(FIELDP)
(FIELDP-COMPOUND-RECOGNIZER)
(INTEGERP-FORWARD-CHAIN-FIELDP)
(SYMBOLP-FORWARD-CHAIN-FIELDP)
(FIELD-<)
(FIELD-<-IRREFLEXIVE
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 )
(FIELD-<-TRANSITIVE
 (6 6 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (6 3 (:REWRITE DEFAULT-<-2))
 (6 3 (:REWRITE DEFAULT-<-1))
 )
(FIELD-<-ASYMMETRIC
 (20 6 (:REWRITE SYMBOL<-TRICHOTOMY))
 (6 6 (:REWRITE SYMBOL<-TRANSITIVE))
 (4 4 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (4 4 (:REWRITE FIELD-<-TRANSITIVE))
 (4 2 (:REWRITE DEFAULT-<-2))
 (4 2 (:REWRITE DEFAULT-<-1))
 )
(FIELD-<-TRICHOTOMY
 (40 4 (:REWRITE FIELD-<-ASYMMETRIC))
 (23 4 (:REWRITE SYMBOL<-ASYMMETRIC))
 (9 9 (:REWRITE SYMBOL<-TRANSITIVE))
 (8 8 (:REWRITE FIELD-<-TRANSITIVE))
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 )
(SAP)
(LSP)
(G)
(S-AUX)
(DELETE-KEY)
(S)
(NOT-FIELD-<-X-X)
(DELETE-KEY-NO-OP
 (105 105 (:REWRITE DEFAULT-CAR))
 (42 6 (:REWRITE FIELD-<-ASYMMETRIC))
 (41 41 (:REWRITE DEFAULT-CDR))
 (36 12 (:REWRITE FIELD-<-TRICHOTOMY))
 (24 24 (:TYPE-PRESCRIPTION FIELDP))
 (12 12 (:REWRITE FIELD-<-TRANSITIVE))
 )
(VALUES-NOT-NIL
 (125 125 (:REWRITE DEFAULT-CAR))
 (51 51 (:REWRITE DEFAULT-CDR))
 (49 7 (:REWRITE FIELD-<-ASYMMETRIC))
 (42 14 (:REWRITE FIELD-<-TRICHOTOMY))
 (28 28 (:TYPE-PRESCRIPTION FIELDP))
 (14 14 (:REWRITE FIELD-<-TRANSITIVE))
 )
(KEY-ORDER-LEMMA
 (390 111 (:REWRITE FIELD-<-TRICHOTOMY))
 (361 58 (:REWRITE FIELD-<-ASYMMETRIC))
 (174 174 (:REWRITE DEFAULT-CAR))
 (81 81 (:REWRITE DEFAULT-CDR))
 )
(S-AUX-TO-SAME
 (207 206 (:REWRITE DEFAULT-CAR))
 (74 73 (:REWRITE DEFAULT-CDR))
 )
(S-SAME-G
 (1281 1281 (:REWRITE DEFAULT-CAR))
 (641 641 (:REWRITE DEFAULT-CDR))
 (579 193 (:REWRITE FIELD-<-TRICHOTOMY))
 (567 81 (:REWRITE FIELD-<-ASYMMETRIC))
 (209 193 (:REWRITE FIELD-<-TRANSITIVE))
 (196 18 (:REWRITE KEY-ORDER-LEMMA))
 (8 8 (:REWRITE NOT-FIELD-<-X-X))
 )
(VALUE-S-AUX
 (267 210 (:REWRITE DEFAULT-CAR))
 (246 6 (:REWRITE KEY-ORDER-LEMMA))
 (117 84 (:REWRITE DEFAULT-CDR))
 (35 35 (:REWRITE FIELD-<-TRANSITIVE))
