(ZF::TC-N)
(ZF::TC-FN$PROP)
(ZF::TC-FN)
(ZF::TC-FN$FUNP)
(ZF::TC-FN$DOMAIN-1
 (6 6 (:TYPE-PRESCRIPTION NATP))
 (5 2 (:REWRITE ZF::NATP-IMPLIES-TRANSITIVE))
 (4 1 (:REWRITE ZF::NATP-<-IMPLIES-IN))
 (4 1 (:REWRITE ZF::HONS-ASSOC-EQUAL-PRESERVES-IN-FOR-TRANSITIVE))
 (4 1 (:REWRITE ZF::<=-IMPLIES-SUBSET-ON-NATPS))
 (3 3 (:REWRITE ZF::IN-NATP-IMPLIES-NATP))
 (1 1 (:REWRITE ZF::SUBSET-TRANSITIVITY))
 (1 1 (:REWRITE ZF::SUBSET-PRESERVES-IN-2))
 (1 1 (:REWRITE ZF::SUBSET-PRESERVES-IN-1))
 (1 1 (:REWRITE ZF::FN-EQUAL-FORWARD-TO-EQUAL-DOMAINS))
 )
(ZF::TC-FN$DOMAIN-2)
(ZF::TC-FN$CHOOSES)
(ZF::TC-N$DOMAIN-LEMMA
 (42 1 (:REWRITE ZF::SUBSET-CRITERION))
 (26 5 (:REWRITE ZF::HONS-ASSOC-EQUAL-PRESERVES-IN-FOR-TRANSITIVE))
 (15 6 (:REWRITE ZF::NATP-IMPLIES-TRANSITIVE))
 (13 13 (:TYPE-PRESCRIPTION NATP))
 (11 5 (:REWRITE ZF::NATP-<-IMPLIES-IN))
 (9 9 (:REWRITE ZF::IN-NATP-IMPLIES-NATP))
 (8 8 (:TYPE-PRESCRIPTION ZF::TRANSITIVE))
 (7 1 (:REWRITE ZF::TRANSITIVE-NECC))
 (6 3 (:REWRITE ZF::IN-ASYMMETRIC))
 (5 5 (:REWRITE ZF::SUBSET-PRESERVES-IN-2))
 (5 5 (:REWRITE ZF::SUBSET-PRESERVES-IN-1))
 (4 4 (:REWRITE ZF::TRANSITIVE-OMEGA))
 (4 1 (:REWRITE ZF::<=-IMPLIES-SUBSET-ON-NATPS))
 (1 1 (:REWRITE ZF::SUBSET-TRANSITIVITY))
 (1 1 (:REWRITE ZF::SUBSET-NECC-BETTER-2))
 (1 1 (:REWRITE ZF::SUBSET-NECC-BETTER-1))
 (1 1 (:REWRITE ZF::IN-CAR-DOMAIN-ALT))
 (1 1 (:REWRITE ZF::FN-EQUAL-FORWARD-TO-EQUAL-DOMAINS))
 )
(ZF::TC-N$DOMAIN
 (1 1 (:REWRITE ZF::FN-EQUAL-FORWARD-TO-EQUAL-DOMAINS))
 )
(ZF::TC)
(ZF::TC-FN-MAPS-N-TO-TC-N
 (22 4 (:REWRITE ZF::HONS-ASSOC-EQUAL-PRESERVES-IN-FOR-TRANSITIVE))
 (16 2 (:REWRITE ZF::APPLY-DEFAULT))
 (12 1 (:REWRITE ZF::IN-CONS-APPLY))
 (10 4 (:REWRITE ZF::NATP-IMPLIES-TRANSITIVE))
 (7 4 (:REWRITE ZF::NATP-<-IMPLIES-IN))
 (6 6 (:TYPE-PRESCRIPTION NATP))
 (6 3 (:REWRITE ZF::IN-ASYMMETRIC))
 (5 5 (:TYPE-PRESCRIPTION ZF::TRANSITIVE))
 (4 4 (:REWRITE ZF::SUBSET-PRESERVES-IN-2))
