(ALL->=-ALL-BECOMES-ALL-<=-ALL
 (4822 43 (:DEFINITION ALL->=))
 (3105 50 (:REWRITE USE-ALL->=-FOR-CAR))
 (2274 26 (:REWRITE ALL-<=-ALL-OF-CDR-ARG2))
 (1806 71 (:REWRITE ALL->=-OF-CDR))
 (1622 811 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (1622 811 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (1573 77 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1328 41 (:REWRITE DEFAULT-<-1))
 (1179 41 (:REWRITE DEFAULT-<-2))
 (987 44 (:REWRITE USE-ALL-<=-FOR-CAR))
 (811 811 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (811 811 (:TYPE-PRESCRIPTION NAT-LISTP))
 (490 71 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (424 53 (:REWRITE ALL-<=-WHEN-ALL-<))
 (386 50 (:REWRITE USE-ALL-<-FOR-CAR))
 (248 248 (:TYPE-PRESCRIPTION ALL-<))
 (228 6 (:REWRITE ALL->=-ALL-OF-CDR-ARG1))
 (196 196 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (185 128 (:REWRITE ALL->=-WHEN-NOT-CONSP))
 (147 147 (:REWRITE DEFAULT-CDR))
 (135 27 (:REWRITE ALL-RATIONALP-OF-CDR))
 (128 128 (:REWRITE ALL->=-WHEN-NOT-CONSP-CHEAP))
 (128 128 (:REWRITE ALL->=-MONOTONE))
 (112 14 (:REWRITE ALL-<-OF-CDR))
 (100 50 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (99 99 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (99 99 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (99 99 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (99 99 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (99 99 (:REWRITE ALL-<-TRANSITIVE))
 (98 98 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (98 98 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (87 87 (:REWRITE DEFAULT-CAR))
 (77 77 (:REWRITE USE-ALL-RATIONALP-2))
 (77 77 (:REWRITE USE-ALL-RATIONALP))
 (68 50 (:REWRITE USE-ALL-<=))
 (50 50 (:REWRITE USE-ALL->=-2))
 (50 50 (:REWRITE USE-ALL->=))
 (50 50 (:REWRITE USE-ALL-<=-2))
 (50 50 (:REWRITE USE-ALL-<-2))
 (50 50 (:REWRITE USE-ALL-<))
 (47 47 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (47 47 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (40 40 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (40 40 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG1))
 (22 22 (:REWRITE NOT-ALL->=-WHEN-<-AND-MEMBER-EQUAL))
 (18 18 (:TYPE-PRESCRIPTION MEMBERP))
 (16 16 (:REWRITE NOT-ALL-<=-WHEN-<-AND-MEMBER-EQUAL))
 )
(NOT-INTERSECTION-EQUAL-WHEN-ALL->-OF-CAR-AND-SORTEDP->=
 (28808 14404 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (28808 14404 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (14404 14404 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (14404 14404 (:TYPE-PRESCRIPTION NAT-LISTP))
 (14140 1475 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (11095 507 (:REWRITE USE-ALL-<=-FOR-CAR))
 (7571 582 (:REWRITE ALL-<=-WHEN-ALL-<))
 (3251 552 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (3032 1077 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (2383 2383 (:TYPE-PRESCRIPTION ALL-<))
 (2233 61 (:REWRITE SORTEDP->=-OF-CDR))
 (1409 1409 (:REWRITE USE-ALL-RATIONALP-2))
 (1409 1409 (:REWRITE USE-ALL-RATIONALP))
 (1336 281 (:REWRITE ALL->-OF-CDR))
 (1282 1282 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (1191 1191 (:REWRITE DEFAULT-CDR))
 (1188 83 (:REWRITE ALL-<=-OF-CDR))
 (1164 1164 (:TYPE-PRESCRIPTION ALL-<=))
 (1107 1077 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (1077 1077 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (1077 1077 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (1077 1077 (:REWRITE ALL-<-TRANSITIVE))
