(OMAP::MAPP)
(OMAP::BOOLEANP-OF-MAPP)
(OMAP::SETP-WHEN-MAPP
 (202 202 (:REWRITE DEFAULT-CAR))
 (202 202 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (129 129 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (129 129 (:REWRITE CONSP-BY-LEN))
 (124 124 (:REWRITE DEFAULT-CDR))
 (98 98 (:REWRITE <<-TRANSITIVE))
 (32 32 (:REWRITE ALPHORDER-TRANSITIVE))
 (22 22 (:TYPE-PRESCRIPTION ALPHORDER))
 (21 7 (:REWRITE SET::NONEMPTY-MEANS-SET))
 (14 14 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (8 8 (:REWRITE CONSP-OF-CDR-BY-LEN))
 (7 7 (:REWRITE SET::IN-SET))
 )
(OMAP::ALISTP-WHEN-MAPP
 (116 36 (:REWRITE <<-TRICHOTOMY))
 (103 21 (:REWRITE <<-ASYMMETRIC))
 (62 62 (:REWRITE DEFAULT-CAR))
 (62 62 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (48 48 (:REWRITE DEFAULT-CDR))
 (42 34 (:REWRITE <<-TRANSITIVE))
 (35 35 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (35 35 (:REWRITE CONSP-BY-LEN))
 (6 6 (:REWRITE CONSP-OF-CDR-BY-LEN))
 (2 2 (:REWRITE <<-IRREFLEXIVE))
 )
(OMAP::CONSP-CAR-WHEN-MAPP-NON-NIL
 (2 1 (:REWRITE CONSP-UNDER-IFF-WHEN-TRUE-LISTP))
 (1 1 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (1 1 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE CONSP-BY-LEN))
 (1 1 (:REWRITE CAR-WHEN-ALL-EQUALP))
 )
(OMAP::MFIX
 (1 1 (:TYPE-PRESCRIPTION OMAP::MFIX))
 )
(OMAP::MAPP-OF-MFIX
 (3 3 (:TYPE-PRESCRIPTION OMAP::MFIX))
 )
(OMAP::MFIX-WHEN-MAPP
 (19 19 (:TYPE-PRESCRIPTION OMAP::MFIX))
 )
(OMAP::MFIX-IMPLIES-MAPP
 (3 3 (:TYPE-PRESCRIPTION OMAP::MFIX))
 )
(OMAP::EMPTYP
 (6 6 (:TYPE-PRESCRIPTION OMAP::MFIX))
 )
(OMAP::BOOLEANP-OF-EMPTYP)
(OMAP::MAPP-WHEN-NOT-EMPTYP
 (14 14 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (5 1 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (2 2 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 )
(OMAP::MFIX-WHEN-EMPTYP
 (4 4 (:TYPE-PRESCRIPTION OMAP::MFIX))
 )
(OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP
 (15 15 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (8 3 (:REWRITE OMAP::MFIX-WHEN-EMPTYP))
 (5 1 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (1 1 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 )
(OMAP::ACL2-COUNT-HEAD-WHEN-NOT-EMPTYP
 (1585 543 (:REWRITE DEFAULT-+-2))
 (1011 543 (:REWRITE DEFAULT-+-1))
 (500 222 (:REWRITE CONSP-UNDER-IFF-WHEN-TRUE-LISTP))
 (320 16 (:LINEAR ACL2-COUNT-CAR-CDR-LINEAR))
 (256 64 (:REWRITE LEN-WHEN-ATOM))
 (180 117 (:REWRITE DEFAULT-CAR))
 (164 107 (:REWRITE DEFAULT-CDR))
 (150 150 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (150 150 (:REWRITE CONSP-BY-LEN))
 (138 130 (:REWRITE DEFAULT-<-1))
 (134 130 (:REWRITE DEFAULT-UNARY-MINUS))
 (132 130 (:REWRITE DEFAULT-<-2))
 (131 131 (:REWRITE FOLD-CONSTS-IN-+))
 (128 128 (:REWRITE DEFAULT-COERCE-2))
 (128 128 (:REWRITE DEFAULT-COERCE-1))
 (117 117 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (109 20 (:LINEAR ACL2-COUNT-OF-CONSP-POSITIVE))
 (64 64 (:REWRITE DEFAULT-REALPART))
 (64 64 (:REWRITE DEFAULT-NUMERATOR))
 (64 64 (:REWRITE DEFAULT-IMAGPART))
 (64 64 (:REWRITE DEFAULT-DENOMINATOR))
 (50 9 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (40 40 (:LINEAR ACL2-COUNT-WHEN-MEMBER))
 (38 6 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (35 8 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (33 33 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (26 26 (:REWRITE CONSP-OF-CDR-BY-LEN))
 (24 2 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (12 4 (:REWRITE OMAP::MFIX-WHEN-EMPTYP))
 )
(OMAP::HEAD
 (40 2 (:REWRITE FAST-<<-IS-<<))
 (31 8 (:REWRITE <<-TRICHOTOMY))
 (29 29 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (23 7 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (23 4 (:REWRITE <<-ASYMMETRIC))
 (22 11 (:REWRITE CONSP-UNDER-IFF-WHEN-TRUE-LISTP))
 (20 20 (:TYPE-PRESCRIPTION <<))
 (20 9 (:REWRITE OMAP::MFIX-WHEN-EMPTYP))
 (13 13 (:REWRITE DEFAULT-CAR))
 (13 13 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (11 11 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (11 11 (:REWRITE CONSP-BY-LEN))
 (10 10 (:REWRITE DEFAULT-CDR))
 (8 8 (:REWRITE <<-TRANSITIVE))
 (2 2 (:REWRITE CONSP-OF-CDR-BY-LEN))
 )
(OMAP::HEAD-KEY-WHEN-EMPTYP
 (73 3 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (60 1 (:DEFINITION OMAP::MAPP))
 (15 1 (:REWRITE FAST-<<-IS-<<))
 (12 3 (:REWRITE <<-TRICHOTOMY))
 (10 2 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (10 2 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (9 9 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (8 8 (:TYPE-PRESCRIPTION <<))
 (8 4 (:REWRITE CONSP-UNDER-IFF-WHEN-TRUE-LISTP))
 (6 6 (:REWRITE DEFAULT-CAR))
 (6 6 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (6 1 (:REWRITE <<-ASYMMETRIC))
 (5 5 (:REWRITE DEFAULT-CDR))
 (4 4 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (4 4 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (4 4 (:REWRITE CONSP-BY-LEN))
 (4 2 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (3 3 (:REWRITE <<-TRANSITIVE))
 (1 1 (:REWRITE CONSP-OF-CDR-BY-LEN))
 )
(OMAP::HEAD-VALUE-WHEN-EMPTYP
 (73 3 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (60 1 (:DEFINITION OMAP::MAPP))
 (15 1 (:REWRITE FAST-<<-IS-<<))
 (12 3 (:REWRITE <<-TRICHOTOMY))
 (10 2 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (10 2 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (9 9 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (8 8 (:TYPE-PRESCRIPTION <<))
 (8 4 (:REWRITE CONSP-UNDER-IFF-WHEN-TRUE-LISTP))
 (6 6 (:REWRITE DEFAULT-CAR))
 (6 6 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (6 1 (:REWRITE <<-ASYMMETRIC))
 (5 5 (:REWRITE DEFAULT-CDR))
 (4 4 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (4 4 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (4 4 (:REWRITE CONSP-BY-LEN))
 (4 2 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (3 3 (:REWRITE <<-TRANSITIVE))
 (1 1 (:REWRITE CONSP-OF-CDR-BY-LEN))
 )
(OMAP::HEAD-WHEN-EMPTYP
 (24 24 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (13 2 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (5 1 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (5 1 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (4 4 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (2 1 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 )
(OMAP::HEAD-WHEN-EMPTYP-CHEAP)
(OMAP::HEAD-KEY-COUNT
 (519 11 (:DEFINITION ACL2-COUNT))
 (188 60 (:REWRITE DEFAULT-+-2))
 (116 60 (:REWRITE DEFAULT-+-1))
 (70 14 (:REWRITE COMMUTATIVITY-OF-+))
 (61 28 (:REWRITE CONSP-UNDER-IFF-WHEN-TRUE-LISTP))
 (56 14 (:DEFINITION INTEGER-ABS))
 (49 7 (:DEFINITION LENGTH))
 (30 20 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
 (28 7 (:REWRITE LEN-WHEN-ATOM))
 (25 16 (:REWRITE DEFAULT-CAR))
 (23 5 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (21 15 (:REWRITE DEFAULT-CDR))
 (19 19 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (19 19 (:REWRITE CONSP-BY-LEN))
 (19 1 (:REWRITE ACL2-COUNT-WHEN-MEMBER))
 (18 18 (:REWRITE FOLD-CONSTS-IN-+))
 (17 15 (:REWRITE DEFAULT-<-2))
 (17 15 (:REWRITE DEFAULT-<-1))
 (17 4 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (16 16 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (16 16 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (16 5 (:REWRITE OMAP::MFIX-WHEN-EMPTYP))
 (14 14 (:REWRITE DEFAULT-UNARY-MINUS))
 (14 14 (:REWRITE DEFAULT-COERCE-2))
 (14 14 (:REWRITE DEFAULT-COERCE-1))
 (13 1 (:REWRITE SUBSETP-CAR-MEMBER))
 (12 3 (:LINEAR ACL2-COUNT-OF-CONSP-POSITIVE))
 (7 7 (:REWRITE DEFAULT-REALPART))
 (7 7 (:REWRITE DEFAULT-NUMERATOR))
 (7 7 (:REWRITE DEFAULT-IMAGPART))
 (7 7 (:REWRITE DEFAULT-DENOMINATOR))
 (6 6 (:LINEAR ACL2-COUNT-WHEN-MEMBER))
 (4 1 (:REWRITE SUBSETP-WHEN-ATOM-RIGHT))
 (4 1 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (4 1 (:LINEAR ACL2-COUNT-CAR-CDR-LINEAR))
 (2 2 (:TYPE-PRESCRIPTION SUBSETP-EQUAL))
 (2 2 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (2 1 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (1 1 (:REWRITE SUBSETP-TRANS2))
 (1 1 (:REWRITE SUBSETP-TRANS))
 (1 1 (:REWRITE SUBSETP-MEMBER . 2))
 (1 1 (:REWRITE SUBSETP-MEMBER . 1))
 (1 1 (:REWRITE MEMBER-EQUAL-WHEN-ALL-EQUALP))
 (1 1 (:REWRITE CONSP-OF-CDR-BY-LEN))
 )
(OMAP::HEAD-VALUE-COUNT
 (520 11 (:DEFINITION ACL2-COUNT))
 (188 60 (:REWRITE DEFAULT-+-2))
 (116 60 (:REWRITE DEFAULT-+-1))
 (70 14 (:REWRITE COMMUTATIVITY-OF-+))
 (57 26 (:REWRITE CONSP-UNDER-IFF-WHEN-TRUE-LISTP))
 (56 14 (:DEFINITION INTEGER-ABS))
 (49 7 (:DEFINITION LENGTH))
 (30 20 (:TYPE-PRESCRIPTION OMAP::HEAD-VALUE-WHEN-EMPTYP))
 (28 7 (:REWRITE LEN-WHEN-ATOM))
 (25 16 (:REWRITE DEFAULT-CAR))
 (23 5 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (21 15 (:REWRITE DEFAULT-CDR))
 (18 18 (:REWRITE FOLD-CONSTS-IN-+))
 (17 17 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (17 17 (:REWRITE CONSP-BY-LEN))
 (17 15 (:REWRITE DEFAULT-<-2))
 (17 15 (:REWRITE DEFAULT-<-1))
 (17 4 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (16 16 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (16 16 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (16 5 (:REWRITE OMAP::MFIX-WHEN-EMPTYP))
 (14 14 (:REWRITE DEFAULT-UNARY-MINUS))
 (14 14 (:REWRITE DEFAULT-COERCE-2))
 (14 14 (:REWRITE DEFAULT-COERCE-1))
 (13 3 (:LINEAR ACL2-COUNT-OF-CONSP-POSITIVE))
 (7 7 (:REWRITE DEFAULT-REALPART))
 (7 7 (:REWRITE DEFAULT-NUMERATOR))
 (7 7 (:REWRITE DEFAULT-IMAGPART))
 (7 7 (:REWRITE DEFAULT-DENOMINATOR))
 (6 6 (:LINEAR ACL2-COUNT-WHEN-MEMBER))
 (6 1 (:REWRITE ACL2-COUNT-WHEN-MEMBER))
 (4 1 (:LINEAR ACL2-COUNT-CAR-CDR-LINEAR))
 (3 3 (:REWRITE CONSP-OF-CDR-BY-LEN))
 (2 2 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (2 1 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (1 1 (:REWRITE SUBSETP-MEMBER . 2))
 (1 1 (:REWRITE SUBSETP-MEMBER . 1))
 (1 1 (:REWRITE MEMBER-EQUAL-WHEN-ALL-EQUALP))
 )
(OMAP::HEAD-KEY-COUNT-BUILT-IN
 (519 11 (:DEFINITION ACL2-COUNT))
 (188 60 (:REWRITE DEFAULT-+-2))
