(NOT-INTERSECTION-EQUAL-WHEN-ALL-<-OF-CAR-AND-SORTEDP-<=
 (10058 66 (:DEFINITION ALL-<))
 (5368 110 (:REWRITE USE-ALL-<-FOR-CAR))
 (4078 2039 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (4078 2039 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (3550 45 (:REWRITE USE-ALL-<=-FOR-CAR))
 (3344 31 (:REWRITE ALL-<=-WHEN-ALL-<))
 (3257 192 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (3240 94 (:REWRITE ALL-<-OF-CDR))
 (3158 186 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (3040 120 (:REWRITE DEFAULT-<-1))
 (2885 124 (:REWRITE DEFAULT-<-2))
 (2039 2039 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (2039 2039 (:TYPE-PRESCRIPTION NAT-LISTP))
 (982 143 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (707 192 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (443 22 (:REWRITE <=-OF-CAR-AND-CADR-WHEN-SORTEDP-<=))
 (388 388 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (333 3 (:REWRITE ALL-<=-OF-CDR))
 (268 268 (:REWRITE DEFAULT-CDR))
 (266 184 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (260 52 (:REWRITE ALL-RATIONALP-OF-CDR))
 (224 124 (:REWRITE USE-ALL-<))
 (220 110 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (205 194 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (194 194 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (186 186 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (157 157 (:REWRITE USE-ALL-RATIONALP-2))
 (157 157 (:REWRITE USE-ALL-RATIONALP))
 (124 124 (:REWRITE USE-ALL-<-2))
 (100 100 (:TYPE-PRESCRIPTION MEMBERP))
 (62 62 (:TYPE-PRESCRIPTION ALL-<=))
 (56 56 (:REWRITE USE-ALL-<=-2))
 (56 56 (:REWRITE USE-ALL-<=))
 (34 31 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (31 31 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (31 31 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (31 31 (:REWRITE ALL-<=-MONOTONE))
 (20 4 (:REWRITE SORTEDP-<=-OF-CDR))
 )
(<-OF-CAR-AND-CADR-WHEN-SORTEDP-<=-AND-NO-DUPLICATESP-EQUAL
 (1570 785 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (785 785 (:TYPE-PRESCRIPTION NAT-LISTP))
 (685 50 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NO-DUPLICATESP-EQUAL-OF-CDR))
 (562 22 (:REWRITE SORTEDP-<=-OF-CDR))
 (547 17 (:REWRITE USE-ALL-<-FOR-CAR))
 (518 32 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (496 41 (:REWRITE NO-DUPLICATESP-EQUAL-OF-CDR))
 (449 17 (:REWRITE DEFAULT-<-1))
 (398 41 (:REWRITE ALL-<-OF-CDR))
 (386 15 (:REWRITE USE-ALL-<=-FOR-CAR))
 (379 17 (:REWRITE DEFAULT-<-2))
 (341 12 (:REWRITE <=-OF-CAR-AND-CADR-WHEN-SORTEDP-<=))
 (340 96 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (251 251 (:TYPE-PRESCRIPTION ALL-<))
 (248 23 (:REWRITE ALL-<=-WHEN-ALL-<))
 (142 142 (:REWRITE DEFAULT-CDR))
 (112 8 (:REWRITE ALL-<=-OF-CDR))
 (96 96 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (96 96 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (96 96 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (96 96 (:REWRITE ALL-<-TRANSITIVE))
 (96 32 (:REWRITE USE-ALL-RATIONALP))
 (82 32 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (81 81 (:REWRITE DEFAULT-CAR))
 (64 64 (:TYPE-PRESCRIPTION MEMBERP))
 (62 42 (:REWRITE SORTEDP-<=-WHEN-NOT-CONSP-OF-CDR))
 (50 50 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (46 46 (:TYPE-PRESCRIPTION ALL-<=))
 (34 17 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (32 32 (:REWRITE USE-ALL-RATIONALP-2))
 (30 25 (:REWRITE ALL-RATIONALP-OF-CDR))
 (23 23 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (23 23 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (23 23 (:REWRITE ALL-<=-MONOTONE))
 (17 17 (:REWRITE USE-ALL-<=-2))