 (4 4 (:REWRITE ZF::SUBSET-PRESERVES-IN-1))
 (4 1 (:DEFINITION ZF::TC-N))
 (3 3 (:REWRITE ZF::TRANSITIVE-OMEGA))
 (3 3 (:REWRITE ZF::IN-NATP-IMPLIES-NATP))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(ZF::SUBSET-TC-N-TC
 (7 1 (:REWRITE ZF::HONS-ASSOC-EQUAL-PRESERVES-IN-FOR-TRANSITIVE))
 (4 4 (:REWRITE ZF::IN-NATP-IMPLIES-NATP))
 (4 1 (:REWRITE ZF::NATP-IMPLIES-TRANSITIVE))
 (4 1 (:REWRITE ZF::NATP-<-IMPLIES-IN))
 (4 1 (:REWRITE ZF::<=-IMPLIES-SUBSET-ON-NATPS))
 (4 1 (:DEFINITION ZF::TC-N))
 (2 2 (:TYPE-PRESCRIPTION ZF::TRANSITIVE))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE ZF::SUBSET-PRESERVES-IN-2))
 (1 1 (:REWRITE ZF::SUBSET-PRESERVES-IN-1))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(ZF::SUBSET-TC
 (29 1 (:REWRITE ZF::SUBSET-CRITERION))
 (18 3 (:REWRITE ZF::HONS-ASSOC-EQUAL-PRESERVES-IN-FOR-TRANSITIVE))
 (17 1 (:REWRITE ZF::IN-IMPLIES-SUBSET-UNION))
 (13 4 (:REWRITE ZF::NATP-IMPLIES-TRANSITIVE))
 (12 12 (:TYPE-PRESCRIPTION NATP))
 (9 3 (:REWRITE ZF::NATP-<-IMPLIES-IN))
 (8 8 (:TYPE-PRESCRIPTION ZF::TRANSITIVE))
 (7 1 (:REWRITE ZF::TRANSITIVE-NECC))
 (6 6 (:TYPE-PRESCRIPTION ZF::BOOLEANP-IN))
 (6 6 (:REWRITE ZF::IN-NATP-IMPLIES-NATP))
 (4 2 (:REWRITE ZF::IN-ASYMMETRIC))
 (4 1 (:REWRITE ZF::<=-IMPLIES-SUBSET-ON-NATPS))
 (3 3 (:REWRITE ZF::SUBSET-PRESERVES-IN-2))
 (3 3 (:REWRITE ZF::SUBSET-PRESERVES-IN-1))
 (2 1 (:REWRITE ZF::IN-UNION))
 (1 1 (:REWRITE ZF::SUBSET-TRANSITIVITY))
 (1 1 (:REWRITE ZF::SUBSET-NECC-BETTER-2))
 (1 1 (:REWRITE ZF::SUBSET-NECC-BETTER-1))
 (1 1 (:REWRITE ZF::IN-IN-SUFF))
 (1 1 (:REWRITE ZF::IN-IMAGE-SUFF))
 )
(ZF::TC-IS-TRANSITIVE-1-1
 (57 4 (:REWRITE ZF::APPLY-DEFAULT))
 (49 2 (:REWRITE ZF::IN-CONS-APPLY))
 (36 6 (:REWRITE ZF::HONS-ASSOC-EQUAL-PRESERVES-IN-FOR-TRANSITIVE))
 (19 7 (:REWRITE ZF::NATP-IMPLIES-TRANSITIVE))
 (16 16 (:TYPE-PRESCRIPTION NATP))
 (16 2 (:REWRITE ZF::SUBSET-PRESERVES-IN-1))
 (11 11 (:TYPE-PRESCRIPTION ZF::TRANSITIVE))