 (116 60 (:REWRITE DEFAULT-+-1))
 (70 14 (:REWRITE COMMUTATIVITY-OF-+))
 (59 27 (:REWRITE CONSP-UNDER-IFF-WHEN-TRUE-LISTP))
 (56 14 (:DEFINITION INTEGER-ABS))
 (49 7 (:DEFINITION LENGTH))
 (28 7 (:REWRITE LEN-WHEN-ATOM))
 (25 16 (:REWRITE DEFAULT-CAR))
 (23 5 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (21 15 (:REWRITE DEFAULT-CDR))
 (19 1 (:REWRITE ACL2-COUNT-WHEN-MEMBER))
 (18 18 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (18 18 (:REWRITE FOLD-CONSTS-IN-+))
 (18 18 (:REWRITE CONSP-BY-LEN))
 (17 15 (:REWRITE DEFAULT-<-2))
 (17 15 (:REWRITE DEFAULT-<-1))
 (17 4 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (16 16 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (16 16 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (16 5 (:REWRITE OMAP::MFIX-WHEN-EMPTYP))
 (14 14 (:REWRITE DEFAULT-UNARY-MINUS))
 (14 14 (:REWRITE DEFAULT-COERCE-2))
 (14 14 (:REWRITE DEFAULT-COERCE-1))
 (13 1 (:REWRITE SUBSETP-CAR-MEMBER))
 (8 2 (:LINEAR ACL2-COUNT-OF-CONSP-POSITIVE))
 (7 7 (:REWRITE DEFAULT-REALPART))
 (7 7 (:REWRITE DEFAULT-NUMERATOR))
 (7 7 (:REWRITE DEFAULT-IMAGPART))
 (7 7 (:REWRITE DEFAULT-DENOMINATOR))
 (4 4 (:LINEAR ACL2-COUNT-WHEN-MEMBER))
 (4 1 (:REWRITE SUBSETP-WHEN-ATOM-RIGHT))
 (4 1 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (4 1 (:LINEAR ACL2-COUNT-CAR-CDR-LINEAR))
 (2 2 (:TYPE-PRESCRIPTION SUBSETP-EQUAL))
 (2 2 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (2 1 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (1 1 (:REWRITE SUBSETP-TRANS2))
 (1 1 (:REWRITE SUBSETP-TRANS))
 (1 1 (:REWRITE SUBSETP-MEMBER . 2))
 (1 1 (:REWRITE SUBSETP-MEMBER . 1))
 (1 1 (:REWRITE MEMBER-EQUAL-WHEN-ALL-EQUALP))
 (1 1 (:REWRITE CONSP-OF-CDR-BY-LEN))
 )
(OMAP::HEAD-VALUE-COUNT-BUILT-IN
 (520 11 (:DEFINITION ACL2-COUNT))
 (188 60 (:REWRITE DEFAULT-+-2))
 (116 60 (:REWRITE DEFAULT-+-1))
 (70 14 (:REWRITE COMMUTATIVITY-OF-+))
 (56 14 (:DEFINITION INTEGER-ABS))
 (55 25 (:REWRITE CONSP-UNDER-IFF-WHEN-TRUE-LISTP))
 (49 7 (:DEFINITION LENGTH))
 (28 7 (:REWRITE LEN-WHEN-ATOM))
 (25 16 (:REWRITE DEFAULT-CAR))
 (23 5 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (21 15 (:REWRITE DEFAULT-CDR))
 (18 18 (:REWRITE FOLD-CONSTS-IN-+))
 (17 15 (:REWRITE DEFAULT-<-2))
 (17 15 (:REWRITE DEFAULT-<-1))
 (17 4 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (16 16 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (16 16 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (16 16 (:REWRITE CONSP-BY-LEN))
 (16 16 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (16 5 (:REWRITE OMAP::MFIX-WHEN-EMPTYP))
 (14 14 (:REWRITE DEFAULT-UNARY-MINUS))
 (14 14 (:REWRITE DEFAULT-COERCE-2))
 (14 14 (:REWRITE DEFAULT-COERCE-1))
 (9 2 (:LINEAR ACL2-COUNT-OF-CONSP-POSITIVE))
 (7 7 (:REWRITE DEFAULT-REALPART))
 (7 7 (:REWRITE DEFAULT-NUMERATOR))
 (7 7 (:REWRITE DEFAULT-IMAGPART))
 (7 7 (:REWRITE DEFAULT-DENOMINATOR))
 (6 1 (:REWRITE ACL2-COUNT-WHEN-MEMBER))
 (4 4 (:LINEAR ACL2-COUNT-WHEN-MEMBER))
 (4 1 (:LINEAR ACL2-COUNT-CAR-CDR-LINEAR))
 (3 3 (:REWRITE CONSP-OF-CDR-BY-LEN))
 (2 2 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (2 1 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (1 1 (:REWRITE SUBSETP-MEMBER . 2))
 (1 1 (:REWRITE SUBSETP-MEMBER . 1))
 (1 1 (:REWRITE MEMBER-EQUAL-WHEN-ALL-EQUALP))
 )
(OMAP::HEAD-KEY)
(OMAP::HEAD-VAL)
(OMAP::TAIL)
(OMAP::MAPP-OF-TAIL
 (363 28 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (334 8 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (293 28 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (159 10 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (129 33 (:REWRITE <<-TRICHOTOMY))
 (87 37 (:REWRITE CONSP-UNDER-IFF-WHEN-TRUE-LISTP))
 (87 15 (:REWRITE <<-ASYMMETRIC))
 (54 54 (:REWRITE DEFAULT-CAR))
 (54 54 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (54 47 (:REWRITE DEFAULT-CDR))
 (37 37 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (37 37 (:REWRITE CONSP-BY-LEN))
 (33 33 (:TYPE-PRESCRIPTION OMAP::EMPTYP))
 (33 33 (:REWRITE <<-TRANSITIVE))
 (31 27 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (12 12 (:REWRITE CONSP-OF-CDR-BY-LEN))
 (3 3 (:REWRITE CONSP-OF-CDDR-BY-LEN))
 (3 1 (:REWRITE OMAP::MFIX-WHEN-EMPTYP))
 )
(OMAP::TAIL-WHEN-EMPTYP
 (1 1 (:TYPE-PRESCRIPTION OMAP::MFIX))
 )
(OMAP::TAIL-COUNT
 (892 304 (:REWRITE DEFAULT-+-2))
 (863 808 (:TYPE-PRESCRIPTION ACL2-COUNT-OF-CONSP-POSITIVE))
 (544 304 (:REWRITE DEFAULT-+-1))
 (355 145 (:REWRITE CONSP-UNDER-IFF-WHEN-TRUE-LISTP))
 (174 42 (:REWRITE LEN-WHEN-ATOM))
 (104 56 (:REWRITE DEFAULT-CDR))
 (103 103 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (103 103 (:REWRITE CONSP-BY-LEN))
 (96 54 (:REWRITE DEFAULT-CAR))
 (93 87 (:REWRITE DEFAULT-<-2))
 (93 87 (:REWRITE DEFAULT-<-1))
 (92 92 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (84 84 (:REWRITE DEFAULT-UNARY-MINUS))
 (84 84 (:REWRITE DEFAULT-COERCE-2))
 (84 84 (:REWRITE DEFAULT-COERCE-1))
 (77 13 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (74 15 (:LINEAR ACL2-COUNT-OF-CONSP-POSITIVE))
 (73 73 (:REWRITE FOLD-CONSTS-IN-+))
 (54 54 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (53 12 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (46 10 (:LINEAR ACL2-COUNT-CAR-CDR-LINEAR))
 (46 3 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (42 42 (:REWRITE DEFAULT-REALPART))
 (42 42 (:REWRITE DEFAULT-NUMERATOR))
 (42 42 (:REWRITE DEFAULT-IMAGPART))
 (42 42 (:REWRITE DEFAULT-DENOMINATOR))
 (30 30 (:LINEAR ACL2-COUNT-WHEN-MEMBER))
 (30 20 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 (20 7 (:REWRITE OMAP::MFIX-WHEN-EMPTYP))
 (19 19 (:REWRITE CONSP-OF-CDR-BY-LEN))
 (16 3 (:REWRITE ACL2-COUNT-WHEN-MEMBER))
 (4 4 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (3 3 (:REWRITE SUBSETP-MEMBER . 2))
 (3 3 (:REWRITE SUBSETP-MEMBER . 1))
 (2 2 (:REWRITE MEMBER-SELF))
 (1 1 (:REWRITE MEMBER-EQUAL-WHEN-ALL-EQUALP))
 )
(OMAP::TAIL-COUNT-BUILT-IN
 (758 260 (:REWRITE DEFAULT-+-2))
 (663 663 (:TYPE-PRESCRIPTION ACL2-COUNT-OF-CONSP-POSITIVE))
 (458 260 (:REWRITE DEFAULT-+-1))
 (280 122 (:REWRITE CONSP-UNDER-IFF-WHEN-TRUE-LISTP))
 (144 36 (:REWRITE LEN-WHEN-ATOM))
 (86 86 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (86 86 (:REWRITE CONSP-BY-LEN))
 (84 48 (:REWRITE DEFAULT-CDR))
 (81 75 (:REWRITE DEFAULT-<-2))
 (81 75 (:REWRITE DEFAULT-<-1))
 (77 13 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (76 46 (:REWRITE DEFAULT-CAR))
 (72 72 (:REWRITE DEFAULT-UNARY-MINUS))
 (72 72 (:REWRITE DEFAULT-COERCE-2))
 (72 72 (:REWRITE DEFAULT-COERCE-1))
 (61 61 (:REWRITE FOLD-CONSTS-IN-+))
 (53 12 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (52 12 (:LINEAR ACL2-COUNT-OF-CONSP-POSITIVE))
 (46 46 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (46 3 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (36 36 (:REWRITE DEFAULT-REALPART))
 (36 36 (:REWRITE DEFAULT-NUMERATOR))
 (36 36 (:REWRITE DEFAULT-IMAGPART))
 (36 36 (:REWRITE DEFAULT-DENOMINATOR))
 (32 8 (:LINEAR ACL2-COUNT-CAR-CDR-LINEAR))
 (24 24 (:LINEAR ACL2-COUNT-WHEN-MEMBER))
 (22 22 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (20 7 (:REWRITE OMAP::MFIX-WHEN-EMPTYP))
 (16 16 (:REWRITE CONSP-OF-CDR-BY-LEN))
 (16 3 (:REWRITE ACL2-COUNT-WHEN-MEMBER))
 (4 4 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (3 3 (:REWRITE SUBSETP-MEMBER . 2))
 (3 3 (:REWRITE SUBSETP-MEMBER . 1))
 (2 2 (:REWRITE MEMBER-SELF))
 (1 1 (:REWRITE MEMBER-EQUAL-WHEN-ALL-EQUALP))
 )
(OMAP::HEAD-TAIL-ORDER
 (306 13 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (265 24 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (143 39 (:REWRITE <<-TRICHOTOMY))
 (105 48 (:REWRITE CONSP-UNDER-IFF-WHEN-TRUE-LISTP))
 (100 20 (:REWRITE <<-ASYMMETRIC))
 (77 64 (:REWRITE DEFAULT-CAR))
 (68 52 (:REWRITE DEFAULT-CDR))
 (64 64 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (48 48 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (48 48 (:REWRITE CONSP-BY-LEN))
 (39 39 (:REWRITE <<-TRANSITIVE))
 (35 31 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (13 13 (:REWRITE CONSP-OF-CDR-BY-LEN))
 (12 6 (:REWRITE OMAP::MFIX-WHEN-EMPTYP))
 (2 2 (:REWRITE CONSP-OF-CDDR-BY-LEN))
 )
(OMAP::HEAD-TAIL-ORDER-CONTRAPOSITIVE
 (4 2 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 (3 2 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (3 1 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 )
(OMAP::UPDATE
 (10 5 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 (2 2 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
 )
(OMAP::MAPP-OF-UPDATE
 (1700 1442 (:REWRITE DEFAULT-CAR))
 (1565 1162 (:REWRITE DEFAULT-CDR))
 (1442 1442 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (1380 611 (:REWRITE CONSP-UNDER-IFF-WHEN-TRUE-LISTP))
 (1089 926 (:REWRITE <<-TRANSITIVE))
 (611 611 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (611 611 (:REWRITE CONSP-BY-LEN))
 (610 41 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (177 177 (:REWRITE CONSP-OF-CDR-BY-LEN))
 (56 28 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (51 51 (:REWRITE CONSP-OF-CDDR-BY-LEN))
 (23 23 (:REWRITE <<-IRREFLEXIVE))
 (11 11 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
 )
(OMAP::UPDATE-TYPE-PRESCRIPTION)
(OMAP::UPDATE-OF-HEAD-AND-TAIL
 (899 62 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (729 61 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (219 30 (:REWRITE OMAP::MFIX-WHEN-EMPTYP))
 (186 93 (:REWRITE CONSP-UNDER-IFF-WHEN-TRUE-LISTP))
 (175 162 (:REWRITE DEFAULT-CAR))
 (162 162 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (151 134 (:REWRITE DEFAULT-CDR))
 (93 93 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (93 93 (:REWRITE CONSP-BY-LEN))
 (90 90 (:REWRITE <<-TRANSITIVE))
 (72 72 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (32 32 (:REWRITE CONSP-OF-CDR-BY-LEN))
 (15 3 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (13 13 (:REWRITE CONSP-OF-CDDR-BY-LEN))