 (17 17 (:REWRITE USE-ALL-<=))
 (17 17 (:REWRITE USE-ALL-<-2))
 (17 17 (:REWRITE USE-ALL-<))
 (3 3 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 )
(MERGE-<-AND-REMOVE-DUPS-AUX
 (1788 894 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (1788 894 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (894 894 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (894 894 (:TYPE-PRESCRIPTION NAT-LISTP))
 (144 8 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (125 7 (:REWRITE DEFAULT-<-2))
 (125 7 (:REWRITE DEFAULT-<-1))
 (77 37 (:REWRITE DEFAULT-+-2))
 (56 4 (:REWRITE USE-ALL-<=-FOR-CAR))
 (51 37 (:REWRITE DEFAULT-+-1))
 (32 4 (:REWRITE USE-ALL-<-FOR-CAR))
 (32 4 (:REWRITE ALL-<=-WHEN-ALL-<))
 (29 29 (:REWRITE DEFAULT-CDR))
 (28 14 (:TYPE-PRESCRIPTION TRUE-LISTP-REVAPPEND-TYPE-PRESCRIPTION))
 (24 8 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (24 8 (:REWRITE USE-ALL-RATIONALP))
 (20 20 (:TYPE-PRESCRIPTION ALL-<))
 (16 16 (:TYPE-PRESCRIPTION MEMBERP))
 (16 16 (:REWRITE DEFAULT-CAR))
 (10 10 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (10 10 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (8 8 (:TYPE-PRESCRIPTION ALL-<=))
 (8 8 (:REWRITE USE-ALL-RATIONALP-2))
 (8 8 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (8 8 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (8 8 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (8 8 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (8 8 (:REWRITE ALL-<-TRANSITIVE))
 (8 4 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (7 7 (:REWRITE USE-ALL-<=-2))
 (7 7 (:REWRITE USE-ALL-<=))
 (7 7 (:REWRITE USE-ALL-<-2))
 (7 7 (:REWRITE USE-ALL-<))
 (6 6 (:REWRITE FOLD-CONSTS-IN-+))
 (6 3 (:DEFINITION TRUE-LISTP))
 (4 4 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (4 4 (:REWRITE ALL-<=-MONOTONE))
 )
(NAT-LISTP-OF-MERGE-<-AND-REMOVE-DUPS-AUX
 (119 8 (:REWRITE USE-ALL-<=-FOR-CAR))
 (71 8 (:REWRITE ALL-<=-WHEN-ALL-<))
 (64 8 (:REWRITE USE-ALL-<-FOR-CAR))
 (62 31 (:REWRITE NAT-LISTP-WHEN-ALL-NATP-CHEAP))
 (44 44 (:REWRITE DEFAULT-CAR))
 (42 42 (:TYPE-PRESCRIPTION ALL-<))
 (31 31 (:TYPE-PRESCRIPTION ALL-NATP))
 (24 8 (:REWRITE DEFAULT-<-2))
 (24 8 (:REWRITE DEFAULT-<-1))
 (23 17 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (17 17 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (17 17 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (17 17 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (17 17 (:REWRITE ALL-<-TRANSITIVE))
 (16 16 (:TYPE-PRESCRIPTION ALL-<=))
 (16 8 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (8 8 (:REWRITE USE-ALL-<=-2))
 (8 8 (:REWRITE USE-ALL-<=))
 (8 8 (:REWRITE USE-ALL-<-2))
 (8 8 (:REWRITE USE-ALL-<))
 (8 8 (:REWRITE DEFAULT-CDR))
 (8 8 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (8 8 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (8 8 (:REWRITE ALL-<=-MONOTONE))
 (6 2 (:DEFINITION TRUE-LIST-FIX))
 (2 2 (:TYPE-PRESCRIPTION TRUE-LISTP-REVAPPEND-TYPE-PRESCRIPTION))
 (2 2 (:TYPE-PRESCRIPTION TRUE-LIST-FIX))
 (2 2 (:TYPE-PRESCRIPTION REVAPPEND))
 )
(TRUE-LISTP-OF-MERGE-<-AND-REMOVE-DUPS-AUX
 (1110 555 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (1110 555 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (555 555 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (555 555 (:TYPE-PRESCRIPTION NAT-LISTP))
 (240 12 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (198 6 (:REWRITE DEFAULT-<-2))
 (198 6 (:REWRITE DEFAULT-<-1))
 (91 6 (:REWRITE USE-ALL-<=-FOR-CAR))
 (60 12 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (55 6 (:REWRITE ALL-<=-WHEN-ALL-<))
 (48 6 (:REWRITE USE-ALL-<-FOR-CAR))