 (995 995 (:REWRITE USE-ALL-<-2))
 (995 995 (:REWRITE USE-ALL-<))
 (989 989 (:REWRITE USE-ALL->=-2))
 (989 989 (:REWRITE USE-ALL->=))
 (989 989 (:REWRITE USE-ALL-<=-2))
 (989 989 (:REWRITE USE-ALL-<=))
 (978 129 (:REWRITE ALL-<-OF-CDR))
 (938 90 (:REWRITE USE-ALL-<-FOR-CAR))
 (686 90 (:REWRITE USE-ALL->=-FOR-CAR))
 (671 641 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (641 641 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (606 582 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (582 582 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (582 582 (:REWRITE ALL-<=-MONOTONE))
 (469 105 (:REWRITE ALL-RATIONALP-OF-CDR))
 (224 224 (:TYPE-PRESCRIPTION ALL->=))
 (180 90 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (132 22 (:REWRITE ALL->=-OF-CDR))
 (126 112 (:REWRITE ALL->=-WHEN-NOT-CONSP))
 (112 112 (:REWRITE ALL->=-WHEN-NOT-CONSP-CHEAP))
 (112 112 (:REWRITE ALL->=-MONOTONE))
 )
(>-OF-CAR-AND-CADR-WHEN-SORTEDP->=-AND-NO-DUPLICATESP-EQUAL
 (1502 751 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (762 15 (:REWRITE USE-ALL-<=-FOR-CAR))
 (751 751 (:TYPE-PRESCRIPTION NAT-LISTP))
 (685 50 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NO-DUPLICATESP-EQUAL-OF-CDR))
 (593 17 (:REWRITE SORTEDP->=-OF-CDR))
 (582 30 (:REWRITE ALL-<=-WHEN-ALL-<))
 (496 41 (:REWRITE NO-DUPLICATESP-EQUAL-OF-CDR))
 (466 28 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (399 15 (:REWRITE DEFAULT-<-2))
 (367 43 (:REWRITE ALL-<-OF-CDR))
 (349 15 (:REWRITE DEFAULT-<-1))
 (317 95 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (236 236 (:TYPE-PRESCRIPTION ALL-<))
 (215 15 (:REWRITE ALL-<=-OF-CDR))
 (202 13 (:REWRITE USE-ALL-<-FOR-CAR))
 (130 130 (:REWRITE DEFAULT-CDR))
 (126 13 (:REWRITE USE-ALL->=-FOR-CAR))
 (95 95 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (95 95 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (95 95 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (95 95 (:REWRITE ALL-<-TRANSITIVE))
 (84 28 (:REWRITE USE-ALL-RATIONALP))
 (77 77 (:REWRITE DEFAULT-CAR))
 (74 28 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (60 60 (:TYPE-PRESCRIPTION ALL-<=))
 (56 56 (:TYPE-PRESCRIPTION MEMBERP))
 (50 50 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-NOT-CONSP-CHEAP))
 (48 8 (:REWRITE ALL->=-OF-CDR))
 (43 29 (:REWRITE SORTEDP->=-WHEN-NOT-CONSP-OF-CDR))
 (42 42 (:TYPE-PRESCRIPTION ALL->=))
 (30 30 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (30 30 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (30 30 (:REWRITE ALL-<=-MONOTONE))
 (28 28 (:REWRITE USE-ALL-RATIONALP-2))
 (28 23 (:REWRITE ALL-RATIONALP-OF-CDR))
 (26 13 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (21 21 (:REWRITE ALL->=-WHEN-NOT-CONSP-CHEAP))
 (21 21 (:REWRITE ALL->=-WHEN-NOT-CONSP))
 (21 21 (:REWRITE ALL->=-MONOTONE))
 (15 15 (:REWRITE USE-ALL->=-2))
 (15 15 (:REWRITE USE-ALL->=))
 (15 15 (:REWRITE USE-ALL-<=-2))
 (15 15 (:REWRITE USE-ALL-<=))
 (15 15 (:REWRITE USE-ALL-<-2))
 (15 15 (: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))
 (24 4 (:REWRITE USE-ALL->=-FOR-CAR))
 (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 (: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-<=))
 (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))
 (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))
 (48 8 (:REWRITE USE-ALL->=-FOR-CAR))