 (4 2 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 )
(OMAP::UPDATE-NOT-EMPTYP
 (98 1 (:DEFINITION OMAP::UPDATE))
 (30 9 (:REWRITE OMAP::MFIX-WHEN-EMPTYP))
 (19 5 (:REWRITE <<-TRICHOTOMY))
 (18 2 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (17 3 (:REWRITE <<-ASYMMETRIC))
 (15 2 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (12 12 (:TYPE-PRESCRIPTION <<))
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 (10 6 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (9 1 (:REWRITE OMAP::HEAD-VALUE-WHEN-EMPTYP))
 (9 1 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 (5 5 (:REWRITE <<-TRANSITIVE))
 (4 2 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
 (2 1 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 )
(OMAP::UPDATE-SAME
 (1975 1576 (:REWRITE DEFAULT-CAR))
 (1823 1322 (:REWRITE DEFAULT-CDR))
 (1612 97 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (1576 1576 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (1411 1077 (:REWRITE <<-TRANSITIVE))
 (1347 624 (:REWRITE CONSP-UNDER-IFF-WHEN-TRUE-LISTP))
 (622 622 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (622 622 (:REWRITE CONSP-BY-LEN))
 (154 154 (:REWRITE CONSP-OF-CDR-BY-LEN))
 (126 63 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (48 48 (:REWRITE CONSP-OF-CDDR-BY-LEN))
 (36 36 (:REWRITE <<-IRREFLEXIVE))
 (11 11 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
 )
(OMAP::UPDATE-DIFFERENT
 (16183 13961 (:REWRITE DEFAULT-CAR))
 (15672 890 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (13970 11157 (:REWRITE DEFAULT-CDR))
 (13961 13961 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (6367 2681 (:REWRITE CONSP-UNDER-IFF-WHEN-TRUE-LISTP))
 (2679 2679 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (2679 2679 (:REWRITE CONSP-BY-LEN))
 (1220 610 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (770 770 (:REWRITE CONSP-OF-CDR-BY-LEN))
 (299 299 (:REWRITE CONSP-OF-CDDR-BY-LEN))
 (11 11 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
 )
(OMAP::UPDATE-WHEN-EMPTYP
 (22 3 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (10 2 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (7 7 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (6 2 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (4 4 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (4 2 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 )
(OMAP::HEAD-KEY-OF-UPDATE-OF-NIL
 (5 1 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (5 1 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (3 3 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (3 1 (:REWRITE OMAP::MFIX-WHEN-EMPTYP))
 (2 2 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 1 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (1 1 (:REWRITE OMAP::UPDATE-WHEN-EMPTYP))
 )
(OMAP::HEAD-VALUE-OF-UPDATE-OF-NIL
 (5 1 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (5 1 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (3 3 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (3 1 (:REWRITE OMAP::MFIX-WHEN-EMPTYP))
 (2 2 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 1 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (1 1 (:REWRITE OMAP::UPDATE-WHEN-EMPTYP))
 )
(OMAP::TAIL-OF-UPDATE-OF-NIL
 (23 2 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (16 4 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (8 4 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (5 1 (:REWRITE DEFAULT-CDR))
 (3 1 (:REWRITE OMAP::MFIX-WHEN-EMPTYP))
 (2 1 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (2 1 (:REWRITE CONSP-UNDER-IFF-WHEN-TRUE-LISTP))
 (1 1 (:REWRITE OMAP::UPDATE-WHEN-EMPTYP))
 )
(OMAP::HEAD-OF-UPDATE
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 (127 127 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (127 127 (:REWRITE CONSP-BY-LEN))
 (115 23 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (113 113 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (102 102 (:REWRITE <<-TRANSITIVE))
 (66 64 (:REWRITE OMAP::MFIX-WHEN-EMPTYP))
 (44 11 (:REWRITE CONS-CAR-CDR))
 (40 40 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (21 21 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (1 1 (:REWRITE OMAP::UPDATE-NOT-EMPTYP))
 )
(OMAP::HEAD-KEY-OF-UPDATE
 (57 15 (:REWRITE <<-TRICHOTOMY))
 (51 9 (:REWRITE <<-ASYMMETRIC))
 (47 1 (:DEFINITION OMAP::UPDATE))
 (27 5 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (15 15 (:REWRITE <<-TRANSITIVE))
 (10 2 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (10 2 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (8 8 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (5 5 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (4 4 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (4 4 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 (4 2 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (3 1 (:REWRITE OMAP::UPDATE-WHEN-EMPTYP))
 (2 2 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (1 1 (:REWRITE OMAP::HEAD-VALUE-WHEN-EMPTYP))
 )
(OMAP::HEAD-VALUE-OF-UPDATE
 (57 15 (:REWRITE <<-TRICHOTOMY))
 (51 9 (:REWRITE <<-ASYMMETRIC))
 (47 1 (:DEFINITION OMAP::UPDATE))
 (27 5 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (15 15 (:REWRITE <<-TRANSITIVE))
 (10 2 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
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 (8 8 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (5 5 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (4 4 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (4 2 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (3 3 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 (3 1 (:REWRITE OMAP::UPDATE-WHEN-EMPTYP))
 (2 2 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
 (2 2 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (2 2 (:REWRITE OMAP::HEAD-VALUE-WHEN-EMPTYP))
 )
(OMAP::TAIL-OF-UPDATE
 (139 23 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (78 21 (:REWRITE DEFAULT-CDR))
 (59 57 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
 (50 10 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (39 39 (:REWRITE <<-TRANSITIVE))
 (32 16 (:REWRITE CONSP-UNDER-IFF-WHEN-TRUE-LISTP))
 (19 19 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (18 18 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 (16 16 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (16 16 (:REWRITE CONSP-BY-LEN))
 (16 14 (:REWRITE OMAP::MFIX-WHEN-EMPTYP))
 (11 11 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (8 8 (:REWRITE OMAP::HEAD-VALUE-WHEN-EMPTYP))
 (6 6 (:REWRITE CONSP-OF-CDR-BY-LEN))
 (1 1 (:REWRITE OMAP::UPDATE-NOT-EMPTYP))
 )
(OMAP::HEAD-VALUE-OF-UPDATE-EMPTYP
 (13 2 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (5 1 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (5 1 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (4 4 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (2 2 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (2 1 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 )
(OMAP::HEAD-VALUE-OF-UPDATE-KEY-<<
 (28 9 (:REWRITE <<-TRICHOTOMY))
 (19 4 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (12 11 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
 (7 7 (:REWRITE <<-TRANSITIVE))
 (7 3 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (6 6 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (5 1 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (4 4 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (4 4 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 (2 2 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (2 2 (:REWRITE OMAP::UPDATE-WHEN-EMPTYP))
 (2 1 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 )
(OMAP::HEAD-VALUE-OF-UPDATE-WHEN-HEAD-KEY-EQUAL
 (39 11 (:REWRITE <<-TRICHOTOMY))
 (39 6 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (31 7 (:REWRITE <<-ASYMMETRIC))
 (15 3 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (15 3 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (12 12 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (10 10 (:REWRITE <<-TRANSITIVE))
 (6 6 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (6 3 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (4 4 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (3 3 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 )
(OMAP::HEAD-VALUE-OF-UPDATE-NOT-<<
 (31 9 (:REWRITE <<-TRICHOTOMY))
 (23 5 (:REWRITE <<-ASYMMETRIC))
 (16 3 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (12 8 (:REWRITE <<-TRANSITIVE))
 (6 2 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (5 5 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (5 5 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
 (5 1 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (4 4 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (2 2 (:REWRITE OMAP::HEAD-VALUE-WHEN-EMPTYP))
 (2 2 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 (2 1 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (1 1 (:REWRITE OMAP::UPDATE-WHEN-EMPTYP))
 (1 1 (:REWRITE <<-IRREFLEXIVE))
 )
(OMAP::TAIL-OF-UPDATE-EMPTYP
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 (5 1 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (5 1 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (4 4 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (2 2 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (2 1 (:REWRITE OMAP::MFIX-WHEN-MAPP))
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(OMAP::TAIL-OF-UPDATE-<<
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 (23 5 (:REWRITE <<-ASYMMETRIC))
 (16 3 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (12 8 (:REWRITE <<-TRANSITIVE))
 (6 2 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (5 5 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (5 5 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