 (32 32 (:TYPE-PRESCRIPTION ALL-<))
 (32 32 (:REWRITE DEFAULT-CAR))
 (24 24 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (19 13 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (18 9 (:DEFINITION TRUE-LISTP))
 (15 15 (:REWRITE DEFAULT-CDR))
 (13 13 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (13 13 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (13 13 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (13 13 (:REWRITE ALL-<-TRANSITIVE))
 (12 12 (:TYPE-PRESCRIPTION ALL-<=))
 (12 12 (:REWRITE USE-ALL-RATIONALP-2))
 (12 12 (:REWRITE USE-ALL-RATIONALP))
 (12 12 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (12 12 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (12 6 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (6 6 (:REWRITE USE-ALL-<=-2))
 (6 6 (:REWRITE USE-ALL-<=))
 (6 6 (:REWRITE USE-ALL-<-2))
 (6 6 (:REWRITE USE-ALL-<))
 (6 6 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (6 6 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (6 6 (:REWRITE ALL-<=-MONOTONE))
 )
(RATIONAL-LISTP-OF-MERGE-<-AND-REMOVE-DUPS-AUX
 (2046 1023 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (1023 1023 (:TYPE-PRESCRIPTION NAT-LISTP))
 (119 8 (:REWRITE USE-ALL-<=-FOR-CAR))
 (71 8 (:REWRITE ALL-<=-WHEN-ALL-<))
 (64 8 (:REWRITE USE-ALL-<-FOR-CAR))
 (51 51 (:REWRITE DEFAULT-CAR))
 (42 42 (:TYPE-PRESCRIPTION ALL-<))
 (32 8 (:REWRITE DEFAULT-<-2))
 (32 8 (:REWRITE DEFAULT-<-1))
 (23 17 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (17 17 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (17 17 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (17 17 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (17 17 (:REWRITE ALL-<-TRANSITIVE))
 (16 16 (:TYPE-PRESCRIPTION ALL-<=))
 (16 8 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (13 13 (:REWRITE DEFAULT-CDR))
 (8 8 (:REWRITE USE-ALL-<=-2))
 (8 8 (:REWRITE USE-ALL-<=))
 (8 8 (:REWRITE USE-ALL-<-2))
 (8 8 (:REWRITE USE-ALL-<))
 (8 8 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (8 8 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (8 8 (:REWRITE ALL-<=-MONOTONE))
 )
(SORTEDP-<=-OF-MERGE-<-AND-REMOVE-DUPS-AUX
 (1556 778 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (1556 778 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (778 778 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (778 778 (:TYPE-PRESCRIPTION NAT-LISTP))
 (627 19 (:REWRITE CDR-OF-REVERSE-LIST))
 (456 19 (:DEFINITION TAKE))
 (347 45 (:REWRITE ALL-<=-WHEN-ALL-<))
 (276 23 (:REWRITE ZP-OPEN))
 (276 4 (:DEFINITION BINARY-APPEND))
 (230 230 (:TYPE-PRESCRIPTION LEN))
 (178 27 (:REWRITE DEFAULT-<-2))
 (161 92 (:REWRITE DEFAULT-+-2))
 (160 8 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (155 27 (:REWRITE DEFAULT-<-1))
 (132 4 (:REWRITE CAR-OF-REVERSE-LIST))
 (130 34 (:REWRITE NOT-ALL-<=-WHEN-<-AND-MEMBER-EQUAL))
 (115 23 (:DEFINITION LEN))
 (111 111 (:TYPE-PRESCRIPTION ALL-<))
 (110 110 (:REWRITE DEFAULT-CDR))
 (105 7 (:REWRITE USE-ALL-<=-FOR-CAR))
 (96 4 (:DEFINITION NTH))
 (92 92 (:REWRITE DEFAULT-+-1))
 (92 23 (:REWRITE FOLD-CONSTS-IN-+))
 (88 4 (:DEFINITION MEMBER-EQUAL))
 (83 83 (:REWRITE DEFAULT-CAR))
 (80 7 (:REWRITE USE-ALL-<-FOR-CAR))
 (78 54 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (54 54 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (54 54 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG1))
 (54 54 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (54 54 (:REWRITE ALL-<-TRANSITIVE))
 (52 52 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (52 52 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (49 19 (:REWRITE CONSP-OF-REVERSE-LIST))
