(FIND-VARIABLES*)
(FIND-ALL-VARIABLES-1-PASS)
(LEN-SET-UNION-MORE-THAN-Y
 (35 35 (:TYPE-PRESCRIPTION SET-UNION))
 (33 12 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (32 16 (:REWRITE DEFAULT-+-2))
 (26 25 (:REWRITE DEFAULT-CDR))
 (16 16 (:REWRITE DEFAULT-+-1))
 (15 15 (:REWRITE DEFAULT-CAR))
 (14 7 (:REWRITE DEFAULT-<-1))
 (12 12 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (12 12 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (12 12 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (12 12 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (12 7 (:REWRITE DEFAULT-<-2))
 )
(UNIQUEP-MEMBER-REDUCTION
 (165 165 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (165 165 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (165 165 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (165 165 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (149 145 (:REWRITE DEFAULT-CAR))
 (121 118 (:REWRITE DEFAULT-CDR))
 (67 67 (:TYPE-PRESCRIPTION SET-UNION))
 )
(UNIQUEP-UNION-REDUCTION
 (504 126 (:REWRITE <<-TRICHOTOMY))
 (336 336 (:TYPE-PRESCRIPTION <<))
 (252 42 (:REWRITE <<-ASYMMETRIC))
 (159 140 (:REWRITE DEFAULT-CAR))
 (126 126 (:REWRITE <<-TRANSITIVE))
 (111 111 (:TYPE-PRESCRIPTION SET-UNION))
 (54 54 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (54 54 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (54 54 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (54 54 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 )
(FIND-VARIABLES-IS-UNIQUE
 (372 210 (:REWRITE DEFAULT-CDR))
 (240 60 (:REWRITE <<-TRICHOTOMY))
 (170 116 (:REWRITE DEFAULT-CAR))
 (160 160 (:TYPE-PRESCRIPTION <<))
 (142 71 (:REWRITE DEFAULT-+-2))
 (120 20 (:REWRITE <<-ASYMMETRIC))
 (84 4 (:DEFINITION SET-UNION))
 (71 71 (:REWRITE DEFAULT-+-1))
 (68 34 (:TYPE-PRESCRIPTION SET-UNION))
 (60 60 (:REWRITE <<-TRANSITIVE))
 (58 58 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (58 58 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (58 58 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (58 58 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (2 2 (:LINEAR CONSP-TO-LEN-EXPANDED))
 )
(FIND-VARIABLES*-IS-UNIQUE
 (243 3 (:DEFINITION FIND-VARIABLES))
 (207 6 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (189 6 (:DEFINITION ORDEREDP))
 (168 18 (:DEFINITION MEMBERP))
 (135 3 (:DEFINITION UNIQUEP))
 (126 6 (:DEFINITION SET-UNION))
 (104 77 (:REWRITE DEFAULT-CDR))
 (87 78 (:REWRITE DEFAULT-CAR))
 (72 18 (:REWRITE <<-TRICHOTOMY))
 (57 57 (:TYPE-PRESCRIPTION FIND-VARIABLES*))
 (48 48 (:TYPE-PRESCRIPTION <<))
 (36 6 (:REWRITE <<-ASYMMETRIC))
 (33 33 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (33 33 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (33 33 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (33 33 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (33 9 (:DEFINITION LEN))
 (30 30 (:TYPE-PRESCRIPTION ORDEREDP))
 (18 18 (:TYPE-PRESCRIPTION LEN))
 (18 18 (:TYPE-PRESCRIPTION FIND-VARIABLES))
 (18 18 (:REWRITE <<-TRANSITIVE))
 (12 6 (:REWRITE DEFAULT-+-2))
 (9 9 (:TYPE-PRESCRIPTION MEMBERP))
 (6 6 (:REWRITE DEFAULT-+-1))
 )
(FIND-ALL-VARIABLES-1-PASS-IS-UNIQUE
 (363 3 (:DEFINITION FIND-VARIABLES*))
 (291 3 (:DEFINITION FIND-VARIABLES))
 (243 21 (:DEFINITION MEMBERP))
 (207 6 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (189 9 (:DEFINITION SET-UNION))
 (189 6 (:DEFINITION ORDEREDP))
 (135 3 (:DEFINITION UNIQUEP))
 (116 89 (:REWRITE DEFAULT-CDR))
 (111 102 (:REWRITE DEFAULT-CAR))
 (72 18 (:REWRITE <<-TRICHOTOMY))
 (57 57 (:TYPE-PRESCRIPTION FIND-ALL-VARIABLES-1-PASS))
 (48 48 (:TYPE-PRESCRIPTION <<))
 (39 39 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (39 39 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (39 39 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (39 39 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (36 6 (:REWRITE <<-ASYMMETRIC))
 (33 9 (:DEFINITION LEN))
 (30 30 (:TYPE-PRESCRIPTION ORDEREDP))
 (18 18 (:TYPE-PRESCRIPTION LEN))
 (18 18 (:TYPE-PRESCRIPTION FIND-VARIABLES))
 (18 18 (:REWRITE <<-TRANSITIVE))
 (15 15 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (15 15 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (15 15 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (12 12 (:TYPE-PRESCRIPTION MEMBERP))
 (12 12 (:TYPE-PRESCRIPTION FIND-VARIABLES*))
 (12 6 (:REWRITE DEFAULT-+-2))
 (6 6 (:REWRITE DEFAULT-+-1))
 )
(DEL)
(LEN-DEL-REDUCTION-1
 (43 22 (:REWRITE DEFAULT-+-2))
 (22 22 (:REWRITE DEFAULT-+-1))
 (16 16 (:REWRITE DEFAULT-CAR))
 (14 14 (:REWRITE DEFAULT-CDR))
 (8 8 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (8 8 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (8 8 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (8 8 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 )
(INDUCTION-HINT-FOR-LEN-<=)
(DEL-NOT-MEMBER-REDUCTION
 (14 14 (:REWRITE DEFAULT-CAR))
 (8 8 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (8 8 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (8 8 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (8 8 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (7 7 (:REWRITE DEFAULT-CDR))
 )
(MEMBER-DEL-REDUCTION
 (50 50 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (50 50 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (50 50 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (50 50 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (47 47 (:REWRITE DEFAULT-CAR))
 (37 37 (:REWRITE DEFAULT-CDR))
 )
(SUBSET-DEL-MEMBER
 (340 20 (:REWRITE DEL-NOT-MEMBER-REDUCTION))
 (220 10 (:DEFINITION DEL))
 (85 85 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (85 85 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (85 85 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (85 85 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (85 19 (:REWRITE SUBSET-IS-TRANSITIVE))
 (83 83 (:REWRITE DEFAULT-CAR))
 (76 19 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (66 66 (:REWRITE DEFAULT-CDR))
 (38 38 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (19 19 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 )
(UNIQUEP-DEL-REDUCTION
 (276 69 (:REWRITE <<-TRICHOTOMY))
 (184 184 (:TYPE-PRESCRIPTION <<))
 (138 23 (:REWRITE <<-ASYMMETRIC))