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 (2 2 (:TYPE-PRESCRIPTION OMAP::MFIX))
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 (2 2 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 (2 1 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (1 1 (:REWRITE OMAP::UPDATE-WHEN-EMPTYP))
 (1 1 (:REWRITE OMAP::TAIL-OF-UPDATE-EMPTYP))
 (1 1 (:REWRITE <<-IRREFLEXIVE))
 )
(OMAP::TAIL-OF-UPDATE-EQUAL
 (20 20 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
 (16 3 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (10 4 (:REWRITE <<-TRICHOTOMY))
 (8 2 (:REWRITE <<-ASYMMETRIC))
 (8 1 (:REWRITE OMAP::TAIL-OF-UPDATE-<<))
 (7 7 (:TYPE-PRESCRIPTION <<))
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 (5 5 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (5 1 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (4 4 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (4 4 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
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 (2 1 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (1 1 (:REWRITE OMAP::UPDATE-WHEN-EMPTYP))
 (1 1 (:REWRITE OMAP::TAIL-OF-UPDATE-EMPTYP))
 )
(OMAP::TAIL-OF-UPDATE-<<-REV
 (29 10 (:REWRITE <<-TRICHOTOMY))
 (29 5 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (12 12 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
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 (10 2 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (9 9 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (8 8 (:REWRITE <<-TRANSITIVE))
 (7 7 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (7 7 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 (7 1 (:REWRITE OMAP::TAIL-OF-UPDATE-EQUAL))
 (7 1 (:REWRITE OMAP::TAIL-OF-UPDATE-<<))
 (5 3 (:REWRITE OMAP::UPDATE-WHEN-EMPTYP))
 (4 4 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (4 2 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (3 3 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (1 1 (:REWRITE OMAP::TAIL-OF-UPDATE-EMPTYP))
 )
(OMAP::UPDATE*
 (2 1 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 )
(OMAP::MAPP-OF-UPDATE*
 (191 23 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (160 25 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (104 24 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (50 36 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (44 18 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (26 26 (:TYPE-PRESCRIPTION OMAP::UPDATE*))
 (3 1 (:REWRITE OMAP::UPDATE-WHEN-EMPTYP))
 (3 1 (:REWRITE OMAP::MFIX-WHEN-EMPTYP))
 (1 1 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (1 1 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (1 1 (:REWRITE OMAP::HEAD-VALUE-WHEN-EMPTYP))
 (1 1 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 )
(OMAP::UPDATE*)
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 (30 6 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (27 27 (:TYPE-PRESCRIPTION OMAP::MFIX))
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 (15 15 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (6 2 (:REWRITE OMAP::MFIX-WHEN-EMPTYP))
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(OMAP::UPDATE*-WHEN-RIGHT-EMPTYP
 (173 29 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (149 149 (:TYPE-PRESCRIPTION OMAP::UPDATE*))
 (137 115 (:TYPE-PRESCRIPTION OMAP::MFIX))
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 (9 9 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (7 7 (:REWRITE OMAP::HEAD-VALUE-WHEN-EMPTYP))
 (7 7 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
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(OMAP::DELETE
 (12 6 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 )
(OMAP::MAPP-OF-DELETE
 (245 33 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (183 33 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (115 31 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (83 77 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
 (42 42 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (42 21 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (9 9 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (9 9 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 (3 1 (:REWRITE OMAP::UPDATE-WHEN-EMPTYP))
 (2 2 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (2 2 (:REWRITE OMAP::HEAD-VALUE-WHEN-EMPTYP))
 )
(OMAP::DELETE
 (2 2 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
 )
(OMAP::DELETE-WHEN-EMPTYP
 (22 3 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (10 2 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (7 7 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (6 2 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (4 4 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (4 2 (:REWRITE OMAP::MFIX-WHEN-MAPP))
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(OMAP::DELETE*)
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 (114 17 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (87 9 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (55 17 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (30 30 (:TYPE-PRESCRIPTION OMAP::EMPTYP))
 (30 11 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (22 22 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (3 1 (:REWRITE OMAP::MFIX-WHEN-EMPTYP))
 (3 1 (:REWRITE OMAP::DELETE-WHEN-EMPTYP))
 (1 1 (:REWRITE SET::TAIL-WHEN-EMPTYP))
 (1 1 (:REWRITE SET::IN-TAIL-OR-HEAD))
 (1 1 (:REWRITE SET::HEAD-WHEN-EMPTYP))
 )
(OMAP::DELETE*)
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 (26 4 (:REWRITE OMAP::MFIX-WHEN-MAPP))
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 (8 8 (:TYPE-PRESCRIPTION OMAP::MAPP))
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 (6 2 (:REWRITE OMAP::MFIX-WHEN-EMPTYP))
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(OMAP::DELETE*-WHEN-RIGHT-EMPTYP
 (65 10 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
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 (25 5 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (20 20 (:TYPE-PRESCRIPTION OMAP::MAPP))
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 (4 4 (:REWRITE SET::IN-TAIL-OR-HEAD))
 (4 4 (:REWRITE SET::HEAD-WHEN-EMPTYP))
 (3 3 (:REWRITE SET::TAIL-WHEN-EMPTYP))
 )
(OMAP::ASSOC
 (6 3 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 (2 2 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
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(OMAP::LISTP-OF-ASSOC
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(OMAP::ASSOC-OF-MFIX
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 (46 38 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
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 (4 4 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
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(OMAP::ASSOC-WHEN-EMPTYP
 (22 3 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
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 (4 4 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (4 2 (:REWRITE OMAP::MFIX-WHEN-MAPP))
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(OMAP::CONSP-OF-ASSOC
 (58 29 (:TYPE-PRESCRIPTION OMAP::ASSOC-WHEN-EMPTYP))
 (48 2 (:DEFINITION OMAP::ASSOC))
 (41 41 (:TYPE-PRESCRIPTION OMAP::EMPTYP))
 (26 4 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
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 (2 2 (:REWRITE OMAP::HEAD-VALUE-WHEN-EMPTYP))
 (2 2 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 (1 1 (:REWRITE CONSP-BY-LEN))
 )
(OMAP::ASSOC-OF-HEAD
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 (14 7 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
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 (1 1 (:TYPE-PRESCRIPTION OMAP::HEAD-VALUE-WHEN-EMPTYP))
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 )
(OMAP::ASSOC-WHEN-ASSOC-TAIL
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 (12 4 (:REWRITE OMAP::ASSOC-WHEN-EMPTYP))
 (10 5 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
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 (2 2 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 (2 1 (:TYPE-PRESCRIPTION OMAP::HEAD-VALUE-WHEN-EMPTYP))
 (2 1 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (1 1 (:REWRITE OMAP::MAPP-OF-TAIL))
 )
(OMAP::ACL2-COUNT-ASSOC-<-MAP
 (1699 15 (:REWRITE OMAP::CONSP-OF-ASSOC))
 (1232 20 (:DEFINITION ACL2-COUNT))
 (1189 40 (:REWRITE OMAP::ASSOC-WHEN-ASSOC-TAIL))
 (1163 11 (:LINEAR ACL2-COUNT-OF-CONSP-POSITIVE))
 (1046 537 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 (375 130 (:REWRITE OMAP::MFIX-WHEN-EMPTYP))
 (229 37 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (212 60 (:REWRITE DEFAULT-+-2))
 (206 76 (:REWRITE DEFAULT-CAR))
 (201 38 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (133 36 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (116 60 (:REWRITE DEFAULT-+-1))
 (104 47 (:REWRITE DEFAULT-CDR))
 (78 78 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (71 15 (:REWRITE DEFAULT-<-1))
 (70 19 (:REWRITE CONSP-UNDER-IFF-WHEN-TRUE-LISTP))
 (48 24 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (40 8 (:REWRITE COMMUTATIVITY-OF-+))
 (34 4 (:DEFINITION LENGTH))
 (33 15 (:REWRITE DEFAULT-<-2))
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 (8 8 (:REWRITE DEFAULT-COERCE-2))
 (8 8 (:REWRITE DEFAULT-COERCE-1))
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 (6 6 (:REWRITE SUBSETP-MEMBER . 1))
 (6 6 (:REWRITE MEMBER-EQUAL-WHEN-ALL-EQUALP))
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 (4 4 (:REWRITE DEFAULT-NUMERATOR))
 (4 4 (:REWRITE DEFAULT-IMAGPART))
 (4 4 (:REWRITE DEFAULT-DENOMINATOR))
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 (1 1 (:REWRITE SUBSETP-TRANS))
 )
(OMAP::ASSOC-OF-UPDATE
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 (8247 63 (:REWRITE OMAP::ASSOC-WHEN-ASSOC-TAIL))
 (7262 6218 (:REWRITE DEFAULT-CAR))
 (6257 5079 (:REWRITE DEFAULT-CDR))