 (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 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 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))
 (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))
 (36 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 (: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 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))
 (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
 (2042 1021 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (1021 1021 (: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))
 (48 8 (:REWRITE USE-ALL->=-FOR-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 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 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))
 (8 8 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (8 8 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (8 8 (:REWRITE ALL-<=-MONOTONE))
 )
(HELPER
 (522 261 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (522 261 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (319 9 (:REWRITE DEFAULT-<-2))
 (261 261 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (261 261 (:TYPE-PRESCRIPTION NAT-LISTP))
 (229 18 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (190 14 (:REWRITE ALL-<=-WHEN-ALL-<))
 (118 5 (:REWRITE ALL-<=-OF-CDR))
 (101 24 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (69 6 (:REWRITE ALL-<-OF-CDR))
 (69 4 (:REWRITE NOT-ALL-<=-WHEN-<-AND-MEMBER-EQUAL))
 (67 9 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (63 3 (:DEFINITION MEMBER-EQUAL))
 (48 48 (:TYPE-PRESCRIPTION ALL-<))
 (36 9 (:REWRITE DEFAULT-<-1))
 (26 26 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (26 26 (:REWRITE DEFAULT-CDR))
 (26 24 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (24 24 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (24 24 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (24 24 (:REWRITE ALL-<-TRANSITIVE))
 (22 22 (:REWRITE DEFAULT-CAR))
 (20 4 (:REWRITE ALL-RATIONALP-OF-CDR))
 (18 18 (:REWRITE USE-ALL-RATIONALP-2))
 (18 18 (:REWRITE USE-ALL-RATIONALP))
 (18 14 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (15 13 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (14 14 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (14 14 (:REWRITE ALL-<=-MONOTONE))
 (13 13 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (12 10 (:REWRITE USE-ALL-<=))
 (10 10 (:REWRITE USE-ALL->=-2))
 (10 10 (:REWRITE USE-ALL->=))
 (10 10 (:REWRITE USE-ALL-<=-2))
 (10 10 (:REWRITE USE-ALL-<-2))
 (10 10 (:REWRITE USE-ALL-<))
 (4 4 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (2 2 (:TYPE-PRESCRIPTION MEMBERP))
 )
(SORTEDP->=-OF-MERGE->-AND-REMOVE-DUPS-AUX
 (1294 647 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (1294 647 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (647 647 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (647 647 (:TYPE-PRESCRIPTION NAT-LISTP))
 (525 15 (:REWRITE CDR-OF-REVERSE-LIST))
 (390 15 (:DEFINITION TAKE))
 (292 4 (:DEFINITION BINARY-APPEND))
 (266 19 (:REWRITE ZP-OPEN))
 (217 26 (:REWRITE DEFAULT-<-2))
 (212 10 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (190 190 (:TYPE-PRESCRIPTION LEN))
 (186 26 (:REWRITE DEFAULT-<-1))
 (140 4 (:REWRITE CAR-OF-REVERSE-LIST))
 (133 76 (:REWRITE DEFAULT-+-2))
 (104 4 (:DEFINITION NTH))
 (95 19 (:DEFINITION LEN))
 (89 12 (:REWRITE USE-ALL-<-FOR-CAR))