 (85 85 (:REWRITE DEFAULT-CAR))
 (69 69 (:REWRITE <<-TRANSITIVE))
 (36 36 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (36 36 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (36 36 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (36 36 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 )
(UNIQUEP-AND-SUBSET-IMPLIES-LEN-<=
 (288 72 (:REWRITE <<-TRICHOTOMY))
 (216 27 (:DEFINITION MEMBERP))
 (192 192 (:TYPE-PRESCRIPTION <<))
 (144 24 (:REWRITE <<-ASYMMETRIC))
 (110 5 (:DEFINITION DEL))
 (108 108 (:REWRITE DEFAULT-CAR))
 (106 10 (:REWRITE DEL-NOT-MEMBER-REDUCTION))
 (72 72 (:REWRITE <<-TRANSITIVE))
 (54 54 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (54 54 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (54 54 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (54 54 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (44 11 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (34 17 (:REWRITE DEFAULT-+-2))
 (22 22 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (17 17 (:REWRITE DEFAULT-+-1))
 (11 11 (:REWRITE SUBSET-IS-TRANSITIVE))
 (11 11 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (10 5 (:REWRITE DEFAULT-<-1))
 (9 5 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE MEMBER-DEL-REDUCTION))
 )
(SUBSET-FROM-UNION
 (136 34 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (65 65 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (52 51 (:REWRITE DEFAULT-CAR))
 (48 48 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (48 48 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (48 48 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (48 48 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (41 40 (:REWRITE DEFAULT-CDR))
 (34 34 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (11 11 (:TYPE-PRESCRIPTION SET-UNION))
 (3 3 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 )
(SUBSET-FROM-UNION-2
 (1056 264 (:REWRITE <<-TRICHOTOMY))
 (704 704 (:TYPE-PRESCRIPTION <<))
 (528 88 (:REWRITE <<-ASYMMETRIC))
 (510 506 (:REWRITE DEFAULT-CAR))
 (420 105 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (375 17 (:REWRITE SUBSET-FROM-UNION))
 (320 320 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (320 320 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (320 320 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (320 320 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (264 264 (:REWRITE <<-TRANSITIVE))
 (207 207 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (105 105 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (71 71 (:TYPE-PRESCRIPTION SET-UNION))
 (3 3 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 )
(DEL-E-TO-CONS-SUBSET
 (612 153 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (420 420 (:REWRITE DEFAULT-CAR))
 (339 339 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (339 339 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (339 339 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (339 339 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (306 306 (:REWRITE SUBSET-FROM-UNION-2))
 (304 304 (:REWRITE DEFAULT-CDR))
 (302 302 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (210 210 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (210 210 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (210 210 (:META CANCEL-ADDENDS-EQUAL-THM))
 (153 153 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (4 4 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 )
(LEN-EQUAL-TO-SET-EQUAL
 (384 96 (:REWRITE <<-TRICHOTOMY))
 (256 256 (:TYPE-PRESCRIPTION <<))
 (196 7 (:DEFINITION DEL))
 (192 32 (:REWRITE <<-ASYMMETRIC))
 (185 14 (:REWRITE DEL-NOT-MEMBER-REDUCTION))
 (161 161 (:REWRITE DEFAULT-CAR))
 (120 30 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (96 96 (:REWRITE <<-TRANSITIVE))
 (87 87 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (87 87 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (87 87 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (87 87 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (62 62 (:REWRITE SUBSET-FROM-UNION-2))
 (59 59 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (58 30 (:REWRITE |Non-numeric y in (+ x y)|))
 (57 57 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (57 57 (:META CANCEL-ADDENDS-EQUAL-THM))
 (30 30 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (30 30 (:REWRITE |Non-numeric x in (+ x y)|))
 (30 30 (:META COLLECT-ADDENDS-THM))
 (4 1 (:REWRITE MEMBER-DEL-REDUCTION))
 (1 1 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 )
(FIND-ALL-VARIABLES
 (1464 8 (:DEFINITION FIND-ALL-VARIABLES-1-PASS))
 (1224 8 (:DEFINITION FIND-VARIABLES*))
 (1115 79 (:DEFINITION MEMBERP))
 (1008 8 (:DEFINITION FIND-VARIABLES))
 (928 40 (:DEFINITION SET-UNION))
 (544 91 (:DEFINITION LEN))
 (432 16 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (431 7 (:DEFINITION SUBSET))
 (384 16 (:DEFINITION ORDEREDP))
 (369 369 (:REWRITE DEFAULT-CDR))
 (342 3 (:REWRITE SUBSET-FROM-UNION))
 (334 334 (:REWRITE DEFAULT-CAR))
 (192 48 (:REWRITE <<-TRICHOTOMY))
 (181 90 (:REWRITE |Non-numeric y in (+ x y)|))
 (150 150 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (150 150 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (150 150 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (150 150 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (137 137 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (137 137 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (137 137 (:META CANCEL-ADDENDS-EQUAL-THM))
 (128 128 (:TYPE-PRESCRIPTION <<))
 (113 14 (:REWRITE SUBSET-IS-TRANSITIVE))
 (97 90 (:REWRITE |Non-numeric x in (+ x y)|))
 (96 16 (:REWRITE <<-ASYMMETRIC))
 (93 93 (:META COLLECT-ADDENDS-THM))
 (88 52 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (80 80 (:TYPE-PRESCRIPTION ORDEREDP))
 (64 16 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (48 48 (:TYPE-PRESCRIPTION FIND-VARIABLES))
 (48 48 (:REWRITE <<-TRANSITIVE))
 (40 40 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (40 40 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (40 40 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (32 32 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (32 32 (:TYPE-PRESCRIPTION FIND-VARIABLES*))