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 (5210 2504 (:REWRITE CONSP-UNDER-IFF-WHEN-TRUE-LISTP))
 (3941 19 (:REWRITE OMAP::HEAD-OF-UPDATE))
 (3760 295 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (2504 2504 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (2504 2504 (:REWRITE CONSP-BY-LEN))
 (1360 19 (:REWRITE OMAP::TAIL-OF-UPDATE-<<-REV))
 (1189 19 (:REWRITE OMAP::TAIL-OF-UPDATE-EMPTYP))
 (870 870 (:REWRITE CONSP-OF-CDR-BY-LEN))
 (739 114 (:REWRITE OMAP::UPDATE-WHEN-EMPTYP))
 (600 300 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (454 454 (:REWRITE CONSP-OF-CDDR-BY-LEN))
 (378 19 (:REWRITE OMAP::TAIL-OF-UPDATE-<<))
 (234 19 (:REWRITE OMAP::TAIL-OF-UPDATE-EQUAL))
 (129 69 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 (96 96 (:REWRITE CONSP-OF-CDDDR-BY-LEN))
 (40 40 (:REWRITE OMAP::UPDATE-NOT-EMPTYP))
 (32 20 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
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(OMAP::ASSOC-OF-UPDATE*
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 (283 183 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 (234 54 (:REWRITE OMAP::MFIX-WHEN-MAPP))
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 (202 42 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (187 187 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (167 167 (:TYPE-PRESCRIPTION OMAP::UPDATE*))
 (164 118 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
 (88 88 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (76 30 (:REWRITE OMAP::UPDATE*-WHEN-RIGHT-EMPTYP))
 (73 53 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (53 53 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (53 53 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
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 (17 6 (:TYPE-PRESCRIPTION OMAP::HEAD-VALUE-WHEN-EMPTYP))
 (9 9 (:REWRITE OMAP::MAPP-OF-TAIL))
 (8 8 (:TYPE-PRESCRIPTION OMAP::UPDATE-TYPE-PRESCRIPTION))
 (8 8 (:REWRITE OMAP::MAPP-OF-UPDATE*))
 )
(OMAP::UPDATE-OF-CDR-OF-ASSOC-WHEN-ASSOC
 (592 30 (:REWRITE OMAP::ASSOC-WHEN-ASSOC-TAIL))
 (346 233 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 (259 45 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (182 138 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
 (82 30 (:REWRITE OMAP::ASSOC-WHEN-EMPTYP))
 (75 19 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (73 73 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (70 42 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (70 14 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (40 32 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 (38 34 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
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 (12 12 (:REWRITE OMAP::MAPP-OF-TAIL))
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 (3 2 (:REWRITE DEFAULT-CAR))
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 (2 2 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (2 1 (:REWRITE SET::NONEMPTY-MEANS-SET))
 (1 1 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (1 1 (:REWRITE SET::IN-SET))
 (1 1 (:REWRITE CONSP-BY-LEN))
 )
(OMAP::HEAD-KEY-MINIMAL
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 (124 22 (:REWRITE <<-ASYMMETRIC))
 (95 77 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
 (68 12 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (31 29 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
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 (2 2 (:REWRITE OMAP::MAPP-OF-TAIL))
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 (60 30 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 (54 8 (:REWRITE <<-TRICHOTOMY))
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(OMAP::ASSOC-OF-TAIL-WHEN-ASSOC-OF-TAIL
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 (56 8 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
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(OMAP::ASSOC-OF-TAIL-WHEN-NOT-HEAD
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 (3 3 (:REWRITE OMAP::HEAD-VALUE-WHEN-EMPTYP))
 (2 2 (:REWRITE OMAP::MAPP-OF-TAIL))
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(OMAP::IN*
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(OMAP::BOOLEANP-OF-IN*
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(OMAP::IN*-WHEN-LEFT-EMPTYP)
(OMAP::IN*-WHEN-RIGTH-EMPTYP
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(OMAP::IN*-OF-TAIL
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(OMAP::LIST-IN
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(OMAP::BOOLEANP-OF-LIST-IN
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(OMAP::LIST-NOTIN
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(OMAP::BOOLEANP-OF-LIST-NOTIN
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(OMAP::NOT-ASSOC-MAP-WHEN-MEMBER-OF-LIST-NOTIN
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(OMAP::WEAK-UPDATE-INDUCTION-HELPER-1
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(OMAP::WEAK-UPDATE-INDUCTION
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(OMAP::USE-WEAK-UPDATE-INDUCTION)
(OMAP::LOOKUP
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(OMAP::LOOKUP-WHEN-EMPTYP)
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(OMAP::LOOKUP-OF-UPDATE
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(OMAP::LOOKUP-OF-UPDATE*
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(OMAP::LOOKUP*
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(OMAP::LOOKUP*
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(OMAP::LOOKUP*-WHEN-LEFT-EMPTYP)
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(OMAP::TRUE-LISTP-OF-LIST-LOOKUP)
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(OMAP::RLOOKUP
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(OMAP::RLOOKUP*-WHEN-LEFT-EMPTYP)
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 (16 10 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (15 5 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (12 12 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (12 6 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (10 4 (:REWRITE OMAP::ASSOC-WHEN-EMPTYP))
 (7 7 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (7 7 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 (1 1 (:REWRITE OMAP::MAPP-OF-TAIL))
 (1 1 (:REWRITE OMAP::HEAD-KEY-NOT-ASSOC-TAIL))
 )
(OMAP::SET-EMPTYP-OF-KEYS
 (98 16 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (35 7 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (33 9 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (30 30 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (15 3 (:REWRITE SET::INSERT-IDENTITY))
 (14 14 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (14 7 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (9 9 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (9 3 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (6 3 (:REWRITE SET::IN-TAIL))
 (3 3 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (3 3 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (3 3 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 (2 2 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 (1 1 (:REWRITE OMAP::MAPP-OF-TAIL))
 )
(OMAP::LIST-IN-TO-SUBSET-KEYS
 (330 11 (:DEFINITION OMAP::KEYS))
 (143 22 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (130 130 (:TYPE-PRESCRIPTION OMAP::EMPTYP))
 (127 15 (:REWRITE SET::INSERT-IDENTITY))
 (85 25 (:REWRITE SET::IN-TAIL))
 (66 22 (:REWRITE OMAP::KEYS-WHEN-EMPTYP))
 (64 4 (:REWRITE SET::IN-MERGESORT-UNDER-IFF))
 (62 31 (:REWRITE OMAP::SET-EMPTYP-OF-KEYS))
 (56 15 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (55 11 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (55 11 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (44 44 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (44 22 (:TYPE-PRESCRIPTION OMAP::ASSOC-WHEN-EMPTYP))
 (44 4 (:REWRITE SUBSETP-CAR-MEMBER))
 (28 7 (:REWRITE SET::TAIL-WHEN-EMPTYP))
 (28 7 (:REWRITE SET::NEVER-IN-EMPTY))
 (28 4 (:REWRITE SET::MERGESORT-SET-IDENTITY))
 (27 9 (:REWRITE SET::EMPTYP-SUBSET-2))
 (22 22 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (22 11 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (20 4 (:REWRITE SUBSETP-WHEN-ATOM-RIGHT))
 (14 7 (:REWRITE CONSP-UNDER-IFF-WHEN-TRUE-LISTP))
 (12 4 (:REWRITE SET::NONEMPTY-MEANS-SET))
 (11 11 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (11 11 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (11 11 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 (9 9 (:REWRITE DEFAULT-CAR))
 (9 9 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (8 8 (:TYPE-PRESCRIPTION SUBSETP-EQUAL))
 (8 8 (:TYPE-PRESCRIPTION SET::SETP-TYPE))
 (7 7 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (7 7 (:REWRITE CONSP-BY-LEN))
 (5 5 (:REWRITE SET::PICK-A-POINT-SUBSET-CONSTRAINT-HELPER))
 (4 4 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (4 4 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (4 4 (:REWRITE SUBSETP-TRANS2))
 (4 4 (:REWRITE SUBSETP-TRANS))
 (4 4 (:REWRITE SUBSETP-MEMBER . 2))
 (4 4 (:REWRITE SUBSETP-MEMBER . 1))
 (4 4 (:REWRITE MEMBER-EQUAL-WHEN-ALL-EQUALP))
 (4 4 (:REWRITE SET::IN-SET))
 (4 4 (:REWRITE CONSP-OF-CDR-BY-LEN))
 (3 3 (:REWRITE SET::INSERT-NEVER-EMPTY))
 )
(OMAP::IN-KEYS-WHEN-ASSOC-FORWARD
 (140 104 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 (94 16 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (75 20 (:REWRITE SET::IN-TAIL))
 (42 38 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
 (40 20 (:REWRITE OMAP::SET-EMPTYP-OF-KEYS))
 (32 8 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (30 16 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (30 6 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (30 6 (:REWRITE SET::INSERT-IDENTITY))
 (28 28 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (28 7 (:REWRITE SET::TAIL-WHEN-EMPTYP))
 (28 7 (:REWRITE SET::NEVER-IN-EMPTY))
