CDR-NESTP))
 (53469 37449 (:REWRITE O-P-DEF-O-FINP-1))
 (27516 1136 (:REWRITE MEMBER-EQUAL-NEWVAR-COMPONENTS-1))
 (17120 80 (:REWRITE COLLECT$+-SINGLETON))
 (14384 14384 (:TYPE-PRESCRIPTION O-FINP))
 (12460 6230 (:REWRITE DEFAULT-+-2))
 (11531 5914 (:REWRITE APPLY$-PRIMITIVE))
 (6467 6467 (:TYPE-PRESCRIPTION PSSUBST))
 (6238 6238 (:REWRITE TRUE-LIST-LISTP-IMPLIES-TRUE-LISTP))
 (6230 6230 (:REWRITE DEFAULT-+-1))
 (6034 6034 (:REWRITE LEN-MEMBER-EQUAL-LOOP$-AS))
 (4141 4141 (:REWRITE SYMBOL-LISTP-IMPLIES-SYMBOLP))
 (4074 4074 (:REWRITE SUBSETP-IMPLIES-MEMBER))
 (2180 2180 (:REWRITE MEMBER-EQUAL-NEWVAR-COMPONENTS-3))
 (2150 2150 (:REWRITE MEMBER-EQUAL-NEWVAR-COMPONENTS-2))
 (1351 1351 (:REWRITE DEFAULT-COERCE-2))
 (1351 1351 (:REWRITE DEFAULT-COERCE-1))
 (489 97 (:REWRITE APPLY$-BADGEP-PROPERTIES . 3))
 (381 381 (:REWRITE APPLY$-WARRANT-PSTERMP-NECC))
 (381 381 (:REWRITE APPLY$-WARRANT-PSSUBST-NECC))
 (295 97 (:DEFINITION APPLY$-BADGEP))
 (196 97 (:DEFINITION WEAK-APPLY$-BADGE-P))
 (166 166 (:LINEAR BOUNDS-POSITION-EQUAL-AC))
 (166 166 (:LINEAR BOUNDS-POSITION-EQUAL))
 (97 97 (:TYPE-PRESCRIPTION APPLY$-BADGEP))
 )
(PSTERMP-PSSUBST-[2]
 (1139137 2821 (:DEFINITION COLLECT$+))
 (654617 545669 (:REWRITE DEFAULT-CAR))
 (401339 391371 (:REWRITE DEFAULT-CDR))
 (143259 32709 (:REWRITE O-P-O-INFP-CAR))
 (116217 116217 (:REWRITE TAMEP-TRUE-CAR/CDR-NESTP))
 (46634 31958 (:REWRITE O-P-DEF-O-FINP-1))
 (32945 1395 (:REWRITE MEMBER-EQUAL-NEWVAR-COMPONENTS-1))
 (13112 13112 (:TYPE-PRESCRIPTION O-FINP))
 (12108 6054 (:REWRITE DEFAULT-+-2))
 (10476 5246 (:REWRITE APPLY$-PRIMITIVE))
 (6062 6062 (:REWRITE TRUE-LIST-LISTP-IMPLIES-TRUE-LISTP))
 (6054 6054 (:REWRITE DEFAULT-+-1))
 (5858 5858 (:REWRITE LEN-MEMBER-EQUAL-LOOP$-AS))
 (5684 5684 (:TYPE-PRESCRIPTION PSSUBST))
 (4056 4056 (:REWRITE SUBSETP-IMPLIES-MEMBER))
 (4009 4009 (:REWRITE SYMBOL-LISTP-IMPLIES-SYMBOLP))
 (2730 2730 (:REWRITE MEMBER-EQUAL-NEWVAR-COMPONENTS-3))
 (2700 2700 (:REWRITE MEMBER-EQUAL-NEWVAR-COMPONENTS-2))
 (1307 1307 (:REWRITE DEFAULT-COERCE-2))
 (1307 1307 (:REWRITE DEFAULT-COERCE-1))
 (489 97 (:REWRITE APPLY$-BADGEP-PROPERTIES . 3))
 (381 381 (:REWRITE APPLY$-WARRANT-PSTERMP-NECC))
 (381 381 (:REWRITE APPLY$-WARRANT-PSSUBST-NECC))
 (295 97 (:DEFINITION APPLY$-BADGEP))
 (196 97 (:DEFINITION WEAK-APPLY$-BADGE-P))
 (166 166 (:LINEAR BOUNDS-POSITION-EQUAL-AC))
 (166 166 (:LINEAR BOUNDS-POSITION-EQUAL))