 (16 16 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (10 5 (:REWRITE |Non-Numeric y in (< x y)|))
 (10 5 (:REWRITE |Non-Numeric x in (< x y)|))
 (8 4 (:REWRITE |Non-numeric x in (- x)|))
 (6 6 (:META CANCEL-FACTORS-GATHER-EXPONENTS-<-THM))
 (6 3 (:REWRITE DEFAULT-<-2))
 (6 3 (:REWRITE DEFAULT-<-1))
 (3 3 (:REWRITE |(+ c (+ d x))|))
 (1 1 (:REWRITE FOLD-CONSTS-IN-+))
 )
(FIND-ALL-EQUATIONS)
(REMOVE-DUPLICATE-OCCURRENCES)
(CORRESPONDING-STATE)
(CORRESPONDING-STATES)
(CONE-VARIABLES)
(CONE-OF-INFLUENCE-REDUCTION)
(FIND-ALL-VARIABLES-SUBSET-OF-VARIABLES
 (2422 60 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (1830 10 (:DEFINITION FIND-ALL-VARIABLES-1-PASS))
 (1704 130 (:DEFINITION MEMBERP))
 (1530 10 (:DEFINITION FIND-VARIABLES*))
 (1404 52 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (1292 56 (:DEFINITION SET-UNION))
 (1260 10 (:DEFINITION FIND-VARIABLES))
 (1248 52 (:DEFINITION ORDEREDP))
 (1028 167 (:DEFINITION LEN))
 (832 832 (:TYPE-PRESCRIPTION LEN))
 (695 695 (:REWRITE DEFAULT-CDR))
 (648 16 (:LINEAR LEN-SET-UNION-MORE-THAN-Y))
 (624 156 (:REWRITE <<-TRICHOTOMY))
 (550 550 (:REWRITE DEFAULT-CAR))
 (416 416 (:TYPE-PRESCRIPTION <<))
 (314 157 (:REWRITE |Non-numeric y in (+ x y)|))
 (312 52 (:REWRITE <<-ASYMMETRIC))
 (297 165 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (260 260 (:TYPE-PRESCRIPTION ORDEREDP))
 (250 250 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (250 250 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (250 250 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (250 250 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (233 233 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (233 233 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (233 233 (:META CANCEL-ADDENDS-EQUAL-THM))
 (188 47 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (160 160 (:TYPE-PRESCRIPTION FIND-ALL-VARIABLES-1-PASS))
 (157 157 (:REWRITE |Non-numeric x in (+ x y)|))
 (157 157 (:META COLLECT-ADDENDS-THM))
 (156 156 (:REWRITE <<-TRANSITIVE))
 (126 126 (:TYPE-PRESCRIPTION SET-UNION))
 (89 89 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (60 60 (:TYPE-PRESCRIPTION FIND-VARIABLES))
 (56 38 (:TYPE-PRESCRIPTION FIND-ALL-VARIABLES))
 (50 50 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (50 50 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (50 50 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (47 47 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (40 40 (:TYPE-PRESCRIPTION FIND-VARIABLES*))
 (5 5 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 )
(MEMBER-REMOVE-DUPLICATE-REDUCTION
 (125 125 (:REWRITE DEFAULT-CAR))
 (123 123 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (123 123 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (123 123 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (123 123 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (116 116 (:REWRITE DEFAULT-CDR))
 (67 67 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (67 67 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (67 67 (:META CANCEL-ADDENDS-EQUAL-THM))
 )
(UNIQUE-DUPLICATE-REDUCTION
 (168 42 (:REWRITE <<-TRICHOTOMY))
 (112 112 (:TYPE-PRESCRIPTION <<))
 (84 14 (:REWRITE <<-ASYMMETRIC))
 (55 55 (:REWRITE DEFAULT-CAR))
 (42 42 (:REWRITE <<-TRANSITIVE))
 (24 24 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (24 24 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (24 24 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (24 24 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (12 12 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (12 12 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (12 12 (:META CANCEL-ADDENDS-EQUAL-THM))
 )
(UNIQUEP-INTERSECT-REDUCTION
 (480 120 (:REWRITE <<-TRICHOTOMY))
 (320 320 (:TYPE-PRESCRIPTION <<))
 (240 40 (:REWRITE <<-ASYMMETRIC))
 (152 133 (:REWRITE DEFAULT-CAR))
 (120 120 (:REWRITE <<-TRANSITIVE))
 (50 50 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (50 50 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (50 50 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (50 50 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (25 25 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (25 25 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (25 25 (:META CANCEL-ADDENDS-EQUAL-THM))
 )
(FIND-ALL-VARIABLES-IS-UNIQUE
 (2196 78 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (2078 46 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (1962 78 (:DEFINITION ORDEREDP))
 (1830 10 (:DEFINITION FIND-ALL-VARIABLES-1-PASS))
 (1824 142 (:DEFINITION MEMBERP))
 (1530 10 (:DEFINITION FIND-VARIABLES*))
 (1292 56 (:DEFINITION SET-UNION))
 (1260 10 (:DEFINITION FIND-VARIABLES))
 (936 234 (:REWRITE <<-TRICHOTOMY))
 (902 148 (:DEFINITION LEN))
 (845 791 (:REWRITE DEFAULT-CDR))
 (707 707 (:TYPE-PRESCRIPTION LEN))
 (648 16 (:LINEAR LEN-SET-UNION-MORE-THAN-Y))
 (644 626 (:REWRITE DEFAULT-CAR))
 (624 624 (:TYPE-PRESCRIPTION <<))
 (468 78 (:REWRITE <<-ASYMMETRIC))
 (390 390 (:TYPE-PRESCRIPTION ORDEREDP))
 (276 138 (:REWRITE |Non-numeric y in (+ x y)|))
 (274 274 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (274 274 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (274 274 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (274 274 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (235 235 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (235 235 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (235 235 (:META CANCEL-ADDENDS-EQUAL-THM))
 (234 234 (:REWRITE <<-TRANSITIVE))
 (233 137 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (160 160 (:TYPE-PRESCRIPTION FIND-ALL-VARIABLES-1-PASS))
 (144 36 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (142 142 (:TYPE-PRESCRIPTION SET-UNION))
 (138 138 (:REWRITE |Non-numeric x in (+ x y)|))
 (138 138 (:META COLLECT-ADDENDS-THM))
 (102 68 (:TYPE-PRESCRIPTION FIND-ALL-VARIABLES))
 (71 71 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (60 60 (:TYPE-PRESCRIPTION FIND-VARIABLES))
 (50 50 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (50 50 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (50 50 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (40 40 (:TYPE-PRESCRIPTION FIND-VARIABLES*))