 (40 8 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (34 34 (:TYPE-PRESCRIPTION REVERSE-LIST))
 (34 34 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (34 34 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (32 30 (:REWRITE USE-ALL-<=))
 (30 30 (:TYPE-PRESCRIPTION TAKE))
 (30 30 (:REWRITE USE-ALL-<=-2))
 (30 30 (:REWRITE USE-ALL-<-2))
 (30 30 (:REWRITE USE-ALL-<))
 (24 3 (:REWRITE ALL-<-OF-CDR))
 (20 20 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (16 16 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (14 7 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (14 2 (:REWRITE ALL-<-OF-REVERSE-LIST))
 (8 8 (:REWRITE USE-ALL-RATIONALP-2))
 (8 8 (:REWRITE USE-ALL-RATIONALP))
 (8 8 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (8 8 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (3 3 (:REWRITE <=-OF-CAR-AND-CADR-WHEN-SORTEDP-<=))
 (2 2 (:TYPE-PRESCRIPTION MEMBERP))
 )
(NO-DUPLICATESP-EQUAL-OF-MERGE-<-AND-REMOVE-DUPS-AUX
 (9552 4776 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (9552 4776 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (4776 4776 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (4776 4776 (:TYPE-PRESCRIPTION NAT-LISTP))
 (1518 46 (:REWRITE CDR-OF-REVERSE-LIST))
 (1410 82 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1334 141 (:REWRITE DEFAULT-<-1))
 (1104 46 (:DEFINITION TAKE))
 (869 67 (:REWRITE USE-ALL-<=-FOR-CAR))
 (648 138 (:REWRITE USE-ALL-RATIONALP))
 (624 52 (:REWRITE ZP-OPEN))
 (604 604 (:TYPE-PRESCRIPTION MEMBERP))
 (523 70 (:REWRITE USE-ALL-<-FOR-CAR))
 (520 520 (:TYPE-PRESCRIPTION LEN))
 (396 22 (:DEFINITION BINARY-APPEND))
 (364 208 (:REWRITE DEFAULT-+-2))
 (260 52 (:DEFINITION LEN))
 (244 150 (:REWRITE USE-ALL-<))
 (208 208 (:REWRITE DEFAULT-+-1))
 (208 52 (:REWRITE FOLD-CONSTS-IN-+))
 (198 6 (:REWRITE CAR-OF-REVERSE-LIST))
 (189 183 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (185 185 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (153 153 (:TYPE-PRESCRIPTION REVERSE-LIST))
 (150 150 (:REWRITE USE-ALL-<-2))
 (149 149 (:REWRITE USE-ALL-<=-2))
 (149 149 (:REWRITE USE-ALL-<=))
 (144 6 (:DEFINITION NTH))
 (142 14 (:REWRITE ALL-<-OF-CDR))
 (140 70 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (138 138 (:REWRITE USE-ALL-RATIONALP-2))
 (119 53 (:REWRITE CONSP-OF-REVERSE-LIST))
 (100 100 (:TYPE-PRESCRIPTION ALL-<=))
 (83 3 (:REWRITE NO-DUPLICATESP-EQUAL-OF-CONS-NO-SPLIT))
 (74 74 (:TYPE-PRESCRIPTION TAKE))
 (70 5 (:REWRITE ALL-<=-OF-CDR))
 (52 49 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (50 50 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (49 49 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (49 49 (:REWRITE ALL-<=-MONOTONE))
 (47 47 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (44 20 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (43 1 (:DEFINITION INTERSECTION-EQUAL))
 (20 20 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (11 8 (:REWRITE <=-OF-CAR-AND-CADR-WHEN-SORTEDP-<=))
 (6 6 (:REWRITE CAR-CONS))
 (4 4 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (4 2 (:REWRITE APPEND-TO-NIL))
 )
(ALL-<-OF-MERGE-<-AND-REMOVE-DUPS-AUX
 (8124 4062 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (8124 4062 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (4353 304 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (4062 4062 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (4062 4062 (:TYPE-PRESCRIPTION NAT-LISTP))
 (2528 148 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2395 112 (:REWRITE DEFAULT-<-1))
 (1861 112 (:REWRITE DEFAULT-<-2))