 (11 2 (:REWRITE ZF::NATP-<-IMPLIES-IN))
 (10 8 (:REWRITE ZF::IN-NATP-IMPLIES-NATP))
 (7 1 (:DEFINITION ZF::TC-N))
 (6 3 (:REWRITE ZF::IN-ASYMMETRIC))
 (4 1 (:REWRITE ZP-OPEN))
 (4 1 (:REWRITE ZF::TRANSITIVE-NECC))
 (4 1 (:REWRITE ZF::<=-IMPLIES-SUBSET-ON-NATPS))
 (3 3 (:REWRITE ZF::TRANSITIVE-OMEGA))
 (3 1 (:REWRITE ZF::SUBSET-CRITERION))
 (2 2 (:REWRITE ZF::SUBSET-PRESERVES-IN-2))
 (1 1 (:REWRITE ZF::SUBSET-TRANSITIVITY))
 (1 1 (:REWRITE ZF::IN-IMAGE-SUFF))
 (1 1 (:REWRITE ZF::IN-CAR-DOMAIN-ALT))
 (1 1 (:REWRITE ZF::FN-EQUAL-FORWARD-TO-EQUAL-DOMAINS))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(ZF::TC-IS-TRANSITIVE-1-2-1-1
 (24 3 (:REWRITE ZF::HONS-ASSOC-EQUAL-PRESERVES-IN-FOR-TRANSITIVE))
 (15 3 (:REWRITE ZF::NATP-IMPLIES-TRANSITIVE))
 (13 9 (:REWRITE ZF::IN-NATP-IMPLIES-NATP))
 (8 2 (:REWRITE ZF::NATP-<-IMPLIES-IN))
 (7 1 (:REWRITE ZF::<=-IMPLIES-SUBSET-ON-NATPS))
 (6 6 (:TYPE-PRESCRIPTION ZF::TRANSITIVE))
 (6 3 (:REWRITE ZF::IN-ASYMMETRIC))
 (5 5 (:REWRITE DEFAULT-+-2))
 (5 5 (:REWRITE DEFAULT-+-1))
 (3 3 (:REWRITE ZF::SUBSET-PRESERVES-IN-2))
 (2 2 (:REWRITE ZP-OPEN))
 )
(ZF::TC-IS-TRANSITIVE-1-2-1
 (126 11 (:REWRITE ZF::SUBSET-PRESERVES-IN-1))
 (69 1 (:REWRITE ZF::IN-IMPLIES-SUBSET-UNION))
 (65 11 (:REWRITE ZF::HONS-ASSOC-EQUAL-PRESERVES-IN-FOR-TRANSITIVE))
 (47 1 (:REWRITE ZF::TC-FN$CHOOSES))
 (39 1 (:REWRITE ZF::SUBSET-CRITERION))
 (37 10 (:REWRITE ZF::NATP-IMPLIES-TRANSITIVE))
 (35 11 (:REWRITE ZF::NATP-<-IMPLIES-IN))
 (26 20 (:REWRITE ZF::IN-NATP-IMPLIES-NATP))
 (24 1 (:REWRITE ZF::EQUAL-APPLY))
 (22 2 (:REWRITE ZF::APPLY-DEFAULT))
 (18 18 (:TYPE-PRESCRIPTION ZF::TRANSITIVE))
 (18 1 (:REWRITE ZF::IN-CONS-APPLY))
 (12 6 (:REWRITE ZF::IN-ASYMMETRIC))
 (11 11 (:REWRITE ZF::SUBSET-PRESERVES-IN-2))
 (7 1 (:REWRITE ZF::<=-IMPLIES-SUBSET-ON-NATPS))
 (4 1 (:REWRITE ZF::TRANSITIVE-NECC))
 (3 3 (:TYPE-PRESCRIPTION ZF::SUBSET))
 (2 2 (:REWRITE ZF::TRANSITIVE-OMEGA))