 (97 97 (:TYPE-PRESCRIPTION APPLY$-BADGEP))
 )
(PSTERMP-PSSUBST-[1]-WITHOUT-COMPOSE-RULES
 (194112 179499 (:REWRITE DEFAULT-CAR))
 (156838 5648 (:REWRITE MEMBER-EQUAL-NEWVAR-COMPONENTS-1))
 (142430 141861 (:REWRITE DEFAULT-CDR))
 (47564 9748 (:REWRITE O-P-O-INFP-CAR))
 (46752 46752 (:REWRITE TAMEP-TRUE-CAR/CDR-NESTP))
 (18352 9732 (:REWRITE O-P-DEF-O-FINP-1))
 (17120 80 (:REWRITE COLLECT$+-SINGLETON))
 (14271 14271 (:REWRITE SUBSETP-IMPLIES-MEMBER))
 (11884 5942 (:REWRITE DEFAULT-+-2))
 (9398 9398 (:REWRITE MEMBER-EQUAL-NEWVAR-COMPONENTS-3))
 (9182 9182 (:REWRITE MEMBER-EQUAL-NEWVAR-COMPONENTS-2))
 (8604 8604 (:TYPE-PRESCRIPTION O-FINP))
 (6962 3521 (:REWRITE APPLY$-PRIMITIVE))
 (5958 5958 (:REWRITE TRUE-LIST-LISTP-IMPLIES-TRUE-LISTP))
 (5942 5942 (:REWRITE DEFAULT-+-1))
 (5746 5746 (:REWRITE LEN-MEMBER-EQUAL-LOOP$-AS))
 (3929 3929 (:REWRITE SYMBOL-LISTP-IMPLIES-SYMBOLP))
 (3887 3887 (:TYPE-PRESCRIPTION PSSUBST))
 (1279 1279 (:REWRITE DEFAULT-COERCE-2))
 (1279 1279 (:REWRITE DEFAULT-COERCE-1))
 (489 97 (:REWRITE APPLY$-BADGEP-PROPERTIES . 3))
 (381 381 (:REWRITE APPLY$-WARRANT-PSTERMP-NECC))
 (381 381 (:REWRITE APPLY$-WARRANT-PSSUBST-NECC))
 (295 97 (:DEFINITION APPLY$-BADGEP))
 (196 97 (:DEFINITION WEAK-APPLY$-BADGE-P))
 (166 166 (:LINEAR BOUNDS-POSITION-EQUAL-AC))
 (166 166 (:LINEAR BOUNDS-POSITION-EQUAL))
 (97 97 (:TYPE-PRESCRIPTION APPLY$-BADGEP))
 )
(PSOCCUR
 (1405 31 (:DEFINITION MEMBER-EQUAL))
 (1173 5 (:DEFINITION APPLY$-BADGEP))
 (992 3 (:DEFINITION INTEGER-LISTP))
 (977 11 (:REWRITE APPLY$-BADGEP-PROPERTIES . 1))
 (801 8 (:DEFINITION ALWAYS$))
 (751 16 (:DEFINITION SUBSETP-EQUAL))
 (713 2 (:REWRITE PLAIN-UQI-INTEGER-LISTP))
 (546 1 (:REWRITE FANCY-UQI-INTEGER-1))
 (539 43 (:REWRITE SUBSETP-REFLEXIVE-LEMMA))
 (455 2 (:REWRITE INTEGER-LISTP-IMPLIES-ALWAYS$-INTEGERP))
 (453 8 (:REWRITE APPLY$-SYMBOL-ARITY-1))
 (413 8 (:REWRITE APPLY$-PRIMITIVE))
 (397 8 (:META APPLY$-PRIM-META-FN-CORRECT))
 (317 317 (:REWRITE DEFAULT-CDR))
 (280 28 (:REWRITE MEMBER-EQUAL-NEWVAR-COMPONENTS-1))
 (221 5 (:REWRITE APPLY$-BADGEP-PROPERTIES . 2))
 (149 1 (:REWRITE O<=-O-FINP-DEF))
 (144 144 (:REWRITE DEFAULT-CAR))
 (132 65 (:REWRITE DEFAULT-+-2))
 (127 127 (:TYPE-PRESCRIPTION SUBSETP-EQUAL))
 (126 7 (:DEFINITION LOOP$-AS))
 (100 8 (:DEFINITION NATP))
 (95 2 (:REWRITE PLAIN-UQI-TRUE-LIST-LISTP))
 (88 65 (:REWRITE DEFAULT-+-1))