 (1421 322 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (1038 16 (:REWRITE REVAPPEND-OF-CONS))
 (894 40 (:DEFINITION BINARY-APPEND))
 (692 122 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (592 16 (:REWRITE CDR-OF-REVAPPEND))
 (576 16 (:DEFINITION BUTLAST))
 (544 16 (:REWRITE PERM-OF-APPEND-OF-CONS))
 (528 322 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (408 392 (:REWRITE DEFAULT-CAR))
 (276 276 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (256 16 (:DEFINITION TAKE))
 (249 249 (:REWRITE DEFAULT-CDR))
 (238 114 (:REWRITE USE-ALL-<))
 (176 8 (:REWRITE PERM-OF-APPEND))
 (155 155 (:REWRITE USE-ALL-RATIONALP-2))
 (155 155 (:REWRITE USE-ALL-RATIONALP))
 (144 144 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (144 144 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (138 138 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (138 138 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (128 16 (:REWRITE ZP-OPEN))
 (128 16 (:REWRITE APPEND-TO-NIL))
 (124 124 (:TYPE-PRESCRIPTION MEMBERP))
 (114 114 (:REWRITE USE-ALL-<-2))
 (113 113 (:REWRITE USE-ALL-<=-2))
 (113 113 (:REWRITE USE-ALL-<=))
 (96 80 (:REWRITE DEFAULT-+-2))
 (96 16 (:REWRITE CAR-OF-REVAPPEND))
 (90 18 (:REWRITE ALL-RATIONALP-OF-CDR))
 (84 6 (:REWRITE ALL-<=-OF-CDR))
 (80 80 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (80 80 (:REWRITE DEFAULT-+-1))
 (80 16 (:DEFINITION TRUE-LISTP))
 (80 16 (:DEFINITION LEN))
 (64 64 (:TYPE-PRESCRIPTION LEN))
 (61 61 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (61 61 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (61 61 (:REWRITE ALL-<=-MONOTONE))
 (48 16 (:REWRITE FOLD-CONSTS-IN-+))
 (48 16 (:REWRITE COMMUTATIVITY-OF-+))
 (48 16 (:DEFINITION LAST))
 (40 24 (:REWRITE PERM-OF-APPEND-WHEN-NOT-CONSP))
 (24 6 (:REWRITE <=-OF-CAR-AND-CADR-WHEN-SORTEDP-<=))
 (16 16 (:TYPE-PRESCRIPTION TRUE-LISTP-REVAPPEND-TYPE-PRESCRIPTION))
 (16 16 (:TYPE-PRESCRIPTION REVAPPEND))
 (16 16 (:TYPE-PRESCRIPTION LAST))
 (16 16 (:REWRITE CONSP-OF-REVAPPEND))
 (12 12 (:TYPE-PRESCRIPTION SORTEDP-<=))
 (8 8 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (8 8 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (8 8 (:REWRITE CDR-CONS))
 (8 8 (:REWRITE CAR-CONS))
 (6 6 (:REWRITE SORTEDP-<=-WHEN-NOT-CONSP-OF-CDR))
 )
(MERGE-<-AND-REMOVE-DUPS)
(TRUE-LISTP-OF-MERGE-<-AND-REMOVE-DUPS)
(RATIONAL-LISTP-OF-MERGE-<-AND-REMOVE-DUPS)
(NAT-LISTP-OF-MERGE-<-AND-REMOVE-DUPS)
(SORTEDP-<=-OF-MERGE-<-AND-REMOVE-DUPS
 (4 2 (:REWRITE SORTEDP-<=-WHEN-NOT-CONSP-OF-CDR))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG2))
 )
(NO-DUPLICATESP-EQUAL-OF-MERGE-<-AND-REMOVE-DUPS
 (26 6 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NO-DUPLICATESP-EQUAL-OF-CDR))
 (12 2 (:REWRITE NO-DUPLICATESP-EQUAL-OF-CDR))
 (6 6 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 2 (:REWRITE SORTEDP-<=-WHEN-NOT-CONSP-OF-CDR))
 (2 2 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (2 2 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (2 2 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (2 2 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (2 2 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (2 2 (:REWRITE ALL-<-TRANSITIVE))
 )
(ALL-<-OF-MERGE-<-AND-REMOVE-DUPS
 (6 6 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (6 6 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (6 6 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (6 6 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (6 6 (:REWRITE ALL-<-TRANSITIVE))
 (5 5 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (5 5 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 )