 (26 10 (:REWRITE OMAP::KEYS-WHEN-EMPTYP))
 (24 10 (:REWRITE OMAP::ASSOC-WHEN-EMPTYP))
 (24 6 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (21 21 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (12 12 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (12 6 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (8 8 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (8 8 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 (6 1 (:REWRITE SET::SETS-ARE-TRUE-LISTS-CHEAP))
 (4 1 (:REWRITE TRUE-LISTP-WHEN-ATOM))
 (3 1 (:REWRITE OMAP::UPDATE-WHEN-EMPTYP))
 (2 2 (:TYPE-PRESCRIPTION SET::SETP-TYPE))
 (2 2 (:REWRITE OMAP::MAPP-OF-TAIL))
 (2 1 (:REWRITE SET::NONEMPTY-MEANS-SET))
 (1 1 (:REWRITE SET::IN-SET))
 (1 1 (:REWRITE CONSP-BY-LEN))
 )
(OMAP::IN-KEYS-WHEN-ASSOC-IS-CONS
 (94 16 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (84 76 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 (75 20 (:REWRITE SET::IN-TAIL))
 (42 38 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
 (40 20 (:REWRITE OMAP::SET-EMPTYP-OF-KEYS))
 (32 8 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (30 6 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (30 6 (:REWRITE SET::INSERT-IDENTITY))
 (28 28 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (28 7 (:REWRITE SET::TAIL-WHEN-EMPTYP))
 (28 7 (:REWRITE SET::NEVER-IN-EMPTY))
 (26 10 (:REWRITE OMAP::KEYS-WHEN-EMPTYP))
 (25 13 (:REWRITE OMAP::ASSOC-WHEN-EMPTYP))
 (24 6 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (21 21 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (12 12 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (12 6 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (9 9 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (8 8 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (8 8 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 (6 1 (:REWRITE SET::SETS-ARE-TRUE-LISTS-CHEAP))
 (4 1 (:REWRITE TRUE-LISTP-WHEN-ATOM))
 (3 1 (:REWRITE OMAP::UPDATE-WHEN-EMPTYP))
 (2 2 (:TYPE-PRESCRIPTION SET::SETP-TYPE))
 (2 2 (:REWRITE OMAP::MAPP-OF-TAIL))
 (2 1 (:REWRITE SET::NONEMPTY-MEANS-SET))
 (1 1 (:REWRITE SET::IN-SET))
 (1 1 (:REWRITE CONSP-BY-LEN))
 )
(OMAP::KEYS-OF-UPDATE
 (3418 30 (:DEFINITION OMAP::KEYS))
 (1334 41 (:REWRITE SET::INSERT-IDENTITY))
 (1187 103 (:REWRITE OMAP::ASSOC-WHEN-ASSOC-TAIL))
 (630 14 (:REWRITE OMAP::TAIL-OF-UPDATE))
 (604 260 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 (532 140 (:REWRITE <<-TRICHOTOMY))
 (490 14 (:REWRITE OMAP::HEAD-OF-UPDATE))
 (476 84 (:REWRITE <<-ASYMMETRIC))
 (420 420 (:TYPE-PRESCRIPTION <<))
 (362 116 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (224 14 (:REWRITE OMAP::WEAK-UPDATE-INDUCTION-HELPER-3))
 (196 14 (:REWRITE OMAP::WEAK-UPDATE-INDUCTION-HELPER-2))
 (182 14 (:REWRITE OMAP::WEAK-UPDATE-INDUCTION-HELPER-1))
 (176 60 (:REWRITE OMAP::KEYS-WHEN-EMPTYP))
 (164 44 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (164 44 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (164 41 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (149 81 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (148 148 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (140 140 (:REWRITE <<-TRANSITIVE))
 (112 112 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
 (108 54 (:REWRITE OMAP::SET-EMPTYP-OF-KEYS))
 (90 30 (:REWRITE OMAP::UPDATE-WHEN-EMPTYP))
 (83 37 (:REWRITE OMAP::ASSOC-WHEN-EMPTYP))
 (72 72 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (66 24 (:REWRITE SET::EMPTYP-SUBSET))
 (60 60 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (60 30 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (58 58 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 (56 14 (:REWRITE OMAP::TAIL-OF-UPDATE-EQUAL))
 (56 14 (:REWRITE OMAP::TAIL-OF-UPDATE-<<-REV))
 (56 14 (:REWRITE OMAP::TAIL-OF-UPDATE-<<))
 (50 25 (:REWRITE SET::NONEMPTY-MEANS-SET))
 (49 24 (:REWRITE SET::EMPTYP-SUBSET-2))
 (42 14 (:REWRITE OMAP::TAIL-OF-UPDATE-EMPTYP))
 (35 35 (:REWRITE OMAP::UPDATE-NOT-EMPTYP))
 (25 25 (:REWRITE SET::IN-SET))
 (16 16 (:REWRITE OMAP::HEAD-KEY-NOT-ASSOC-TAIL))
 (12 12 (:REWRITE SET::SUBSET-IN))
 (8 8 (:REWRITE SET::TAIL-WHEN-EMPTYP))
 (8 8 (:REWRITE SET::SUBSET-IN-2))
 (8 8 (:REWRITE SET::IN-TAIL-OR-HEAD))
 (8 8 (:REWRITE SET::HEAD-WHEN-EMPTYP))
 (6 6 (:REWRITE SET::INSERT-NEVER-EMPTY))
 )
(OMAP::KEYS-OF-UPDATE*
 (338 41 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (235 79 (:TYPE-PRESCRIPTION OMAP::KEYS-WHEN-EMPTYP))
 (115 26 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (99 23 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (97 21 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (88 88 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (85 85 (:TYPE-PRESCRIPTION OMAP::UPDATE*))
 (71 15 (:REWRITE SET::INSERT-IDENTITY))
 (57 15 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (48 24 (:REWRITE OMAP::SET-EMPTYP-OF-KEYS))
 (42 42 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (42 42 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (36 14 (:REWRITE OMAP::UPDATE*-WHEN-RIGHT-EMPTYP))
 (28 14 (:REWRITE SET::IN-TAIL))
 (21 6 (:REWRITE SET::UNION-EMPTYP-Y))
 (20 20 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (20 20 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 (18 18 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (17 7 (:REWRITE OMAP::UPDATE-WHEN-EMPTYP))
 (9 3 (:REWRITE OMAP::MFIX-WHEN-EMPTYP))
 (7 7 (:REWRITE OMAP::HEAD-VALUE-WHEN-EMPTYP))
 (4 4 (:TYPE-PRESCRIPTION OMAP::UPDATE-TYPE-PRESCRIPTION))
 (4 4 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 (4 4 (:REWRITE OMAP::MAPP-OF-UPDATE*))
 (4 1 (:REWRITE SET::SFIX-WHEN-EMPTYP))
 (2 2 (:REWRITE OMAP::MAPP-OF-TAIL))
 (1 1 (:REWRITE SET::INSERT-NEVER-EMPTY))
 )
(OMAP::LEMMA1
 (699 44 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (323 85 (:REWRITE SET::IN-TAIL))
 (244 122 (:TYPE-PRESCRIPTION OMAP::RESTRICT-WHEN-LEFT-EMPTYP))
 (118 34 (:REWRITE SET::TAIL-WHEN-EMPTYP))
 (96 92 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 (94 47 (:REWRITE OMAP::SET-EMPTYP-OF-KEYS))
 (66 66 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (64 24 (:REWRITE OMAP::KEYS-WHEN-EMPTYP))
 (63 19 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (60 15 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (55 11 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (54 18 (:REWRITE OMAP::RESTRICT-WHEN-LEFT-EMPTYP))
 (32 32 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (32 32 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 (30 30 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (28 12 (:REWRITE OMAP::UPDATE-WHEN-EMPTYP))
 (22 22 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (22 11 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (14 14 (:REWRITE OMAP::HEAD-VALUE-WHEN-EMPTYP))
 (8 8 (:TYPE-PRESCRIPTION OMAP::UPDATE-TYPE-PRESCRIPTION))
 (8 8 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
 (8 8 (:REWRITE OMAP::MAPP-OF-RESTRICT))
 (6 6 (:REWRITE OMAP::MAPP-OF-TAIL))
 )
(OMAP::LEMMA2
 (528 6 (:DEFINITION OMAP::KEYS))
 (491 26 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (193 51 (:REWRITE SET::IN-TAIL))
 (168 84 (:TYPE-PRESCRIPTION OMAP::RESTRICT-WHEN-LEFT-EMPTYP))
 (69 21 (:REWRITE SET::TAIL-WHEN-EMPTYP))
 (42 14 (:REWRITE OMAP::RESTRICT-WHEN-LEFT-EMPTYP))
 (42 7 (:REWRITE SET::INSERT-IDENTITY))
 (40 40 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 (40 40 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (38 19 (:REWRITE OMAP::SET-EMPTYP-OF-KEYS))
 (37 9 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (36 12 (:REWRITE OMAP::KEYS-WHEN-EMPTYP))
 (35 7 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (28 7 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (22 22 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (21 9 (:REWRITE OMAP::UPDATE-WHEN-EMPTYP))
 (18 18 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (18 18 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 (14 14 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (14 7 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (13 13 (:REWRITE OMAP::LEMMA1))
 (10 10 (:REWRITE OMAP::HEAD-VALUE-WHEN-EMPTYP))
 (9 9 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
 (6 6 (:TYPE-PRESCRIPTION OMAP::UPDATE-TYPE-PRESCRIPTION))
 (6 6 (:REWRITE OMAP::MAPP-OF-RESTRICT))
 (4 4 (:REWRITE OMAP::MAPP-OF-TAIL))
 )
(OMAP::LEMMA3
 (702 42 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (372 89 (:REWRITE SET::IN-TAIL))
 (245 245 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (238 76 (:TYPE-PRESCRIPTION OMAP::RESTRICT-WHEN-RIGHT-EMPTYP))
 (152 76 (:TYPE-PRESCRIPTION OMAP::RESTRICT-WHEN-LEFT-EMPTYP))
 (122 36 (:REWRITE SET::TAIL-WHEN-EMPTYP))
 (122 36 (:REWRITE SET::NEVER-IN-EMPTY))
 (119 17 (:REWRITE SET::INSERT-IDENTITY))
 (98 94 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 (90 45 (:REWRITE OMAP::SET-EMPTYP-OF-KEYS))
 (68 17 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (64 24 (:REWRITE OMAP::KEYS-WHEN-EMPTYP))
 (62 62 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (58 18 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (54 18 (:REWRITE OMAP::RESTRICT-WHEN-LEFT-EMPTYP))
 (50 10 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (46 18 (:REWRITE OMAP::RESTRICT-WHEN-RIGHT-EMPTYP))
 (32 32 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (32 32 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 (31 13 (:REWRITE OMAP::UPDATE-WHEN-EMPTYP))
 (30 30 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (20 20 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (20 10 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (14 14 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
 (14 14 (:REWRITE OMAP::HEAD-VALUE-WHEN-EMPTYP))
 (8 8 (:TYPE-PRESCRIPTION OMAP::UPDATE-TYPE-PRESCRIPTION))
 (8 8 (:REWRITE OMAP::MAPP-OF-RESTRICT))
 (6 6 (:REWRITE OMAP::MAPP-OF-TAIL))