 (36 36 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (1 1 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 )
(SUBSET-REMOVE-REDUCTION
 (1762 54 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (788 114 (:DEFINITION LEN))
 (700 700 (:TYPE-PRESCRIPTION LEN))
 (287 287 (:REWRITE DEFAULT-CDR))
 (240 120 (:REWRITE |Non-numeric y in (+ x y)|))
 (213 54 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (188 157 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (174 174 (:REWRITE DEFAULT-CAR))
 (159 159 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (159 159 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (159 159 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (159 159 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (141 141 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (141 141 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (141 141 (:META CANCEL-ADDENDS-EQUAL-THM))
 (120 120 (:REWRITE |Non-numeric x in (+ x y)|))
 (120 120 (:META COLLECT-ADDENDS-THM))
 (108 108 (:REWRITE SUBSET-FROM-UNION-2))
 (106 106 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (54 54 (:REWRITE SUBSET-IS-TRANSITIVE))
 (53 53 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 )
(SUBSET-SET-INTERSECT-REDUCTION
 (5443 143 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (2327 290 (:DEFINITION LEN))
 (1825 1825 (:TYPE-PRESCRIPTION LEN))
 (953 413 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (933 913 (:REWRITE DEFAULT-CDR))
 (663 649 (:REWRITE DEFAULT-CAR))
 (608 304 (:REWRITE |Non-numeric y in (+ x y)|))
 (563 143 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (537 537 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (537 537 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (537 537 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
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(EVALUATION-EQ-SUBSET-SUBSET-REDUCTION
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(CORRESPONDING-STATE-IS-MEMBER-OF-CORRESPONDING-STATES
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(CORRESPONDING-STATES-ARE-EVALUATION-EQ-2
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(CORRESPONDING-STATES-ONLY-EVALUATIONS-P
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(INITIAL-STATES-STRICT-EVALUATION-LIST-P
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(INITIAL-CONE-OF-INFLUENCE-STATES-ARE-STRICT-EVALUATION-LIST-P
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(EQUATION-EQUAL-P)
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(FIND-EQUATIONS-FOR-NOT-MEMBER-P
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(CONS-LIST-P-SUBSET-REDUCTION
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(EQUATIONS-OF-CONE-AND-ORIG-ARE-EQUAL
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(EQUATIONS-OF-CONE-ARE-CONS-LIST-P
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(FIND-VARIABLES-VARIABLES*-REDUCTION
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(FIND-VARIABLES-1-PASS-REDUCTION
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(FIND-ALL-VARIABLES-COMPUTES-CLOSURE
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(FIND-ALL-VARIABLES-IS-EQUATION-RECORD-P
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(EQUATION-EQUAL-P-MEMBER-REDUCTION
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(CONSISTENT-EQN-RECORD-P-EXPANDED)
(EQUATION-EQUAL-P-TO-CONSISTENT
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(CONE-OF-INFLUENCE-REDUCTION-IS-CONSISTENT
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 (130 130 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (130 130 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (130 130 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (130 130 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (109 109 (:REWRITE DEFAULT-CAR))
 (106 106 (:REWRITE DEFAULT-CDR))
 (88 88 (:TYPE-PRESCRIPTION SET-INTERSECT))
 (58 58 (:TYPE-PRESCRIPTION MEMBERP))
 (54 2 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (52 52 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (52 52 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (52 52 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (52 52 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (48 2 (:DEFINITION ORDEREDP))
 (46 1 (:DEFINITION UNIQUEP))
 (38 1 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (35 35 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (35 35 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (35 35 (:META CANCEL-ADDENDS-EQUAL-THM))
 (32 32 (:TYPE-PRESCRIPTION CORRESPONDING-STATES))
 (24 6 (:REWRITE <<-TRICHOTOMY))
 (16 16 (:TYPE-PRESCRIPTION <<))
 (15 1 (:DEFINITION ONLY-EVALUATIONS-P))
 (14 2 (:DEFINITION LEN))
 (13 13 (:TYPE-PRESCRIPTION LEN))
 (12 2 (:REWRITE <<-ASYMMETRIC))
 (10 10 (:TYPE-PRESCRIPTION ORDEREDP))
 (9 3 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (9 1 (:DEFINITION EVALUATION-P))
 (8 8 (:REWRITE G-OF-NIL-IS-NIL))
 (8 1 (:DEFINITION CONS-LIST-P))
 (6 6 (:REWRITE <<-TRANSITIVE))
 (5 1 (:DEFINITION STRICT-EVALUATION-LIST-P))
 (4 4 (:REWRITE EQUATION-EQUAL-P-TO-CONSISTENT))
 (4 2 (:REWRITE |Non-numeric y in (+ x y)|))
 (4 1 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (2 2 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (2 2 (:REWRITE SUBSET-FROM-UNION-2))
 (2 2 (:REWRITE |Non-numeric x in (+ x y)|))
 (2 2 (:REWRITE EVALUATIONP-FOR-SUBSET))
 (2 2 (:REWRITE EVALUATION-P-ONLY-EVALUATIONS-REDUCTION))
 (2 2 (:REWRITE CONS-LIST-P-SUBSET-REDUCTION))
 (2 2 (:META COLLECT-ADDENDS-THM))
 (1 1 (:TYPE-PRESCRIPTION STRICT-EVALUATION-P))
 (1 1 (:TYPE-PRESCRIPTION EVALUATION-P))
 (1 1 (:REWRITE TRUTHP-LABEL-IS-A-SUBSET))
 (1 1 (:REWRITE STRICT-EVALUATION-P-NECC))
 (1 1 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (1 1 (:REWRITE CONS-LIST-P-EQUATION-EQUAL-REDUCTION))
 )
(CONE-OF-INFLUENCE-REDUCTION-IS-CIRCUIT-P
 (9 9 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (9 9 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (9 9 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (9 9 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 )
(CONE-OF-INFLUENCE-REDUCTION-PRODUCES-CIRCUIT-MODEL)
(EVALUATION-EQ-IS-REFLEXIVE
 (25 6 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (13 1 (:DEFINITION MEMBERP))