 (84 84 (:REWRITE MEMBER-EQUAL-NEWVAR-COMPONENTS-3))
 (78 78 (:REWRITE SUBSETP-IMPLIES-MEMBER))
 (74 13 (:DEFINITION LEN))
 (68 2 (:REWRITE PLAIN-UQI-ACL2-NUMBER-LISTP))
 (63 7 (:DEFINITION LENGTH))
 (62 2 (:REWRITE PLAIN-UQI-SYMBOL-LISTP))
 (62 2 (:REWRITE PLAIN-UQI-RATIONAL-LISTP))
 (56 56 (:REWRITE MEMBER-EQUAL-NEWVAR-COMPONENTS-2))
 (56 14 (:REWRITE COMMUTATIVITY-OF-+))
 (56 14 (:DEFINITION INTEGER-ABS))
 (54 6 (:DEFINITION TRUE-LISTP))
 (54 3 (:DEFINITION TRUE-LIST-LISTP))
 (54 2 (:REWRITE PLAIN-UQI-RATIONAL-LIST-LISTP))
 (46 10 (:REWRITE O-P-O-INFP-CAR))
 (43 43 (:REWRITE TRANSITIVITY-OF-SUBSETP-EQUAL))
 (43 5 (:DEFINITION RATIONAL-LISTP))
 (42 42 (:TYPE-PRESCRIPTION APPLY$-BADGEP))
 (42 7 (:DEFINITION CDR-LOOP$-AS-TUPLE))
 (42 7 (:DEFINITION CAR-LOOP$-AS-TUPLE))
 (42 2 (:REWRITE TRUE-LIST-LISTP-IMPLIES-ALWAYS$-TRUE-LISTP))
 (41 41 (:TYPE-PRESCRIPTION LEN))
 (40 40 (:TYPE-PRESCRIPTION ALWAYS$))
 (35 7 (:DEFINITION EMPTY-LOOP$-AS-TUPLEP))
 (34 1 (:REWRITE FANCY-UQI-RATIONAL-LISTP-1))
 (33 12 (:LINEAR APPLY$-BADGEP-PROPERTIES . 1))
 (32 16 (:REWRITE APPLY$-PRIMP-BADGE))
 (31 2 (:REWRITE STRUCTURE-OF-LOOP$-AS-ELEMENTS-BRIDGE))
 (27 3 (:DEFINITION ACL2-NUMBER-LISTP))
 (26 10 (:REWRITE APPLY$-BADGEP-PROPERTIES . 3))
 (25 25 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (25 25 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (25 23 (:REWRITE DEFAULT-<-2))
 (24 24 (:TYPE-PRESCRIPTION APPLY$-PRIMP))
 (24 23 (:REWRITE DEFAULT-<-1))
 (24 4 (:DEFINITION ALL-NILS))
 (24 2 (:REWRITE ACL2-NUMBER-LISTP-IMPLIES-ALWAYS$-ACL2-NUMBERP))
 (22 22 (:REWRITE CDR-CONS))
 (22 5 (:DEFINITION WEAK-APPLY$-BADGE-P))
 (22 1 (:REWRITE FANCY-UQI-IDENTITY-1))
 (21 21 (:REWRITE CAR-CONS))
 (21 3 (:DEFINITION SYMBOL-LISTP))
 (21 1 (:REWRITE FANCY-UQI-TRUE-LIST-1))
 (20 20 (:TYPE-PRESCRIPTION ALL-NILS))
 (20 2 (:REWRITE SYMBOL-LISTP-IMPLIES-ALWAYS$-SYMBOLP))
 (20 2 (:REWRITE RATIONAL-LISTP-IMPLIES-ALWAYS$-RATIONALP))
 (18 18 (:REWRITE INTEGER-LISTP-IMPLIES-INTEGERP))
 (17 17 (:REWRITE RATIONAL-LISTP-IMPLIES-RATIONALP))
 (16 16 (:REWRITE FOLD-CONSTS-IN-+))
 (16 10 (:REWRITE O-P-DEF-O-FINP-1))
 (15 15 (:TYPE-PRESCRIPTION TRUE-LIST-LISTP))
 (15 15 (:TYPE-PRESCRIPTION SYMBOL-LISTP))
 (15 15 (:TYPE-PRESCRIPTION INTEGER-LISTP))
 (15 15 (:TYPE-PRESCRIPTION ACL2-NUMBER-LISTP))
 (14 14 (:REWRITE DEFAULT-UNARY-MINUS))
 (13 13 (:REWRITE LEN-MEMBER-EQUAL-LOOP$-AS))