 )
(OMAP::KEYS-OF-RESTRICT
 (1105 35 (:DEFINITION OMAP::KEYS))
 (455 54 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (230 35 (:REWRITE SET::INSERT-IDENTITY))
 (210 70 (:REWRITE OMAP::KEYS-WHEN-EMPTYP))
 (157 53 (:REWRITE SET::IN-TAIL))
 (146 73 (:REWRITE OMAP::SET-EMPTYP-OF-KEYS))
 (140 35 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (112 56 (:TYPE-PRESCRIPTION OMAP::RESTRICT-WHEN-RIGHT-EMPTYP))
 (112 56 (:TYPE-PRESCRIPTION OMAP::RESTRICT-WHEN-LEFT-EMPTYP))
 (95 19 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (95 19 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (92 92 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (60 15 (:REWRITE SET::INTERSECT-EMPTYP-Y))
 (49 14 (:REWRITE SET::EMPTYP-SUBSET-2))
 (48 16 (:REWRITE OMAP::RESTRICT-WHEN-RIGHT-EMPTYP))
 (48 16 (:REWRITE OMAP::RESTRICT-WHEN-LEFT-EMPTYP))
 (46 14 (:REWRITE SET::EMPTYP-SUBSET))
 (45 15 (:REWRITE SET::INTERSECT-EMPTYP-X))
 (38 38 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (38 19 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (37 13 (:REWRITE SET::TAIL-WHEN-EMPTYP))
 (35 35 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (35 35 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (35 35 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 (33 9 (:REWRITE SET::NEVER-IN-EMPTY))
 (16 16 (:REWRITE OMAP::MAPP-OF-RESTRICT))
 (4 4 (:REWRITE SET::IN-TAIL-OR-HEAD))
 (4 4 (:REWRITE SET::HEAD-WHEN-EMPTYP))
 )
(OMAP::HEAD-KEY-NOT-IN-KEYS-OF-TAIL
 (24 4 (:TYPE-PRESCRIPTION OMAP::ASSOC-WHEN-EMPTYP))
 (12 12 (:TYPE-PRESCRIPTION OMAP::EMPTYP))
 (8 4 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 (8 4 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
 )
(OMAP::VALUES
 (2 1 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 )
(OMAP::SETP-OF-VALUES
 (90 14 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (35 7 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (32 8 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (28 28 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (14 14 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (14 7 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (8 8 (:REWRITE SET::IN-SET))
 (5 1 (:REWRITE SET::INSERT-IDENTITY))
 (3 3 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (3 1 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (2 1 (:REWRITE SET::IN-TAIL))
 (1 1 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (1 1 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (1 1 (:REWRITE OMAP::HEAD-VALUE-WHEN-EMPTYP))
 )
(OMAP::VALUES)
(OMAP::VALUES-WHEN-EMPTYP
 (22 3 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (10 2 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (7 7 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (6 2 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (4 4 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (4 2 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 )
(OMAP::IN-VALUES-WHEN-ASSOC
 (94 16 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (68 62 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 (68 20 (:REWRITE SET::IN-TAIL))
 (42 38 (:TYPE-PRESCRIPTION OMAP::HEAD-VALUE-WHEN-EMPTYP))
 (41 41 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (32 8 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (30 6 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (30 6 (:REWRITE SET::INSERT-IDENTITY))
 (28 28 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (27 13 (:REWRITE OMAP::ASSOC-WHEN-EMPTYP))
 (26 10 (:REWRITE OMAP::VALUES-WHEN-EMPTYP))
 (21 7 (:REWRITE SET::TAIL-WHEN-EMPTYP))
 (21 7 (:REWRITE SET::NEVER-IN-EMPTY))
 (18 6 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (12 12 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (12 6 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (9 9 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (8 8 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (8 8 (:REWRITE OMAP::HEAD-VALUE-WHEN-EMPTYP))
 (6 2 (:REWRITE OMAP::UPDATE-WHEN-EMPTYP))
 (6 1 (:REWRITE SET::SETS-ARE-TRUE-LISTS-CHEAP))
 (4 1 (:REWRITE TRUE-LISTP-WHEN-ATOM))
 (2 2 (:TYPE-PRESCRIPTION SET::SETP-TYPE))
 (2 2 (:REWRITE OMAP::MAPP-OF-TAIL))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (2 1 (:REWRITE SET::NONEMPTY-MEANS-SET))
 (1 1 (:REWRITE SET::IN-SET))
 (1 1 (:REWRITE CONSP-BY-LEN))
 )
(OMAP::VALUES-OF-UPDATE-WHEN-NOT-ASSOC
 (241 29 (:REWRITE SET::INSERT-IDENTITY))
 (187 61 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (145 122 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 (124 9 (:REWRITE SET::IN-INSERT))
 (119 3 (:REWRITE OMAP::TAIL-OF-UPDATE))
 (113 113 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (109 38 (:REWRITE SET::IN-TAIL))
 (83 83 (:REWRITE <<-TRANSITIVE))
 (83 29 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (61 61 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (56 56 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (52 12 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (33 33 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 (27 27 (:TYPE-PRESCRIPTION OMAP::HEAD-VALUE-WHEN-EMPTYP))
 (25 9 (:REWRITE SET::TAIL-WHEN-EMPTYP))
 (20 20 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (19 15 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (12 12 (:REWRITE OMAP::HEAD-VALUE-WHEN-EMPTYP))
 (12 3 (:REWRITE OMAP::TAIL-OF-UPDATE-EQUAL))
 (12 3 (:REWRITE OMAP::TAIL-OF-UPDATE-<<-REV))
 (12 3 (:REWRITE OMAP::TAIL-OF-UPDATE-<<))
 (9 9 (:REWRITE SET::INSERT-NEVER-EMPTY))
 (9 3 (:REWRITE OMAP::TAIL-OF-UPDATE-EMPTYP))
 (6 6 (:REWRITE <<-IRREFLEXIVE))
 (3 3 (:REWRITE OMAP::MFIX-WHEN-EMPTYP))
 (2 2 (:REWRITE OMAP::MAPP-OF-TAIL))
 (1 1 (:REWRITE OMAP::HEAD-KEY-NOT-ASSOC-TAIL))
 (1 1 (:INDUCTION SET::USE-WEAK-INSERT-INDUCTION))
 )
(OMAP::COMPATIBLEP
 (60 46 (:TYPE-PRESCRIPTION OMAP::ASSOC-WHEN-EMPTYP))
 (27 9 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (21 7 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (19 19 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
 (9 3 (:REWRITE OMAP::ASSOC-WHEN-EMPTYP))
 (7 7 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (7 5 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (6 6 (:TYPE-PRESCRIPTION OMAP::HEAD-VALUE-WHEN-EMPTYP))
 (3 3 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 (3 3 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (3 3 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 (2 2 (:REWRITE OMAP::HEAD-VALUE-WHEN-EMPTYP))
 (2 2 (:REWRITE DEFAULT-CDR))
 )
(OMAP::BOOLEANP-OF-COMPATIBLEP
 (2 2 (:TYPE-PRESCRIPTION OMAP::ASSOC-WHEN-EMPTYP))
 )
(OMAP::COMPATIBLEP-WHEN-LEFT-EMPTYP
 (22 3 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (10 2 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (7 7 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (6 2 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (4 4 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (4 2 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 )
(OMAP::COMPATIBLEP-WHEN-RIGHT-EMPTYP
 (107 17 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (41 9 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (40 8 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (33 33 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (21 21 (:TYPE-PRESCRIPTION OMAP::ASSOC-WHEN-EMPTYP))
 (16 16 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (16 8 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (4 4 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (4 4 (:REWRITE OMAP::HEAD-VALUE-WHEN-EMPTYP))
 (4 4 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 (2 2 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 )
(OMAP::SUBMAP
 (42 36 (:TYPE-PRESCRIPTION OMAP::ASSOC-WHEN-EMPTYP))
 (6 3 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 )
(OMAP::BOOLEANP-OF-SUBMAP
 (6 2 (:TYPE-PRESCRIPTION OMAP::ASSOC-WHEN-EMPTYP))
 (2 2 (:TYPE-PRESCRIPTION OMAP::HEAD-VALUE-WHEN-EMPTYP))
 (2 2 (:TYPE-PRESCRIPTION OMAP::HEAD-KEY-WHEN-EMPTYP))
 )
(OMAP::SUBMAP-WHEN-LEFT-EMPTYP
 (22 3 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (10 2 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (7 7 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (6 2 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (4 4 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (4 2 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 )
(OMAP::SUBMAP-WHEN-RIGHT-EMPTYP
 (40 7 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (15 3 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (15 3 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (12 12 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (6 6 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (6 3 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (3 1 (:REWRITE OMAP::SUBMAP-WHEN-LEFT-EMPTYP))
 (1 1 (:TYPE-PRESCRIPTION OMAP::HEAD-VALUE-WHEN-EMPTYP))
 (1 1 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (1 1 (:REWRITE OMAP::HEAD-VALUE-WHEN-EMPTYP))
 (1 1 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 )
(OMAP::SIZE
 (1 1 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 )
(OMAP::NATP-OF-SIZE)
(OMAP::UNFOLD-EQUAL-SIZE-CONST
 (62 10 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (20 4 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (20 4 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (18 18 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (9 5 (:REWRITE DEFAULT-+-2))
 (8 8 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (8 4 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (5 5 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (5 5 (:REWRITE DEFAULT-+-1))
 (4 4 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 (2 2 (:REWRITE OMAP::MAPP-OF-TAIL))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 )
(OMAP::UNFOLD-GTEQ-SIZE-CONST