 (2 2 (:REWRITE ZF::TC-N$DOMAIN))
 (2 2 (:REWRITE ZF::INFINITY))
 (2 2 (:REWRITE DEFAULT-CDR))
 (1 1 (:TYPE-PRESCRIPTION ZF::FUNP))
 (1 1 (:REWRITE ZF::TC-FN$FUNP))
 (1 1 (:REWRITE ZF::SUBSET-TRANSITIVITY))
 )
(ZF::TC-IS-TRANSITIVE-1-2
 (23 2 (:REWRITE ZF::APPLY-DEFAULT))
 (21 3 (:REWRITE ZF::HONS-ASSOC-EQUAL-PRESERVES-IN-FOR-TRANSITIVE))
 (19 1 (:REWRITE ZF::IN-CONS-APPLY))
 (12 12 (:TYPE-PRESCRIPTION NATP))
 (12 3 (:REWRITE ZF::NATP-IMPLIES-TRANSITIVE))
 (12 3 (:REWRITE ZF::NATP-<-IMPLIES-IN))
 (7 7 (:REWRITE ZF::IN-NATP-IMPLIES-NATP))
 (7 1 (:DEFINITION ZF::TC-N))
 (6 6 (:TYPE-PRESCRIPTION ZF::TRANSITIVE))
 (6 3 (:REWRITE ZF::IN-ASYMMETRIC))
 (4 1 (:REWRITE ZP-OPEN))
 (3 3 (:REWRITE ZF::SUBSET-PRESERVES-IN-2))
 (3 3 (:REWRITE ZF::SUBSET-PRESERVES-IN-1))
 (1 1 (:REWRITE ZF::IN-CAR-DOMAIN-ALT))
 (1 1 (:REWRITE ZF::FN-EQUAL-FORWARD-TO-EQUAL-DOMAINS))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(ZF::TC-IS-TRANSITIVE-1-3-1
 (48 6 (:REWRITE ZF::APPLY-DEFAULT))
 (38 2 (:REWRITE ZF::IN-CONS-APPLY))
 (36 6 (:REWRITE ZF::HONS-ASSOC-EQUAL-PRESERVES-IN-FOR-TRANSITIVE))
 (21 6 (:REWRITE ZF::NATP-IMPLIES-TRANSITIVE))
 (16 16 (:TYPE-PRESCRIPTION NATP))
 (13 3 (:REWRITE ZF::IN-IMAGE-NECC))
 (11 11 (:TYPE-PRESCRIPTION ZF::TRANSITIVE))
 (10 5 (:REWRITE ZF::IN-ASYMMETRIC))
 (10 4 (:REWRITE ZF::NATP-<-IMPLIES-IN))
 (8 8 (:REWRITE ZF::IN-NATP-IMPLIES-NATP))
 (5 5 (:REWRITE ZF::SUBSET-PRESERVES-IN-2))
 (4 1 (:REWRITE ZF::TRANSITIVE-NECC))
 (4 1 (:REWRITE ZF::<=-IMPLIES-SUBSET-ON-NATPS))
 (2 2 (:REWRITE ZF::IN-CAR-DOMAIN-ALT))
 (2 2 (:REWRITE ZF::FN-EQUAL-FORWARD-TO-EQUAL-DOMAINS))
 (1 1 (:REWRITE ZF::TRANSITIVE-OMEGA))
 (1 1 (:REWRITE ZF::SUBSET-TRANSITIVITY))
 )
(ZF::TC-IS-TRANSITIVE-1-3)
(ZF::TC-IS-TRANSITIVE-1)
(ZF::TC-IS-TRANSITIVE
 (78 1 (:REWRITE ZF::IN-IMPLIES-SUBSET-UNION))
 (76 11 (:REWRITE ZF::HONS-ASSOC-EQUAL-PRESERVES-IN-FOR-TRANSITIVE))
 (68 11 (:REWRITE ZF::SUBSET-PRESERVES-IN-1))