 (82 7 (:REWRITE ALL-<=-WHEN-ALL-<))
 (78 78 (:REWRITE DEFAULT-CDR))
 (76 76 (:REWRITE DEFAULT-+-1))
 (76 19 (:REWRITE FOLD-CONSTS-IN-+))
 (66 66 (:REWRITE DEFAULT-CAR))
 (62 10 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (54 54 (:TYPE-PRESCRIPTION ALL-<))
 (47 21 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (38 8 (:REWRITE USE-ALL->=-FOR-CAR))
 (37 15 (:REWRITE CONSP-OF-REVERSE-LIST))
 (31 31 (:REWRITE USE-ALL-<-2))
 (31 31 (:REWRITE USE-ALL-<))
 (31 3 (:REWRITE ALL-<-OF-CDR))
 (27 27 (:REWRITE USE-ALL->=-2))
 (27 27 (:REWRITE USE-ALL->=))
 (27 27 (:REWRITE USE-ALL-<=-2))
 (27 27 (:REWRITE USE-ALL-<=))
 (26 26 (:TYPE-PRESCRIPTION REVERSE-LIST))
 (24 24 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (24 24 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG2))
 (24 12 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (23 21 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (22 22 (:TYPE-PRESCRIPTION TAKE))
 (22 22 (:REWRITE ALL-<=-ALL-WHEN-NOT-CONSP-ARG1-CHEAP))
 (21 21 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (21 21 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (21 21 (:REWRITE ALL-<-TRANSITIVE))
 (14 12 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (12 12 (:TYPE-PRESCRIPTION ALL->=))
 (12 12 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (10 10 (:REWRITE USE-ALL-RATIONALP-2))
 (10 10 (:REWRITE USE-ALL-RATIONALP))
 (10 2 (:REWRITE ALL-RATIONALP-OF-CDR))
 (7 7 (:REWRITE ALL-<=-MONOTONE))
 (6 6 (:REWRITE ALL->=-WHEN-NOT-CONSP-CHEAP))
 (6 6 (:REWRITE ALL->=-WHEN-NOT-CONSP))
 (6 6 (:REWRITE ALL->=-MONOTONE))
 (3 3 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (2 2 (:REWRITE NOT-ALL-<=-WHEN-<-AND-MEMBER-EQUAL))
 )
(HELPER2
 (808 21 (:REWRITE USE-ALL-<=-FOR-CAR))
 (596 12 (:REWRITE HELPER))
 (578 289 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (578 289 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (425 26 (:REWRITE DEFAULT-<-2))
 (306 34 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (289 289 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (289 289 (:TYPE-PRESCRIPTION NAT-LISTP))
 (140 12 (:REWRITE ALL-<=-WHEN-ALL-<))
 (77 26 (:REWRITE DEFAULT-<-1))
 (60 12 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (56 18 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (38 38 (:TYPE-PRESCRIPTION ALL-<))
 (34 34 (:REWRITE USE-ALL-RATIONALP-2))
 (34 34 (:REWRITE USE-ALL-RATIONALP))
 (33 33 (:TYPE-PRESCRIPTION ALL-<=))
 (26 26 (:REWRITE USE-ALL->=-2))
 (26 26 (:REWRITE USE-ALL->=))
 (26 26 (:REWRITE USE-ALL-<=-2))
 (26 26 (:REWRITE USE-ALL-<=))
 (26 26 (:REWRITE USE-ALL-<-2))
 (26 26 (:REWRITE USE-ALL-<))
 (24 24 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (23 23 (:REWRITE DEFAULT-CAR))
 (18 18 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (18 18 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (18 18 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (18 18 (:REWRITE ALL-<-TRANSITIVE))
 (16 4 (:REWRITE ALL->-OF-CDR))
 (12 12 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (12 12 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (12 12 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (12 12 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (12 12 (:REWRITE ALL-<=-MONOTONE))
 (6 6 (:REWRITE DEFAULT-CDR))
 (4 4 (:TYPE-PRESCRIPTION SORTEDP->=))
 (4 2 (:REWRITE SORTEDP->=-WHEN-NOT-CONSP-OF-CDR))
 )