 (49 8 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (15 3 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (15 3 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (14 14 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (10 5 (:REWRITE DEFAULT-+-2))
 (7 4 (:REWRITE DEFAULT-<-1))
 (6 6 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (6 3 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (5 5 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (5 5 (:REWRITE DEFAULT-+-1))
 (5 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 (4 4 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:REWRITE OMAP::MAPP-OF-TAIL))
 )
(OMAP::LEMMA
 (34 7 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (16 8 (:REWRITE DEFAULT-+-2))
 (9 9 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (8 8 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (8 8 (:REWRITE DEFAULT-+-1))
 (7 4 (:REWRITE DEFAULT-<-2))
 (7 3 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (6 6 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 (5 4 (:REWRITE DEFAULT-<-1))
 (5 1 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (3 3 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (3 3 (:REWRITE OMAP::MAPP-OF-TAIL))
 (2 2 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (2 1 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 )
(OMAP::UNFOLD-GT-SIZE-CONST
 (221 37 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (70 14 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (63 63 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (62 14 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (41 23 (:REWRITE DEFAULT-<-2))
 (28 28 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (28 14 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (23 23 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (22 22 (:REWRITE DEFAULT-+-1))
 (18 18 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 (14 14 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (9 9 (:REWRITE OMAP::MAPP-OF-TAIL))
 )
(OMAP::EQUAL-OF-OMAP-SIZE-AND-0
 (32 6 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (10 2 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (10 2 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (9 9 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (6 3 (:REWRITE DEFAULT-+-2))
 (4 4 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (4 2 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (3 3 (:REWRITE OMAP::TAIL-WHEN-EMPTYP))
 (3 3 (:REWRITE DEFAULT-+-1))
 (2 2 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 (1 1 (:REWRITE OMAP::MAPP-OF-TAIL))
 )
(OMAP::SIZE-TO-CARDINALITY-OF-KEYS
 (41 7 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (15 3 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (13 13 (:TYPE-PRESCRIPTION OMAP::MAPP))
 (13 5 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (10 10 (:LINEAR SET::SUBSET-CARDINALITY))
 (10 10 (:LINEAR SET::PROPER-SUBSET-CARDINALITY))
 (6 6 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (6 3 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (4 2 (:REWRITE DEFAULT-+-2))
 (4 1 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (3 1 (:REWRITE SET::INSERT-IDENTITY))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 1 (:REWRITE OMAP::SET-EMPTYP-OF-KEYS))
 (2 1 (:REWRITE SET::DOUBLE-CONTAINMENT))
 (1 1 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (1 1 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (1 1 (:REWRITE OMAP::HEAD-WHEN-EMPTYP-CHEAP))
 (1 1 (:REWRITE OMAP::HEAD-KEY-WHEN-EMPTYP))
 )
(OMAP::CARDINALITY-OF-KEYS-TO-SIZE)
(OMAP::FROM-LISTS
 (165 22 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (162 27 (:REWRITE SET::SETS-ARE-TRUE-LISTS-CHEAP))
 (132 11 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (108 27 (:REWRITE TRUE-LISTP-WHEN-ATOM))
 (100 100 (:LINEAR LOWER-BOUND-OF-LEN-WHEN-SUBLISTP))
 (100 100 (:LINEAR LISTPOS-UPPER-BOUND-STRONG-2))
 (100 100 (:LINEAR LEN-WHEN-PREFIXP))
 (88 22 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (74 39 (:REWRITE LEN-WHEN-ATOM))
 (66 49 (:REWRITE DEFAULT-CDR))
 (57 57 (:TYPE-PRESCRIPTION OMAP::EMPTYP))
 (54 54 (:TYPE-PRESCRIPTION SET::SETP-TYPE))
 (54 27 (:REWRITE SET::NONEMPTY-MEANS-SET))
 (50 50 (:LINEAR INDEX-OF-<-LEN))
 (44 22 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (36 12 (:REWRITE OMAP::UPDATE-WHEN-EMPTYP))
 (34 21 (:REWRITE DEFAULT-CAR))
 (30 15 (:REWRITE DEFAULT-+-2))
 (27 27 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (27 27 (:REWRITE SET::IN-SET))
 (27 27 (:REWRITE CONSP-BY-LEN))
 (22 11 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (21 21 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (16 16 (:TYPE-PRESCRIPTION OMAP::FROM-LISTS))
 (15 15 (:REWRITE DEFAULT-+-1))
 )
(OMAP::MAPP-OF-FROM-LISTS
 (105 14 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (84 7 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (56 14 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (28 14 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (23 23 (:TYPE-PRESCRIPTION OMAP::EMPTYP))
 (16 8 (:REWRITE CONSP-UNDER-IFF-WHEN-TRUE-LISTP))
 (14 7 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (8 8 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (8 8 (:REWRITE CONSP-BY-LEN))
 (5 2 (:REWRITE DEFAULT-CDR))
 (5 2 (:REWRITE DEFAULT-CAR))
 (3 1 (:REWRITE OMAP::UPDATE-WHEN-EMPTYP))
 (2 2 (:REWRITE CAR-WHEN-ALL-EQUALP))
 )
(OMAP::LIST-LOOKUP-OF-FROM-LISTS-OF-APPEND-FIRST
 (1427 592 (:REWRITE CONSP-UNDER-IFF-WHEN-TRUE-LISTP))
 (1214 173 (:REWRITE DEFAULT-CDR))
 (858 858 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (592 592 (:REWRITE CONSP-BY-LEN))
 (428 214 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (353 189 (:REWRITE DEFAULT-CAR))
 (292 27 (:REWRITE LIST-FIX-WHEN-TRUE-LISTP))
 (281 281 (:REWRITE CONSP-OF-CDR-BY-LEN))
 (247 247 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (214 214 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (151 17 (:REWRITE SUBSETP-CAR-MEMBER))
 (150 25 (:REWRITE SET::SETS-ARE-TRUE-LISTS-CHEAP))
 (144 50 (:REWRITE OMAP::UPDATE-WHEN-EMPTYP))
 (134 134 (:TYPE-PRESCRIPTION OMAP::EMPTYP))
 (112 112 (:LINEAR LOWER-BOUND-OF-LEN-WHEN-SUBLISTP))
 (112 112 (:LINEAR LISTPOS-UPPER-BOUND-STRONG-2))
 (112 112 (:LINEAR LEN-WHEN-PREFIXP))
 (71 15 (:REWRITE MEMBER-WHEN-ATOM))
 (63 27 (:REWRITE TRUE-LISTP-WHEN-ATOM))
 (60 20 (:REWRITE OMAP::LOOKUP-WHEN-EMPTYP))
 (59 25 (:REWRITE LIST-FIX-WHEN-NOT-CONSP))
 (56 56 (:LINEAR INDEX-OF-<-LEN))
 (55 11 (:REWRITE SUBSETP-WHEN-ATOM-RIGHT))
 (50 50 (:TYPE-PRESCRIPTION SET::SETP-TYPE))
 (50 25 (:REWRITE SET::NONEMPTY-MEANS-SET))
 (28 28 (:TYPE-PRESCRIPTION SUBSETP-EQUAL))
 (26 26 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-DUPLICITY-BADGUY1))
 (25 25 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (25 25 (:REWRITE SET::IN-SET))
 (24 24 (:REWRITE NO-DUPLICATESP-EQUAL-WHEN-HIGH-DUPLICITY))
 (17 17 (:REWRITE SUBSETP-TRANS2))
 (17 17 (:REWRITE SUBSETP-TRANS))
 (15 15 (:REWRITE SUBSETP-MEMBER . 4))
 (15 15 (:REWRITE SUBSETP-MEMBER . 3))
 (15 15 (:REWRITE SUBSETP-MEMBER . 2))
 (15 15 (:REWRITE SUBSETP-MEMBER . 1))
 (15 15 (:REWRITE MEMBER-EQUAL-WHEN-ALL-EQUALP))
 (15 15 (:REWRITE INTERSECTP-MEMBER . 3))
 (15 15 (:REWRITE INTERSECTP-MEMBER . 2))
 (12 6 (:REWRITE DEFAULT-+-2))
 (11 11 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (6 6 (:REWRITE SUBSETP-REFL))
 (6 6 (:REWRITE DEFAULT-+-1))
 )
(OMAP::LIST-LOOKUP-OF-FROM-LISTS-OF-APPEND-SECOND
 (811 347 (:REWRITE CONSP-UNDER-IFF-WHEN-TRUE-LISTP))
 (647 123 (:REWRITE DEFAULT-CDR))
 (449 449 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (347 347 (:REWRITE CONSP-BY-LEN))
 (240 120 (:REWRITE DEFAULT-CAR))
 (204 102 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (150 150 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (124 124 (:TYPE-PRESCRIPTION OMAP::EMPTYP))
 (111 111 (:REWRITE CONSP-OF-CDR-BY-LEN))
 (102 102 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (102 34 (:REWRITE OMAP::UPDATE-WHEN-EMPTYP))
 (84 28 (:REWRITE OMAP::LOOKUP-WHEN-EMPTYP))
 (64 64 (:LINEAR LOWER-BOUND-OF-LEN-WHEN-SUBLISTP))
 (64 64 (:LINEAR LISTPOS-UPPER-BOUND-STRONG-2))
 (64 64 (:LINEAR LEN-WHEN-PREFIXP))
 (64 16 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-LEFT))
 (32 32 (:LINEAR INDEX-OF-<-LEN))
 (18 18 (:REWRITE INTERSECTP-MEMBER . 1))
 (12 3 (:REWRITE SUBSETP-WHEN-ATOM-RIGHT))
 (8 4 (:REWRITE DEFAULT-+-2))
 (6 6 (:REWRITE SUBSETP-TRANS2))
 (6 6 (:REWRITE SUBSETP-TRANS))
 (4 4 (:REWRITE DEFAULT-+-1))
 (3 3 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (3 3 (:REWRITE INTERSECTP-MEMBER . 3))
 )
(OMAP::FROM-ALIST
 (90 12 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (72 6 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (48 12 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (46 31 (:REWRITE DEFAULT-CAR))
 (40 25 (:REWRITE DEFAULT-CDR))
 (39 39 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (39 39 (:REWRITE CONSP-BY-LEN))
 (31 31 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (30 30 (:TYPE-PRESCRIPTION OMAP::EMPTYP))
 (24 12 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (18 6 (:REWRITE OMAP::UPDATE-WHEN-EMPTYP))
 (12 6 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (5 5 (:REWRITE CONSP-OF-CDR-BY-LEN))
 )
(OMAP::MAPP-OF-FROM-ALIST
 (105 14 (:REWRITE OMAP::MAPP-WHEN-NOT-EMPTYP))
 (84 7 (:REWRITE OMAP::MAPP-NON-NIL-IMPLIES-NOT-EMPTYP))
 (56 14 (:REWRITE OMAP::MFIX-IMPLIES-MAPP))
 (28 14 (:TYPE-PRESCRIPTION OMAP::MFIX))
 (23 23 (:TYPE-PRESCRIPTION OMAP::EMPTYP))
 (16 8 (:REWRITE CONSP-UNDER-IFF-WHEN-TRUE-LISTP))
 (14 7 (:REWRITE OMAP::MFIX-WHEN-MAPP))
 (8 8 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (8 8 (:REWRITE CONSP-BY-LEN))
 (6 3 (:REWRITE DEFAULT-CAR))
 (5 2 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE CAR-WHEN-ALL-EQUALP))
 (3 1 (:REWRITE OMAP::UPDATE-WHEN-EMPTYP))
 )
(OMAP::OMAP-INDUCTION2
 (6 6 (:TYPE-PRESCRIPTION OMAP::TAIL-WHEN-EMPTYP))
 )