 (68 2 (:REWRITE ZF::SUBSET-CRITERION))
 (47 47 (:TYPE-PRESCRIPTION NATP))
 (44 13 (:REWRITE ZF::NATP-IMPLIES-TRANSITIVE))
 (39 11 (:REWRITE ZF::NATP-<-IMPLIES-IN))
 (31 22 (:REWRITE ZF::IN-NATP-IMPLIES-NATP))
 (18 9 (:REWRITE ZF::IN-ASYMMETRIC))
 (13 2 (:REWRITE ZF::TRANSITIVE-NECC))
 (12 2 (:REWRITE ZF::<=-IMPLIES-SUBSET-ON-NATPS))
 (11 11 (:REWRITE ZF::SUBSET-PRESERVES-IN-2))
 (4 4 (:REWRITE ZF::IN-IMAGE-SUFF))
 (2 2 (:TYPE-PRESCRIPTION ZF::SUBSET))
 (2 2 (:REWRITE ZF::SUBSET-TRANSITIVITY))
 (2 2 (:REWRITE ZF::IN-IN-SUFF))
 (1 1 (:REWRITE ZF::SUBSET-NECC-BETTER-2))
 (1 1 (:REWRITE ZF::SUBSET-NECC-BETTER-1))
 )
(ZF::TRANSITIVE-ALT)
(ZF::TRANSITIVE-IMPLIES-TRANSITIVE-ALT
 (49 1 (:REWRITE ZF::SUBSET-CRITERION))
 (27 9 (:REWRITE ZF::HONS-ASSOC-EQUAL-PRESERVES-IN-FOR-TRANSITIVE))
 (22 22 (:TYPE-PRESCRIPTION NATP))
 (20 8 (:REWRITE ZF::NATP-<-IMPLIES-IN))
 (16 8 (:REWRITE ZF::IN-ASYMMETRIC))
 (16 4 (:REWRITE ZF::NATP-IMPLIES-TRANSITIVE))
 (13 11 (:REWRITE ZF::IN-NATP-IMPLIES-NATP))
 (11 2 (:REWRITE ZF::<=-IMPLIES-SUBSET-ON-NATPS))
 (9 9 (:REWRITE ZF::SUBSET-PRESERVES-IN-2))
 (2 2 (:REWRITE ZF::SUBSET-TRANSITIVITY))
 (2 2 (:REWRITE ZF::IN-IN-SUFF))
 (1 1 (:REWRITE ZF::SUBSET-NECC-BETTER-2))
 (1 1 (:REWRITE ZF::SUBSET-NECC-BETTER-1))
 )
(ZF::TRANSITIVE-ALT-IMPLIES-TRANSITIVE
 (105 3 (:REWRITE ZF::SUBSET-CRITERION))
 (94 12 (:REWRITE ZF::HONS-ASSOC-EQUAL-PRESERVES-IN-FOR-TRANSITIVE))
 (38 38 (:TYPE-PRESCRIPTION NATP))
 (34 10 (:REWRITE ZF::NATP-IMPLIES-TRANSITIVE))
 (25 10 (:REWRITE ZF::NATP-<-IMPLIES-IN))
 (23 19 (:REWRITE ZF::IN-NATP-IMPLIES-NATP))
 (22 4 (:REWRITE ZF::<=-IMPLIES-SUBSET-ON-NATPS))
 (16 8 (:REWRITE ZF::IN-ASYMMETRIC))
 (11 4 (:REWRITE ZF::IN-UNION))
 (11 3 (:REWRITE ZF::TRANSITIVE-NECC))
 (4 4 (:TYPE-PRESCRIPTION ZF::IN-IN))
 (4 4 (:REWRITE ZF::IN-IN-SUFF))
 (3 3 (:REWRITE ZF::SUBSET-TRANSITIVITY))
 (2 2 (:REWRITE ZF::SUBSET-NECC-BETTER-2))