 (7 7 (:REWRITE DEFAULT-CAR))
 (6 6 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (6 6 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (6 6 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (6 6 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (5 5 (:TYPE-PRESCRIPTION MEMBERP))
 (3 3 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (2 2 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (2 2 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (2 2 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (1 1 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (1 1 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (1 1 (:META CANCEL-ADDENDS-EQUAL-THM))
 )
(EVALUATION-EQ-IS-TRANSITIVE
 (52 52 (:REWRITE DEFAULT-CAR))
 (49 49 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (49 49 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (32 32 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (23 23 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (23 23 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (23 23 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (23 23 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (21 21 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (12 12 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (12 12 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (12 12 (:META CANCEL-ADDENDS-EQUAL-THM))
 (9 9 (:REWRITE DEFAULT-CDR))
 )
(NEXT-STATE-MEMBER-IMPLIES-CONSISTENT-EQUATION
 (1386 21 (:DEFINITION PRODUCE-NEXT-STATE))
 (1050 21 (:DEFINITION APPLY-EQUATION))
 (345 343 (:REWRITE DEFAULT-CAR))
 (273 271 (:REWRITE DEFAULT-CDR))
 (252 42 (:DEFINITION LEN))
 (182 182 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (182 182 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (182 182 (:META CANCEL-ADDENDS-EQUAL-THM))
 (168 21 (:REWRITE S-SAME-G-BACK-CHAINING))
 (152 142 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (142 142 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (142 142 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (141 141 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (126 126 (:TYPE-PRESCRIPTION LEN))
 (84 42 (:REWRITE |Non-numeric y in (+ x y)|))
 (68 68 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (68 68 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (68 68 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (68 68 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (43 42 (:REWRITE EVALUATION-EQ-IS-TRANSITIVE))
 (42 42 (:REWRITE |Non-numeric x in (+ x y)|))
 (42 42 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (42 42 (:META COLLECT-ADDENDS-THM))
 )
(NEXT-STATE-IS-OK-TO-CONSISTENT-P-EQUATION
 (10 1 (:DEFINITION MEMBERP))
 (3 3 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (2 2 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (2 2 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (2 2 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (2 2 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (2 2 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (2 2 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (1 1 (:REWRITE NEXT-STATE-MEMBER-IMPLIES-CONSISTENT-EQUATION))
 (1 1 (:REWRITE NEXT-STATE-IS-OK-SUFF))
 (1 1 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (1 1 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (1 1 (:META CANCEL-ADDENDS-EQUAL-THM))
 )
(NEXT-STATE-IS-OK-P-TO-ACTUAL
 (66 1 (:DEFINITION PRODUCE-NEXT-STATE))
 (50 1 (:DEFINITION APPLY-EQUATION))
 (27 1 (:DEFINITION CONSISTENT-P-EQUATIONS))
 (15 15 (:REWRITE DEFAULT-CAR))
 (12 12 (:REWRITE DEFAULT-CDR))
 (12 2 (:DEFINITION LEN))
 (10 1 (:DEFINITION MEMBERP))
 (8 8 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (8 8 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (8 8 (:META CANCEL-ADDENDS-EQUAL-THM))
 (8 1 (:REWRITE S-SAME-G-BACK-CHAINING))
 (7 7 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (7 7 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (7 7 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (7 7 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (6 6 (:TYPE-PRESCRIPTION LEN))
 (6 1 (:REWRITE NEXT-STATE-IS-OK-TO-CONSISTENT-P-EQUATION))
 (4 2 (:REWRITE |Non-numeric y in (+ x y)|))
 (2 2 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (2 2 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (2 2 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (2 2 (:REWRITE |Non-numeric x in (+ x y)|))
 (2 2 (:REWRITE NEXT-STATE-MEMBER-IMPLIES-CONSISTENT-EQUATION))
 (2 2 (:REWRITE NEXT-STATE-IS-OK-SUFF))
 (2 2 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (2 2 (:REWRITE EVALUATION-EQ-IS-TRANSITIVE))
 (2 2 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (2 2 (:META COLLECT-ADDENDS-THM))
 (1 1 (:TYPE-PRESCRIPTION MEMBERP))
 )
(THUS-R-IS-EVALUATION-EQ-TO-S
 (264 4 (:DEFINITION PRODUCE-NEXT-STATE))
 (200 4 (:DEFINITION APPLY-EQUATION))
 (173 4 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (96 3 (:DEFINITION EVALUATION-EQ))
 (84 14 (:DEFINITION LEN))
 (67 19 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (63 63 (:TYPE-PRESCRIPTION LEN))
 (58 58 (:REWRITE DEFAULT-CDR))
 (57 57 (:REWRITE DEFAULT-CAR))
 (55 1 (:DEFINITION SUBSET))
 (54 2 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (53 1 (:DEFINITION UNIQUEP))
 (51 5 (:DEFINITION MEMBERP))
 (48 2 (:DEFINITION ORDEREDP))
 (34 34 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (34 34 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (34 34 (:META CANCEL-ADDENDS-EQUAL-THM))
 (32 4 (:REWRITE S-SAME-G-BACK-CHAINING))
 (28 14 (:REWRITE |Non-numeric y in (+ x y)|))
 (24 6 (:REWRITE <<-TRICHOTOMY))
 (19 19 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (19 19 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (18 18 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (17 17 (:TYPE-PRESCRIPTION MEMBERP))
 (16 16 (:TYPE-PRESCRIPTION <<))
 (16 4 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (14 14 (:REWRITE |Non-numeric x in (+ x y)|))
 (14 14 (:META COLLECT-ADDENDS-THM))
 (12 2 (:REWRITE <<-ASYMMETRIC))
 (10 10 (:TYPE-PRESCRIPTION ORDEREDP))