 )
(S-AUX-PRESERVES-SAP
 (285 229 (:REWRITE DEFAULT-CDR))
 (274 205 (:REWRITE FIELD-<-TRANSITIVE))
 )
(CDR-ASSOC-EQUAL-DELETE-KEY
 (197 197 (:REWRITE DEFAULT-CAR))
 (90 90 (:REWRITE DEFAULT-CDR))
 (48 16 (:REWRITE FIELD-<-TRICHOTOMY))
 (46 46 (:TYPE-PRESCRIPTION FIELDP))
 (35 5 (:REWRITE FIELD-<-ASYMMETRIC))
 (24 16 (:REWRITE FIELD-<-TRANSITIVE))
 (4 4 (:REWRITE NOT-FIELD-<-X-X))
 )
(SAP-DELETE-KEY
 (416 416 (:REWRITE DEFAULT-CDR))
 (58 22 (:REWRITE KEY-ORDER-LEMMA))
 )
(SAP-FORWARD-TO-FIELDP-CAAR
 (3 3 (:REWRITE DEFAULT-CAR))
 )
(G-SAME-S
 (5934 5856 (:REWRITE DEFAULT-CAR))
 (2831 2803 (:REWRITE DEFAULT-CDR))
 (1064 1021 (:REWRITE FIELD-<-TRANSITIVE))
 )
(S-AUX-S-AUX-SAME
 (279 222 (:REWRITE DEFAULT-CAR))
 (97 74 (:REWRITE DEFAULT-CDR))
 (62 62 (:REWRITE FIELD-<-TRANSITIVE))
 )
(DELETE-KEY-S-AUX-SAME
 (621 519 (:REWRITE DEFAULT-CAR))
 (266 206 (:REWRITE DEFAULT-CDR))
 (106 82 (:REWRITE FIELD-<-TRANSITIVE))
 (21 13 (:REWRITE S-AUX-PRESERVES-SAP))
 (9 9 (:REWRITE NOT-FIELD-<-X-X))
 )
(FIELD-<-S-AUX
 (417 69 (:REWRITE FIELD-<-ASYMMETRIC))
 (189 131 (:REWRITE FIELD-<-TRANSITIVE))
 (104 84 (:REWRITE DEFAULT-CAR))
 (35 35 (:REWRITE DEFAULT-CDR))
 (30 30 (:TYPE-PRESCRIPTION S-AUX))
 )
(VALUE-NIL-SUFFICIENCY
 (26 1 (:DEFINITION SAP))
 (25 7 (:REWRITE FIELD-<-TRICHOTOMY))
 (24 4 (:REWRITE FIELD-<-ASYMMETRIC))
 (13 13 (:REWRITE DEFAULT-CAR))
 (7 7 (:REWRITE FIELD-<-TRANSITIVE))
 (6 6 (:REWRITE DEFAULT-CDR))
 (5 1 (:DEFINITION ASSOC-EQUAL))
 )
(CAAR-DELETE-KEY
 (104 104 (:REWRITE DEFAULT-CAR))
 (51 51 (:REWRITE DEFAULT-CDR))
 (31 31 (:TYPE-PRESCRIPTION FIELDP))
 (27 9 (:REWRITE FIELD-<-TRICHOTOMY))
 (21 3 (:REWRITE FIELD-<-ASYMMETRIC))
 (17 3 (:REWRITE VALUE-NIL-SUFFICIENCY))
 (13 9 (:REWRITE FIELD-<-TRANSITIVE))
 (9 3 (:REWRITE KEY-ORDER-LEMMA))
 (2 2 (:REWRITE NOT-FIELD-<-X-X))
 )
(S-AUX-DELETE-KEY
 (904 892 (:REWRITE DEFAULT-CAR))
 (422 410 (:REWRITE DEFAULT-CDR))
 (136 20 (:REWRITE VALUE-NIL-SUFFICIENCY))
 (60 20 (:REWRITE KEY-ORDER-LEMMA))
 (44 8 (:REWRITE CAAR-DELETE-KEY))