 (2 2 (:REWRITE ZF::SUBSET-NECC-BETTER-1))
 )
(ZF::TRANSITIVE-IS-TRANSITIVE-ALT
 (24 24 (:TYPE-PRESCRIPTION NATP))
 (23 8 (:REWRITE ZF::NATP-IMPLIES-TRANSITIVE))
 (22 3 (:REWRITE ZF::TRANSITIVE-NECC))
 (20 5 (:REWRITE ZF::<=-IMPLIES-SUBSET-ON-NATPS))
 (12 12 (:REWRITE ZF::IN-NATP-IMPLIES-NATP))
 (12 3 (:REWRITE ZF::HONS-ASSOC-EQUAL-PRESERVES-IN-FOR-TRANSITIVE))
 (9 3 (:REWRITE ZF::NATP-<-IMPLIES-IN))
 (4 3 (:REWRITE ZF::SUBSET-PRESERVES-IN-2))
 (4 2 (:REWRITE ZF::IN-ASYMMETRIC))
 (3 3 (:REWRITE ZF::SUBSET-PRESERVES-IN-1))
 (2 1 (:REWRITE ZF::IN-UNION))
 (1 1 (:REWRITE ZF::SUBSET-NECC-BETTER-2))
 (1 1 (:REWRITE ZF::SUBSET-NECC-BETTER-1))
 (1 1 (:REWRITE ZF::IN-IN-SUFF))
 )
(ZF::UNION-PRESERVES-SUBSET-FOR-TRANSITIVE
 (196 12 (:REWRITE ZF::SUBSET-CRITERION))
 (123 12 (:REWRITE ZF::TRANSITIVE-NECC))
 (101 17 (:REWRITE ZF::HONS-ASSOC-EQUAL-PRESERVES-IN-FOR-TRANSITIVE))
 (47 17 (:REWRITE ZF::NATP-<-IMPLIES-IN))
 (43 43 (:TYPE-PRESCRIPTION ZF::BOOLEANP-IN))
 (40 13 (:REWRITE ZF::<=-IMPLIES-SUBSET-ON-NATPS))
 (38 38 (:TYPE-PRESCRIPTION NATP))
 (30 3 (:REWRITE ZF::IN-IMPLIES-SUBSET-UNION))
 (26 17 (:REWRITE ZF::SUBSET-PRESERVES-IN-2))
 (20 10 (:REWRITE ZF::IN-ASYMMETRIC))
 (19 19 (:REWRITE ZF::IN-NATP-IMPLIES-NATP))
 (18 2 (:REWRITE ZF::UNION-PRESERVES-SUBSET))
 (17 17 (:REWRITE ZF::SUBSET-PRESERVES-IN-1))
 (10 5 (:REWRITE ZF::IN-UNION))
 (8 8 (:TYPE-PRESCRIPTION ZF::TRANSITIVE-ALT))
 (5 5 (:REWRITE ZF::IN-IN-SUFF))
 (2 2 (:REWRITE ZF::SUBSET-NECC-BETTER-2))
 (2 2 (:REWRITE ZF::SUBSET-NECC-BETTER-1))
 )
(ZF::TC-N-PRESERVES-SUBSET-FOR-TRANSITIVE
 (140 8 (:REWRITE ZF::TRANSITIVE-NECC))
 (121 31 (:REWRITE ZF::SUBSET-PRESERVES-IN-2))
 (103 31 (:REWRITE ZF::HONS-ASSOC-EQUAL-PRESERVES-IN-FOR-TRANSITIVE))
 (80 80 (:TYPE-PRESCRIPTION NATP))
 (76 31 (:REWRITE ZF::NATP-<-IMPLIES-IN))
 (64 16 (:REWRITE ZF::NATP-IMPLIES-TRANSITIVE))
 (40 40 (:REWRITE ZF::IN-NATP-IMPLIES-NATP))