(NOT-MEMBER-EQUAL-WHEN-ALL->
 (416 11 (:REWRITE USE-ALL-<=-FOR-CAR))
 (376 188 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (376 188 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (318 7 (:REWRITE HELPER))
 (235 11 (:REWRITE DEFAULT-<-2))
 (188 188 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (188 188 (:TYPE-PRESCRIPTION NAT-LISTP))
 (155 14 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (62 11 (:REWRITE DEFAULT-<-1))
 (56 7 (:REWRITE ALL-<=-WHEN-ALL-<))
 (35 7 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (25 5 (:REWRITE ALL->-OF-CDR))
 (24 24 (:REWRITE DEFAULT-CAR))
 (24 3 (:REWRITE USE-ALL-<-FOR-CAR))
 (23 23 (:TYPE-PRESCRIPTION ALL-<))
 (18 18 (:TYPE-PRESCRIPTION ALL-<=))
 (18 18 (:REWRITE HELPER2))
 (18 3 (:REWRITE USE-ALL->=-FOR-CAR))
 (14 14 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (11 11 (:REWRITE USE-ALL-RATIONALP-2))
 (11 11 (:REWRITE USE-ALL-RATIONALP))
 (11 11 (:REWRITE USE-ALL->=-2))
 (11 11 (:REWRITE USE-ALL->=))
 (11 11 (:REWRITE USE-ALL-<=-2))
 (11 11 (:REWRITE USE-ALL-<=))
 (11 11 (:REWRITE USE-ALL-<-2))
 (11 11 (:REWRITE USE-ALL-<))
 (10 10 (:REWRITE DEFAULT-CDR))
 (10 10 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (10 10 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (10 10 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (10 10 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (10 10 (:REWRITE ALL-<-TRANSITIVE))
 (7 7 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (7 7 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (7 7 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (7 7 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (7 7 (:REWRITE ALL-<=-MONOTONE))
 (6 6 (:TYPE-PRESCRIPTION SORTEDP->=))
 (6 6 (:TYPE-PRESCRIPTION ALL->=))
 (6 3 (:REWRITE SORTEDP->=-WHEN-NOT-CONSP-OF-CDR))
 (6 3 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (3 3 (:REWRITE ALL->=-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:REWRITE ALL->=-WHEN-NOT-CONSP))
 (3 3 (:REWRITE ALL->=-MONOTONE))
 )
(NO-DUPLICATESP-EQUAL-OF-MERGE->-AND-REMOVE-DUPS-AUX
 (16126 8063 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (16126 8063 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (8063 8063 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (8063 8063 (:TYPE-PRESCRIPTION NAT-LISTP))
 (3465 107 (:REWRITE ALL->-OF-CDR))
 (2552 140 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2466 215 (:REWRITE DEFAULT-<-1))
 (2426 219 (:REWRITE DEFAULT-<-2))
 (1820 52 (:REWRITE CDR-OF-REVERSE-LIST))
 (1352 52 (:DEFINITION TAKE))
 (980 131 (:REWRITE USE-ALL-<-FOR-CAR))
 (823 92 (:REWRITE ALL-<=-WHEN-ALL-<))
 (812 58 (:REWRITE ZP-OPEN))
 (694 148 (:REWRITE USE-ALL-RATIONALP))
 (624 131 (:REWRITE USE-ALL->=-FOR-CAR))
 (580 580 (:TYPE-PRESCRIPTION LEN))
 (579 579 (:TYPE-PRESCRIPTION ALL-<))
 (546 546 (:TYPE-PRESCRIPTION MEMBERP))
 (440 30 (:DEFINITION BINARY-APPEND))
 (406 232 (:REWRITE DEFAULT-+-2))
 (395 222 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (290 58 (:DEFINITION LEN))
 (282 140 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (262 131 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (232 232 (:REWRITE DEFAULT-+-1))
 (232 58 (:REWRITE FOLD-CONSTS-IN-+))
 (227 221 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (226 226 (:REWRITE USE-ALL->=-2))
 (226 226 (:REWRITE USE-ALL->=))
 (226 226 (:REWRITE USE-ALL-<=-2))
 (226 226 (:REWRITE USE-ALL-<=))