 (12 12 (:REWRITE TRUE-LIST-LISTP-IMPLIES-TRUE-LISTP))
 (12 1 (:REWRITE FANCY-UQI-ACL2-NUMBER-1))
 (11 4 (:LINEAR APPLY$-BADGEP-PROPERTIES . 2))
 (10 1 (:REWRITE FANCY-UQI-SYMBOL-1))
 (10 1 (:REWRITE FANCY-UQI-RATIONAL-1))
 (9 9 (:LINEAR BOUNDS-POSITION-EQUAL-AC))
 (9 9 (:LINEAR BOUNDS-POSITION-EQUAL))
 (8 8 (:REWRITE APPLY$-CONSP-ARITY-1))
 (8 8 (:REWRITE ALWAYS$-P-LST-IMPLIES-P-ELEMENT))
 (8 4 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (7 7 (:REWRITE INTEGERP==>NUMERATOR-=-X))
 (7 7 (:REWRITE INTEGERP==>DENOMINATOR-=-1))
 (7 7 (:REWRITE DEFAULT-REALPART))
 (7 7 (:REWRITE DEFAULT-NUMERATOR))
 (7 7 (:REWRITE DEFAULT-IMAGPART))
 (7 7 (:REWRITE DEFAULT-DENOMINATOR))
 (7 7 (:REWRITE DEFAULT-COERCE-2))
 (7 7 (:REWRITE DEFAULT-COERCE-1))
 (7 7 (:LINEAR MEMBER-EQUAL-ACL2-COUNT-SMALLER-3))
 (6 6 (:TYPE-PRESCRIPTION O-FINP))
 (5 5 (:LINEAR MEMBER-EQUAL-ACL2-COUNT-SMALLER-2))
 (4 4 (:REWRITE SYMBOL-LISTP-IMPLIES-SYMBOLP))
 (4 4 (:REWRITE ACL2-NUMBER-LISTP-IMPLIES-ACL2-NUMBERP))
 (4 1 (:REWRITE AC-<))
 (3 1 (:REWRITE EQUAL-LEN-1))
 (2 2 (:REWRITE PLAIN-UQI-ALWAYS$))
 (2 2 (:LINEAR MEMBER-EQUAL-ACL2-COUNT-SMALLER-0))
 (2 1 (:REWRITE O-INFP-O-FINP-O<=))
 (1 1 (:REWRITE |a < b & b < c  =>  a < c|))
 (1 1 (:REWRITE FANCY-UQI-ALWAYS$-1))
 (1 1 (:DEFINITION IDENTITY))
 )
(APPLY$-WARRANT-PSOCCUR)
(APPLY$-WARRANT-PSOCCUR-DEFINITION)
(APPLY$-WARRANT-PSOCCUR-NECC)
(APPLY$-PSOCCUR
 (396 22 (:DEFINITION LOOP$-AS))
 (245 213 (:REWRITE DEFAULT-CAR))
 (157 157 (:REWRITE DEFAULT-CDR))
 (132 22 (:DEFINITION CDR-LOOP$-AS-TUPLE))
 (132 22 (:DEFINITION CAR-LOOP$-AS-TUPLE))
 (110 22 (:DEFINITION EMPTY-LOOP$-AS-TUPLEP))
 (44 44 (:REWRITE TAMEP-TRUE-CAR/CDR-NESTP))
 (44 10 (:REWRITE O-P-O-INFP-CAR))
 (20 20 (:TYPE-PRESCRIPTION O-P))
 (19 12 (:REWRITE APPLY$-PRIMITIVE))
 (14 10 (:REWRITE O-P-DEF-O-FINP-1))
 (4 4 (:TYPE-PRESCRIPTION O-FINP))
 (4 4 (:META RELINK-FANCY-SCION-CORRECT))
 )
(PSOCCUR-PSSUBST
 (217746 217746 (:REWRITE TAMEP-TRUE-CAR/CDR-NESTP))
 (150236 34583 (:REWRITE O-P-O-INFP-CAR))
 (48191 33731 (:REWRITE O-P-DEF-O-FINP-1))
 (10772 5386 (:REWRITE APPLY$-PRIMITIVE))
 (10362 10362 (:TYPE-PRESCRIPTION O-FINP))
 (897 897 (:REWRITE APPLY$-WARRANT-PSSUBST-NECC))
 (897 897 (:REWRITE APPLY$-WARRANT-PSOCCUR-NECC))
 (30 6 (:LINEAR APPLY$-BADGEP-PROPERTIES . 1))
 (18 6 (:DEFINITION APPLY$-BADGEP))
 (12 6 (:DEFINITION WEAK-APPLY$-BADGE-P))
 (6 6 (:TYPE-PRESCRIPTION APPLY$-BADGEP))
 )