 (36 9 (:REWRITE ZF::<=-IMPLIES-SUBSET-ON-NATPS))
 (31 31 (:REWRITE ZF::SUBSET-PRESERVES-IN-1))
 (28 14 (:REWRITE ZF::IN-ASYMMETRIC))
 (7 7 (:REWRITE ZF::SUBSET-NECC-BETTER-2))
 (7 7 (:REWRITE ZF::SUBSET-NECC-BETTER-1))
 (4 4 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(ZF::TC-N-OF-NON-NATP
 (1 1 (:REWRITE ZF::IN-NATP-IMPLIES-NATP))
 )
(ZF::IN-TC-0-IMAGE-TC-FN
 (7 1 (:REWRITE ZF::HONS-ASSOC-EQUAL-PRESERVES-IN-FOR-TRANSITIVE))
 (4 4 (:TYPE-PRESCRIPTION NATP))
 (4 1 (:REWRITE ZF::NATP-IMPLIES-TRANSITIVE))
 (4 1 (:REWRITE ZF::NATP-<-IMPLIES-IN))
 (2 2 (:TYPE-PRESCRIPTION ZF::TRANSITIVE))
 (2 2 (:REWRITE ZF::IN-NATP-IMPLIES-NATP))
 (2 1 (:REWRITE ZF::IN-ASYMMETRIC))
 (1 1 (:REWRITE ZF::TC-N-OF-NON-NATP))
 (1 1 (:REWRITE ZF::SUBSET-PRESERVES-IN-2))
 (1 1 (:REWRITE ZF::SUBSET-PRESERVES-IN-1))
 (1 1 (:REWRITE DEFAULT-CDR))
 )
(ZF::IN-TC-N-IMAGE-TC-FN
 (7 1 (:REWRITE ZF::HONS-ASSOC-EQUAL-PRESERVES-IN-FOR-TRANSITIVE))
 (4 4 (:REWRITE ZF::IN-NATP-IMPLIES-NATP))
 (4 1 (:REWRITE ZF::NATP-IMPLIES-TRANSITIVE))
 (4 1 (:REWRITE ZF::NATP-<-IMPLIES-IN))
 (2 2 (:TYPE-PRESCRIPTION ZF::TRANSITIVE))
 (2 1 (:REWRITE ZF::IN-ASYMMETRIC))
 (1 1 (:REWRITE ZF::SUBSET-PRESERVES-IN-2))
 (1 1 (:REWRITE ZF::SUBSET-PRESERVES-IN-1))
 (1 1 (:REWRITE DEFAULT-CDR))
 )
(ZF::IN-IMAGE-TC-FN
 (276 22 (:REWRITE ZF::APPLY-DEFAULT))
 (232 11 (:REWRITE ZF::IN-CONS-APPLY))
 (167 29 (:REWRITE ZF::HONS-ASSOC-EQUAL-PRESERVES-IN-FOR-TRANSITIVE))
 (90 90 (:TYPE-PRESCRIPTION NATP))
 (87 27 (:REWRITE ZF::NATP-IMPLIES-TRANSITIVE))
 (67 25 (:REWRITE ZF::NATP-<-IMPLIES-IN))
 (51 49 (:REWRITE ZF::IN-NATP-IMPLIES-NATP))
 (43 43 (:TYPE-PRESCRIPTION ZF::TRANSITIVE))
 (42 6 (:DEFINITION ZF::TC-N))
 (39 25 (:REWRITE ZF::SUBSET-PRESERVES-IN-1))
 (32 16 (:REWRITE ZF::IN-ASYMMETRIC))
 (25 25 (:REWRITE ZF::SUBSET-PRESERVES-IN-2))
 (24 8 (:REWRITE ZF::INFINITY))
 (24 6 (:REWRITE ZP-OPEN))
 (24 6 (:REWRITE ZF::TC-N-OF-NON-NATP))
 (11 11 (:REWRITE ZF::TRANSITIVE-OMEGA))