 (9 9 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (9 9 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (9 9 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (9 9 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (9 9 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (8 8 (:REWRITE SUBSET-FROM-UNION-2))
 (7 7 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (6 6 (:REWRITE <<-TRANSITIVE))
 (5 5 (:TYPE-PRESCRIPTION UNIQUEP))
 (4 4 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (2 2 (:REWRITE NEXT-STATE-MEMBER-IMPLIES-CONSISTENT-EQUATION))
 (2 2 (:REWRITE NEXT-STATE-IS-OK-SUFF))
 (1 1 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 )
(NEXT-STATE-IS-OK-FROM-CONSISTENT-EQN
 (66 1 (:DEFINITION PRODUCE-NEXT-STATE))
 (50 1 (:DEFINITION APPLY-EQUATION))
 (27 1 (:DEFINITION CONSISTENT-P-EQUATIONS))
 (18 1 (:DEFINITION EVALUATION-EQ))
 (15 15 (:REWRITE DEFAULT-CAR))
 (12 12 (:REWRITE DEFAULT-CDR))
 (12 2 (:DEFINITION LEN))
 (10 1 (:DEFINITION MEMBERP))
 (8 8 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (8 8 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (8 8 (:META CANCEL-ADDENDS-EQUAL-THM))
 (8 1 (:REWRITE S-SAME-G-BACK-CHAINING))
 (7 7 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (7 7 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (7 7 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (7 7 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (6 6 (:TYPE-PRESCRIPTION LEN))
 (4 2 (:REWRITE |Non-numeric y in (+ x y)|))
 (2 2 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (2 2 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (2 2 (:REWRITE THUS-R-IS-EVALUATION-EQ-TO-S))
 (2 2 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (2 2 (:REWRITE |Non-numeric x in (+ x y)|))
 (2 2 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (2 2 (:REWRITE EVALUATION-EQ-IS-TRANSITIVE))
 (2 2 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (2 2 (:META COLLECT-ADDENDS-THM))
 (1 1 (:TYPE-PRESCRIPTION MEMBERP))
 (1 1 (:REWRITE NEXT-STATE-MEMBER-IMPLIES-CONSISTENT-EQUATION))
 )
(MEMBERP-OF-NEXT-STATE-FROM-CONSISTENT-EQUATION
 (40 35 (:REWRITE DEFAULT-CAR))
 (25 25 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (25 25 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (25 25 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (25 25 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (20 20 (:REWRITE NEXT-STATE-IS-OK-FROM-CONSISTENT-EQN))
 (14 14 (:REWRITE NEXT-STATE-IS-OK-SUFF))
 (14 14 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (14 14 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (14 14 (:META CANCEL-ADDENDS-EQUAL-THM))
 (13 12 (:REWRITE DEFAULT-CDR))
 )
(MEMBERP-NOT-USING-NEXT-STATES
 (198 3 (:DEFINITION PRODUCE-NEXT-STATE))
 (193 1 (:DEFINITION CREATE-NEXT-STATES-OF-P))
 (150 3 (:DEFINITION APPLY-EQUATION))
 (93 1 (:REWRITE NEXT-STATE-IS-OK-SUFF))
 (60 3 (:DEFINITION EVALUATION-EQ))
 (42 42 (:REWRITE DEFAULT-CAR))
 (36 6 (:DEFINITION LEN))
 (35 35 (:REWRITE DEFAULT-CDR))
 (27 1 (:DEFINITION CONSISTENT-P-EQUATIONS))
 (24 3 (:REWRITE S-SAME-G-BACK-CHAINING))
 (23 23 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (23 23 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (23 23 (:META CANCEL-ADDENDS-EQUAL-THM))
 (20 2 (:DEFINITION MEMBERP))
 (18 18 (:TYPE-PRESCRIPTION LEN))
 (17 17 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (17 17 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (17 17 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (17 17 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (12 6 (:REWRITE |Non-numeric y in (+ x y)|))
 (6 6 (:REWRITE THUS-R-IS-EVALUATION-EQ-TO-S))
 (6 6 (:REWRITE |Non-numeric x in (+ x y)|))
 (6 6 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (6 6 (:REWRITE EVALUATION-EQ-IS-TRANSITIVE))
 (6 6 (:META COLLECT-ADDENDS-THM))
 (4 4 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (4 4 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (4 4 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (4 4 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (1 1 (:REWRITE NEXT-STATE-MEMBER-IMPLIES-CONSISTENT-EQUATION))
 )
(MEMBER-OF-NEXT-STATES-FROM-ALL-EVALUATIONS-P
 (594 9 (:DEFINITION PRODUCE-NEXT-STATE))
 (582 25 (:DEFINITION EVALUATION-EQ))
 (450 9 (:DEFINITION APPLY-EQUATION))
 (434 7 (:DEFINITION EVALUATION-EQ-MEMBER))
 (386 2 (:DEFINITION CREATE-NEXT-STATES-OF-P))
 (298 2 (:REWRITE MEMBERP-OF-NEXT-STATE-FROM-CONSISTENT-EQUATION))
 (280 4 (:REWRITE NEXT-STATE-IS-OK-SUFF))
 (280 4 (:REWRITE NEXT-STATE-IS-OK-FROM-CONSISTENT-EQN))
 (250 4 (:REWRITE EVALUATION-EQ-MEMBERP-OF-CORRESPONDING-STATES-2))
 (195 195 (:REWRITE DEFAULT-CAR))
 (192 92 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (162 6 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (159 3 (:DEFINITION UNIQUEP))
 (151 151 (:REWRITE DEFAULT-CDR))
 (144 6 (:DEFINITION ORDEREDP))
 (108 18 (:DEFINITION LEN))
 (92 92 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (92 92 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (86 86 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (86 86 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (86 86 (:META CANCEL-ADDENDS-EQUAL-THM))
 (82 82 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (72 18 (:REWRITE <<-TRICHOTOMY))
 (72 9 (:REWRITE S-SAME-G-BACK-CHAINING))
 (54 54 (:TYPE-PRESCRIPTION LEN))
 (52 52 (:REWRITE THUS-R-IS-EVALUATION-EQ-TO-S))
 (51 51 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (48 48 (:TYPE-PRESCRIPTION <<))
 (36 18 (:REWRITE |Non-numeric y in (+ x y)|))
 (36 6 (:REWRITE <<-ASYMMETRIC))
 (30 30 (:TYPE-PRESCRIPTION ORDEREDP))
 (27 27 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (27 27 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (27 27 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (27 27 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (19 1 (:DEFINITION EVALUATION-P))
 (18 18 (:REWRITE |Non-numeric x in (+ x y)|))
 (18 18 (:REWRITE <<-TRANSITIVE))
 (18 18 (:META COLLECT-ADDENDS-THM))
 (15 15 (:TYPE-PRESCRIPTION UNIQUEP))
 (6 6 (:TYPE-PRESCRIPTION NEXT-STATE-IS-OK))
 (4 4 (:REWRITE NEXT-STATE-MEMBER-IMPLIES-CONSISTENT-EQUATION))
 (4 4 (:REWRITE EVALUATION-EQ-MEMBER-SUBSET-REDUCTION))
 (2 2 (:REWRITE EVALUATIONP-FOR-SUBSET))
 (2 2 (:REWRITE EVALUATION-P-ONLY-EVALUATIONS-REDUCTION))