 (4 4 (:DEFINITION EQ))
 )
(FIELD-<-HACK
 (13 4 (:REWRITE FIELD-<-ASYMMETRIC))
 )
(S-SAME-S
 (7866 7760 (:REWRITE DEFAULT-CDR))
 (1428 178 (:REWRITE KEY-ORDER-LEMMA))
 (8 8 (:REWRITE VALUE-S-AUX))
 )
(S-AUX-DIFF-S-AUX
 (1658 1325 (:REWRITE DEFAULT-CAR))
 (576 459 (:REWRITE DEFAULT-CDR))
 )
(SAP-S-AUX
 (38 1 (:DEFINITION S-AUX))
 (28 7 (:REWRITE FIELD-<-TRICHOTOMY))
 (28 4 (:REWRITE FIELD-<-ASYMMETRIC))
 (28 1 (:DEFINITION SAP))
 (14 14 (:TYPE-PRESCRIPTION FIELD-<))
 (13 13 (:REWRITE DEFAULT-CAR))
 (7 7 (:REWRITE FIELD-<-TRANSITIVE))
 (7 7 (:REWRITE FIELD-<-HACK))
 (7 7 (:REWRITE DEFAULT-CDR))
 )
(CONSP-DELETE-KEY
 (91 91 (:REWRITE DEFAULT-CAR))
 (50 50 (:REWRITE DEFAULT-CDR))
 (27 27 (:TYPE-PRESCRIPTION FIELDP))
 (27 9 (:REWRITE FIELD-<-TRICHOTOMY))
 (24 3 (:REWRITE FIELD-<-ASYMMETRIC))
 (17 13 (:REWRITE FIELD-<-HACK))
 (15 9 (:REWRITE FIELD-<-TRANSITIVE))
 (6 2 (:REWRITE VALUE-NIL-SUFFICIENCY))
 (6 2 (:REWRITE KEY-ORDER-LEMMA))
 (4 4 (:REWRITE NOT-FIELD-<-X-X))
 )
(DELETE-KEY-DELETE-KEY
 (1288 1219 (:REWRITE DEFAULT-CAR))
 (691 575 (:REWRITE DEFAULT-CDR))
 (407 89 (:REWRITE CONSP-DELETE-KEY))
 (283 93 (:REWRITE FIELD-<-TRICHOTOMY))
 (261 47 (:REWRITE CAAR-DELETE-KEY))
 (168 111 (:REWRITE FIELD-<-HACK))
 (146 29 (:REWRITE VALUE-NIL-SUFFICIENCY))
 (132 93 (:REWRITE FIELD-<-TRANSITIVE))
 (120 16 (:REWRITE FIELD-<-ASYMMETRIC))
 (69 29 (:REWRITE KEY-ORDER-LEMMA))
 (51 41 (:REWRITE SAP-DELETE-KEY))
 (23 23 (:DEFINITION EQ))
 (18 18 (:REWRITE NOT-FIELD-<-X-X))
 )
(DELETE-KEY-S-AUX
 (1771 1563 (:REWRITE DEFAULT-CAR))
 (824 686 (:REWRITE DEFAULT-CDR))
 (697 367 (:REWRITE FIELD-<-HACK))
 (275 28 (:REWRITE VALUE-NIL-SUFFICIENCY))
 (173 28 (:REWRITE KEY-ORDER-LEMMA))
 (104 22 (:REWRITE CONSP-DELETE-KEY))
 (98 14 (:REWRITE CAAR-DELETE-KEY))
 (60 16 (:REWRITE FIELD-<-S-AUX))
 (27 25 (:REWRITE SAP-S-AUX))
 (10 10 (:DEFINITION EQ))
 (3 1 (:REWRITE S-AUX-PRESERVES-SAP))
 )
(DELETE-KEY-NIL
 (803 34 (:DEFINITION SAP))
 (319 319 (:REWRITE DEFAULT-CAR))
 (155 155 (:REWRITE DEFAULT-CDR))