 (7 7 (:REWRITE ZF::IN-IMAGE-SUFF))
 (6 6 (:REWRITE ZF::IN-CAR-DOMAIN-ALT))
 (6 6 (:REWRITE ZF::FN-EQUAL-FORWARD-TO-EQUAL-DOMAINS))
 (6 6 (:REWRITE DEFAULT-<-2))
 (6 6 (:REWRITE DEFAULT-<-1))
 (6 6 (:REWRITE DEFAULT-+-2))
 (6 6 (:REWRITE DEFAULT-+-1))
 (4 1 (:REWRITE ZF::TRANSITIVE-NECC))
 (4 1 (:REWRITE ZF::<=-IMPLIES-SUBSET-ON-NATPS))
 (3 1 (:REWRITE ZF::SUBSET-CRITERION))
 (1 1 (:REWRITE ZF::SUBSET-TRANSITIVITY))
 )
(ZF::TC-IS-LEAST
 (522 19 (:REWRITE ZF::SUBSET-CRITERION))
 (390 15 (:REWRITE ZF::TC-FN$CHOOSES))
 (328 32 (:REWRITE ZF::APPLY-DEFAULT))
 (306 77 (:REWRITE ZF::SUBSET-PRESERVES-IN-2))
 (296 77 (:REWRITE ZF::HONS-ASSOC-EQUAL-PRESERVES-IN-FOR-TRANSITIVE))
 (279 11 (:REWRITE ZF::IN-CONS-APPLY))
 (213 213 (:TYPE-PRESCRIPTION NATP))
 (200 76 (:REWRITE ZF::NATP-<-IMPLIES-IN))
 (200 5 (:REWRITE ZF::EQUAL-APPLY))
 (166 52 (:REWRITE ZF::NATP-IMPLIES-TRANSITIVE))
 (158 1 (:REWRITE ZF::UNION-PRESERVES-SUBSET-FOR-TRANSITIVE))
 (157 19 (:REWRITE ZF::TRANSITIVE-NECC))
 (115 108 (:REWRITE ZF::IN-NATP-IMPLIES-NATP))
 (112 16 (:DEFINITION ZF::TC-N))
 (87 5 (:REWRITE ZF::SUBSET-NECC-BETTER-2))
 (80 40 (:REWRITE ZF::IN-ASYMMETRIC))
 (70 10 (:REWRITE ZF::IN-IMAGE-IMPLIES-IN-APPLY-INVERSE-DOMAIN))
 (65 5 (:REWRITE ZF::IN-IMAGE-NECC))
 (64 19 (:REWRITE ZF::<=-IMPLIES-SUBSET-ON-NATPS))
 (64 16 (:REWRITE ZP-OPEN))
 (53 19 (:REWRITE ZF::SUBSET-TRANSITIVITY))
 (34 16 (:REWRITE ZF::TC-N-OF-NON-NATP))
 (30 10 (:REWRITE ZF::INFINITY))
 (16 16 (:REWRITE DEFAULT-<-2))
 (16 16 (:REWRITE DEFAULT-<-1))
 (16 16 (:REWRITE DEFAULT-+-2))
 (16 16 (:REWRITE DEFAULT-+-1))
 (10 10 (:REWRITE ZF::TRANSITIVE-OMEGA))
 (10 10 (:REWRITE ZF::TC-N$DOMAIN))
 (6 6 (:REWRITE ZF::IN-CAR-DOMAIN-ALT))
 (6 6 (:REWRITE ZF::FN-EQUAL-FORWARD-TO-EQUAL-DOMAINS))
 (5 5 (:TYPE-PRESCRIPTION ZF::FUNP))
 (5 5 (:REWRITE ZF::TC-FN$FUNP))
 (5 5 (:REWRITE ZF::SUBSET-NECC-BETTER-1))
 (2 2 (:REWRITE ZF::IN-IN-SUFF))
 )