 (226 226 (:REWRITE USE-ALL-<-2))
 (226 226 (:REWRITE USE-ALL-<))
 (222 222 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (222 222 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (222 222 (:REWRITE ALL-<-TRANSITIVE))
 (210 6 (:REWRITE CAR-OF-REVERSE-LIST))
 (193 193 (:TYPE-PRESCRIPTION ALL->=))
 (181 181 (:TYPE-PRESCRIPTION REVERSE-LIST))
 (180 17 (:REWRITE ALL-<-OF-CDR))
 (156 6 (:DEFINITION NTH))
 (148 148 (:REWRITE USE-ALL-RATIONALP-2))
 (137 59 (:REWRITE CONSP-OF-REVERSE-LIST))
 (105 6 (:REWRITE ALL-<=-OF-CDR))
 (99 96 (:REWRITE ALL->=-WHEN-NOT-CONSP))
 (98 98 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (97 97 (:REWRITE ALL->=-WHEN-NOT-CONSP-CHEAP))
 (97 97 (:REWRITE ALL->=-MONOTONE))
 (92 92 (:REWRITE ALL-<=-MONOTONE))
 (92 16 (:LINEAR >=-OF-CAR-AND-CADR-WHEN-SORTEDP->=-LINEAR))
 (90 89 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (89 89 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (86 86 (:TYPE-PRESCRIPTION TAKE))
 (47 1 (:DEFINITION INTERSECTION-EQUAL))
 (44 20 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (42 7 (:REWRITE ALL->=-OF-CDR))
 (36 6 (:REWRITE ALL->-OF-APPEND))
 (20 20 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (20 10 (:REWRITE APPEND-TO-NIL))
 (4 4 (:TYPE-PRESCRIPTION TRUE-LISTP))
 )
(ALL-<-OF-MERGE->-AND-REMOVE-DUPS-AUX
 (8842 4421 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (8842 4421 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (5389 68 (:REWRITE HELPER))
 (5324 289 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (4421 4421 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (4421 4421 (:TYPE-PRESCRIPTION NAT-LISTP))
 (2562 144 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2253 160 (:REWRITE DEFAULT-<-1))
 (2085 160 (:REWRITE DEFAULT-<-2))
 (1251 307 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (1102 16 (:REWRITE REVAPPEND-OF-CONS))
 (958 40 (:DEFINITION BINARY-APPEND))
 (698 124 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (656 16 (:REWRITE CDR-OF-REVAPPEND))
 (640 16 (:DEFINITION BUTLAST))
 (576 16 (:REWRITE PERM-OF-APPEND-OF-CONS))
 (509 123 (:REWRITE USE-ALL->=-FOR-CAR))
 (464 448 (:REWRITE DEFAULT-CAR))
 (403 307 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (300 12 (:REWRITE ALL-<=-OF-CDR))
 (288 16 (:DEFINITION TAKE))
 (286 162 (:REWRITE USE-ALL-<))
 (278 278 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (253 253 (:REWRITE DEFAULT-CDR))
 (176 8 (:REWRITE PERM-OF-APPEND))
 (162 162 (:REWRITE USE-ALL-<-2))
 (161 161 (:REWRITE USE-ALL->=-2))
 (161 161 (:REWRITE USE-ALL->=))
 (161 161 (:REWRITE USE-ALL-<=-2))
 (161 161 (:REWRITE USE-ALL-<=))
 (160 16 (:REWRITE ZP-OPEN))
 (157 157 (:REWRITE USE-ALL-RATIONALP-2))
 (157 157 (:REWRITE USE-ALL-RATIONALP))
 (152 152 (:TYPE-PRESCRIPTION ALL->=))
 (144 144 (:REWRITE NOT-ALL-<-WHEN-MEMBERP))
 (144 144 (:REWRITE NOT-ALL-<-WHEN-MEMBER-EQUAL))
 (139 139 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (139 139 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (128 16 (:REWRITE APPEND-TO-NIL))
 (124 124 (:TYPE-PRESCRIPTION MEMBERP))
 (96 80 (:REWRITE DEFAULT-+-2))
 (96 16 (:REWRITE CAR-OF-REVAPPEND))
 (90 18 (:REWRITE ALL-RATIONALP-OF-CDR))
 (80 80 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (80 80 (:REWRITE DEFAULT-+-1))
 (80 16 (:DEFINITION TRUE-LISTP))
 (80 16 (:DEFINITION LEN))
 (76 76 (:REWRITE ALL->=-WHEN-NOT-CONSP-CHEAP))