 (105 9 (:REWRITE CAAR-DELETE-KEY))
 (97 8 (:REWRITE CONSP-DELETE-KEY))
 (95 95 (:TYPE-PRESCRIPTION FIELDP))
 (90 30 (:REWRITE FIELD-<-TRICHOTOMY))
 (81 3 (:REWRITE SAP-DELETE-KEY))
 (30 30 (:TYPE-PRESCRIPTION FIELD-<))
 (30 30 (:REWRITE FIELD-<-TRANSITIVE))
 (30 30 (:REWRITE FIELD-<-HACK))
 )
(S-DIFF-S
 (25453 24783 (:REWRITE DEFAULT-CDR))
 (5322 584 (:REWRITE VALUE-NIL-SUFFICIENCY))
 (3344 584 (:REWRITE KEY-ORDER-LEMMA))
 )
(ASSOC-EQUAL-S-AUX-DIFFERENT
 (227 174 (:REWRITE DEFAULT-CAR))
 (118 15 (:REWRITE FIELD-<-ASYMMETRIC))
 (89 31 (:REWRITE FIELD-<-TRICHOTOMY))
 (66 55 (:REWRITE DEFAULT-CDR))
 (58 58 (:TYPE-PRESCRIPTION FIELDP))
 (44 31 (:REWRITE FIELD-<-HACK))
 (35 31 (:REWRITE FIELD-<-TRANSITIVE))
 )
(ASSOC-EQUAL-DELETE-KEY-DIFFERENT
 (477 20 (:DEFINITION SAP))
 (316 11 (:REWRITE DELETE-KEY-NO-OP))
 (234 234 (:REWRITE DEFAULT-CAR))
 (113 113 (:TYPE-PRESCRIPTION SAP))
 (108 4 (:REWRITE CONSP-DELETE-KEY))
 (108 4 (:REWRITE CAAR-DELETE-KEY))
 (105 105 (:REWRITE DEFAULT-CDR))
 (60 60 (:TYPE-PRESCRIPTION FIELDP))
 (60 20 (:REWRITE FIELD-<-TRICHOTOMY))
 (20 20 (:TYPE-PRESCRIPTION FIELD-<))
 (20 20 (:REWRITE FIELD-<-TRANSITIVE))
 (20 20 (:REWRITE FIELD-<-HACK))
 )
(G-DIFF-S
 (10560 1601 (:REWRITE FIELD-<-ASYMMETRIC))
 (8138 8115 (:REWRITE DEFAULT-CDR))
 (4899 354 (:REWRITE VALUE-NIL-SUFFICIENCY))
 (2751 354 (:REWRITE KEY-ORDER-LEMMA))
 )
(UPDATE-MACRO
 (197 91 (:REWRITE DEFAULT-+-2))
 (127 91 (:REWRITE DEFAULT-+-1))
 (72 18 (:REWRITE COMMUTATIVITY-OF-+))
 (72 18 (:DEFINITION INTEGER-ABS))
 (72 9 (:DEFINITION LENGTH))
 (45 9 (:DEFINITION LEN))
 (31 23 (:REWRITE DEFAULT-<-2))
 (27 23 (:REWRITE DEFAULT-<-1))
 (18 18 (:REWRITE DEFAULT-UNARY-MINUS))
 (15 15 (:REWRITE DEFAULT-CAR))
 (9 9 (:TYPE-PRESCRIPTION LEN))
 (9 9 (:REWRITE DEFAULT-REALPART))
 (9 9 (:REWRITE DEFAULT-NUMERATOR))
 (9 9 (:REWRITE DEFAULT-IMAGPART))
 (9 9 (:REWRITE DEFAULT-DENOMINATOR))
 (9 9 (:REWRITE DEFAULT-COERCE-2))
 (9 9 (:REWRITE DEFAULT-COERCE-1))
 (1 1 (:REWRITE DEFAULT-SYMBOL-PACKAGE-NAME))
 )