 )
(EVALUATION-EQ-AND-MEMBERP-TO-EVALUATION-EQ-MEMBERP
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 (486 18 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (477 9 (:DEFINITION UNIQUEP))
 (432 18 (:DEFINITION ORDEREDP))
 (252 9 (:REWRITE ALL-EVALUATIONS-CONSIDERS-AN-EVALUATION-A-MEMBER))
 (216 54 (:REWRITE <<-TRICHOTOMY))
 (207 9 (:DEFINITION EVALUATION-P))
 (144 144 (:TYPE-PRESCRIPTION <<))
 (135 135 (:REWRITE DEFAULT-CAR))
 (114 114 (:REWRITE DEFAULT-CDR))
 (108 18 (:REWRITE <<-ASYMMETRIC))
 (90 90 (:TYPE-PRESCRIPTION ORDEREDP))
 (65 65 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (65 65 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (54 54 (:REWRITE <<-TRANSITIVE))
 (50 50 (:REWRITE THUS-R-IS-EVALUATION-EQ-TO-S))
 (49 49 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (45 45 (:TYPE-PRESCRIPTION UNIQUEP))
 (45 45 (:TYPE-PRESCRIPTION EVALUATION-P))
 (42 42 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (42 42 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (42 42 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (42 42 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (40 40 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (36 36 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (36 36 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (36 36 (:META CANCEL-ADDENDS-EQUAL-THM))
 (18 18 (:REWRITE EVALUATIONP-FOR-SUBSET))
 (18 18 (:REWRITE EVALUATION-P-ONLY-EVALUATIONS-REDUCTION))
 (9 9 (:TYPE-PRESCRIPTION BOOLEANP))
 (9 9 (:REWRITE EVALUATION-EQ-SUBSET-TO-MEMBER))
 (9 9 (:REWRITE EVALUATION-EQ-MEMBER-SUBSET-REDUCTION))
 )
(EVALUATION-EQ-MEMBERP-FROM-ALL-EVALUATIONS-P
 (386 2 (:DEFINITION CREATE-NEXT-STATES-OF-P))
 (264 4 (:DEFINITION PRODUCE-NEXT-STATE))
 (252 11 (:DEFINITION EVALUATION-EQ))
 (200 4 (:DEFINITION APPLY-EQUATION))
 (186 2 (:REWRITE NEXT-STATE-IS-OK-SUFF))
 (186 2 (:REWRITE NEXT-STATE-IS-OK-FROM-CONSISTENT-EQN))
 (167 3 (:REWRITE EVALUATION-EQ-MEMBERP-OF-CORRESPONDING-STATES-2))
 (124 2 (:DEFINITION EVALUATION-EQ-MEMBER))
 (119 23 (:REWRITE EVALUATION-EQ-IS-TRANSITIVE))
 (108 4 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (106 2 (:DEFINITION UNIQUEP))
 (96 4 (:DEFINITION ORDEREDP))
 (86 86 (:REWRITE DEFAULT-CAR))
 (72 72 (:REWRITE DEFAULT-CDR))
 (67 37 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (48 12 (:REWRITE <<-TRICHOTOMY))
 (48 8 (:DEFINITION LEN))
 (37 37 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (37 37 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (37 37 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (37 37 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (37 37 (:META CANCEL-ADDENDS-EQUAL-THM))
 (34 34 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (32 32 (:TYPE-PRESCRIPTION <<))
 (32 5 (:DEFINITION MEMBERP))
 (32 4 (:REWRITE S-SAME-G-BACK-CHAINING))
 (24 24 (:TYPE-PRESCRIPTION LEN))
 (24 4 (:REWRITE <<-ASYMMETRIC))
 (23 23 (:REWRITE THUS-R-IS-EVALUATION-EQ-TO-S))
 (23 23 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (20 20 (:TYPE-PRESCRIPTION ORDEREDP))
 (16 8 (:REWRITE |Non-numeric y in (+ x y)|))
 (12 12 (:REWRITE <<-TRANSITIVE))
 (10 10 (:TYPE-PRESCRIPTION UNIQUEP))
 (8 8 (:REWRITE |Non-numeric x in (+ x y)|))
 (8 8 (:META COLLECT-ADDENDS-THM))
 (7 7 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (7 7 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (7 7 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (7 7 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (3 3 (:REWRITE EVALUATION-EQ-MEMBER-SUBSET-REDUCTION))
 (2 2 (:TYPE-PRESCRIPTION NEXT-STATE-IS-OK))
 (2 2 (:REWRITE NEXT-STATE-MEMBER-IMPLIES-CONSISTENT-EQUATION))
 (2 2 (:REWRITE EVALUATION-EQ-SUBSET-TO-MEMBER))
 )
(EVALUATION-EQ-AND-MEMBERP-TO-MEMBERP
 (1411 17 (:REWRITE EVALUATION-EQ-MEMBERP-OF-CORRESPONDING-STATES-2))
 (918 34 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (901 17 (:DEFINITION UNIQUEP))
 (816 34 (:DEFINITION ORDEREDP))
 (426 17 (:REWRITE ALL-EVALUATIONS-CONSIDERS-AN-EVALUATION-A-MEMBER))
 (408 102 (:REWRITE <<-TRICHOTOMY))
 (341 17 (:DEFINITION EVALUATION-P))
 (272 272 (:TYPE-PRESCRIPTION <<))
 (208 208 (:REWRITE DEFAULT-CAR))
 (204 34 (:REWRITE <<-ASYMMETRIC))
 (201 201 (:REWRITE DEFAULT-CDR))
 (170 170 (:TYPE-PRESCRIPTION ORDEREDP))
 (102 102 (:REWRITE <<-TRANSITIVE))
 (90 90 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (90 90 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (85 85 (:TYPE-PRESCRIPTION UNIQUEP))
 (85 85 (:TYPE-PRESCRIPTION EVALUATION-P))
 (71 71 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (59 59 (:REWRITE THUS-R-IS-EVALUATION-EQ-TO-S))
 (54 54 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (53 53 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (53 53 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (53 53 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (53 53 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (44 44 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (44 44 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (44 44 (:META CANCEL-ADDENDS-EQUAL-THM))
 (34 34 (:REWRITE EVALUATIONP-FOR-SUBSET))
 (34 34 (:REWRITE EVALUATION-P-ONLY-EVALUATIONS-REDUCTION))
 (17 17 (:TYPE-PRESCRIPTION BOOLEANP))
 (17 17 (:REWRITE EVALUATION-EQ-SUBSET-TO-MEMBER))
 (17 17 (:REWRITE EVALUATION-EQ-MEMBER-SUBSET-REDUCTION))
 (17 17 (:REWRITE EVALUATION-EQ-AND-MEMBERP-TO-EVALUATION-EQ-MEMBERP))
 )
(NEXT-STATE-OF-ORIG-TO-EVALUATION-EQ-MEMBER-P
 (330 5 (:DEFINITION PRODUCE-NEXT-STATE))
 (250 5 (:DEFINITION APPLY-EQUATION))
 (229 9 (:DEFINITION EVALUATION-EQ))
 (222 2 (:DEFINITION CREATE-NEXT-STATES-OF-P))
 (173 4 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (144 18 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (117 3 (:REWRITE NEXT-STATE-IS-OK-FROM-CONSISTENT-EQN))
 (107 39 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (103 11 (:DEFINITION MEMBERP))
 (96 16 (:DEFINITION LEN))
 (92 92 (:REWRITE DEFAULT-CAR))
 (92 2 (:REWRITE NEXT-STATE-IS-OK-SUFF))
 (83 83 (:REWRITE DEFAULT-CDR))
 (69 69 (:TYPE-PRESCRIPTION LEN))
 (55 1 (:DEFINITION SUBSET))
 (54 2 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (53 1 (:DEFINITION UNIQUEP))