 (76 76 (:REWRITE ALL->=-WHEN-NOT-CONSP))
 (76 76 (:REWRITE ALL->=-MONOTONE))
 (67 67 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (67 67 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (67 67 (:REWRITE ALL-<=-MONOTONE))
 (64 64 (:TYPE-PRESCRIPTION LEN))
 (48 16 (:REWRITE FOLD-CONSTS-IN-+))
 (48 16 (:REWRITE COMMUTATIVITY-OF-+))
 (48 16 (:DEFINITION LAST))
 (40 24 (:REWRITE PERM-OF-APPEND-WHEN-NOT-CONSP))
 (36 6 (:REWRITE ALL->=-OF-CDR))
 (20 20 (:TYPE-PRESCRIPTION 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))
 (14 10 (:REWRITE SORTEDP->=-WHEN-NOT-CONSP-OF-CDR))
 (8 8 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (8 8 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (8 8 (:REWRITE CDR-CONS))
 (8 8 (:REWRITE CAR-CONS))
 )
(CONSP-OF-MERGE->-AND-REMOVE-DUPS-AUX
 (1300 650 (:TYPE-PRESCRIPTION RATIONALP-OF-CAR-WHEN-RATIONAL-LISTP-CHEAP))
 (1300 650 (:TYPE-PRESCRIPTION NATP-OF-CAR-WHEN-NAT-LISTP-TYPE))
 (1139 20 (:REWRITE USE-ALL-<=-FOR-CAR))
 (978 11 (:REWRITE HELPER))
 (650 650 (:TYPE-PRESCRIPTION RATIONAL-LISTP))
 (650 650 (:TYPE-PRESCRIPTION NAT-LISTP))
 (440 22 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (372 20 (:REWRITE DEFAULT-<-2))
 (372 20 (:REWRITE DEFAULT-<-1))
 (110 22 (:REWRITE USE-ALL-RATIONALP-FOR-CAR))
 (97 20 (:REWRITE USE-ALL-<-FOR-CAR))
 (95 11 (:REWRITE ALL-<=-WHEN-ALL-<))
 (75 20 (:REWRITE USE-ALL->=-FOR-CAR))
 (71 71 (:REWRITE DEFAULT-CAR))
 (66 66 (:TYPE-PRESCRIPTION ALL-<))
 (44 44 (:TYPE-PRESCRIPTION ALL-RATIONALP))
 (40 20 (:REWRITE <-OF-CAR-WHEN-ALL-<-CHEAP))
 (31 31 (:TYPE-PRESCRIPTION ALL-<=))
 (29 23 (:REWRITE ALL-<-TRANSITIVE-FREE-2))
 (26 26 (:REWRITE DEFAULT-CDR))
 (23 23 (:REWRITE ALL-<-WHEN-NOT-CONSP-CHEAP))
 (23 23 (:REWRITE ALL-<-WHEN-NOT-CONSP))
 (23 23 (:REWRITE ALL-<-TRANSITIVE-FREE))
 (23 23 (:REWRITE ALL-<-TRANSITIVE))
 (22 22 (:TYPE-PRESCRIPTION ALL->=))
 (22 22 (:REWRITE USE-ALL-RATIONALP-2))
 (22 22 (:REWRITE USE-ALL-RATIONALP))
 (22 22 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (22 22 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 (20 20 (:REWRITE USE-ALL->=-2))
 (20 20 (:REWRITE USE-ALL->=))
 (20 20 (:REWRITE USE-ALL-<=-2))
 (20 20 (:REWRITE USE-ALL-<=))
 (20 20 (:REWRITE USE-ALL-<-2))
 (20 20 (:REWRITE USE-ALL-<))
 (11 11 (:REWRITE ALL->=-WHEN-NOT-CONSP-CHEAP))
 (11 11 (:REWRITE ALL->=-WHEN-NOT-CONSP))
 (11 11 (:REWRITE ALL->=-MONOTONE))
 (11 11 (:REWRITE ALL-<=-WHEN-NOT-CONSP-CHEAP))
 (11 11 (:REWRITE ALL-<=-WHEN-NOT-CONSP))
 (11 11 (:REWRITE ALL-<=-MONOTONE))
 (6 3 (:TYPE-PRESCRIPTION TRUE-LISTP-REVAPPEND-TYPE-PRESCRIPTION))
 (3 3 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (2 2 (:TYPE-PRESCRIPTION SORTEDP->=))
 (2 1 (: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))
 )
(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 HELPER2))
 (2 2 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE ALL-RATIONALP-WHEN-NOT-CONSP))
 )
(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))
 )
(CONSP-<-OF-MERGE->-AND-REMOVE-DUPS)
(<-OF-0-AND-LEN-BECOMES-CONSP
 (8 4 (:REWRITE DEFAULT-<-2))
 (6 3 (:REWRITE DEFAULT-+-2))
 (4 4 (:REWRITE USE-ALL->=-2))
 (4 4 (:REWRITE USE-ALL->=))
 (4 4 (:REWRITE USE-ALL-<=-2))
 (4 4 (:REWRITE USE-ALL-<=))
 (4 4 (:REWRITE USE-ALL-<-2))
 (4 4 (:REWRITE USE-ALL-<))
 (4 4 (:REWRITE DEFAULT-<-1))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-+-1))
 )
(<-OF-0-AND-LEN-OF-MERGE->-AND-REMOVE-DUPS)