 (50 50 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (50 50 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (50 50 (:META CANCEL-ADDENDS-EQUAL-THM))
 (48 2 (:DEFINITION ORDEREDP))
 (40 5 (:REWRITE S-SAME-G-BACK-CHAINING))
 (39 39 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (39 39 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (36 36 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (32 16 (:REWRITE |Non-numeric y in (+ x y)|))
 (27 1 (:DEFINITION CONSISTENT-P-EQUATIONS))
 (24 6 (:REWRITE <<-TRICHOTOMY))
 (20 1 (:REWRITE MEMBERP-OF-NEXT-STATE-FROM-CONSISTENT-EQUATION))
 (20 1 (:REWRITE MEMBERP-NOT-USING-NEXT-STATES))
 (19 19 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (19 19 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (19 19 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (19 19 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (19 1 (:DEFINITION EVALUATION-P))
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 (16 16 (:REWRITE |Non-numeric x in (+ x y)|))
 (16 16 (:META COLLECT-ADDENDS-THM))
 (16 4 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (12 2 (:REWRITE <<-ASYMMETRIC))
 (10 10 (:TYPE-PRESCRIPTION ORDEREDP))
 (9 9 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (8 8 (:REWRITE SUBSET-FROM-UNION-2))
 (7 7 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (6 6 (:REWRITE <<-TRANSITIVE))
 (5 5 (:TYPE-PRESCRIPTION UNIQUEP))
 (4 4 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (2 2 (:TYPE-PRESCRIPTION CREATE-NEXT-STATES-OF-P))
 (2 2 (:REWRITE EVALUATIONP-FOR-SUBSET))
 (2 2 (:REWRITE EVALUATION-P-ONLY-EVALUATIONS-REDUCTION))
 (1 1 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 )
(CREATE-CORRESPONDING-EQUATION)
(EQUATION-EQUAL-TO-SET-REDUCTION
 (40 5 (:REWRITE S-SAME-G-BACK-CHAINING))
 (29 29 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (29 29 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (29 29 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (29 29 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (28 28 (:REWRITE DEFAULT-CAR))
 (23 23 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (23 23 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (23 23 (:META CANCEL-ADDENDS-EQUAL-THM))
 (8 8 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (8 8 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (8 8 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (8 8 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (6 6 (:REWRITE DEFAULT-CDR))
 )
(CREATE-CORRESPONDING-EQUATION-IS-EQUATION-EQUAL
 (519 15 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (253 38 (:DEFINITION LEN))
 (231 25 (:REWRITE S-SAME-G-BACK-CHAINING))
 (206 206 (:TYPE-PRESCRIPTION LEN))
 (182 182 (:REWRITE DEFAULT-CAR))
 (156 39 (:REWRITE <<-TRICHOTOMY))
 (104 104 (:TYPE-PRESCRIPTION <<))
 (86 43 (:REWRITE |Non-numeric y in (+ x y)|))
 (82 82 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (82 82 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (82 82 (:META CANCEL-ADDENDS-EQUAL-THM))
 (78 13 (:REWRITE <<-ASYMMETRIC))
 (76 76 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (76 76 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (76 76 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (76 76 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (71 71 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (71 71 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (71 71 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (60 15 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (57 43 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (43 43 (:REWRITE |Non-numeric x in (+ x y)|))
 (43 43 (:META COLLECT-ADDENDS-THM))
 (39 39 (:REWRITE <<-TRANSITIVE))
 (30 30 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (30 30 (:REWRITE SUBSET-FROM-UNION-2))
 (15 15 (:REWRITE SUBSET-IS-TRANSITIVE))
 (15 15 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (3 3 (:REWRITE G-DIFF-S))
 )
(CONS-CONSISTENT-EQN
 (73 10 (:REWRITE S-SAME-G-BACK-CHAINING))
 (52 52 (:REWRITE DEFAULT-CAR))
 (45 45 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (45 45 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (45 45 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (45 45 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (40 40 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (40 40 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (40 40 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (40 40 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (36 36 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (36 36 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (36 36 (:META CANCEL-ADDENDS-EQUAL-THM))
 (27 27 (:REWRITE DEFAULT-CDR))
 )
(CONSISTENT-P-EQUATION-MEMBERP-REDUCTION
 (22 22 (:REWRITE DEFAULT-CAR))
 (20 20 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (20 20 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (20 20 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (20 20 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (14 14 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (14 14 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (14 14 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (14 14 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (11 11 (:REWRITE DEFAULT-CDR))
 (11 11 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (11 11 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (11 11 (:META CANCEL-ADDENDS-EQUAL-THM))
 )
(CONSISTENT-SET-NOT-MEMBER
 (40 5 (:REWRITE S-SAME-G-BACK-CHAINING))
 (39 39 (:REWRITE DEFAULT-CAR))
 (30 30 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (30 30 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (30 30 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (30 30 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (29 29 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (29 29 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (29 29 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (29 29 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (27 27 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (27 27 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (27 27 (:META CANCEL-ADDENDS-EQUAL-THM))
 (17 17 (:REWRITE DEFAULT-CDR))
 (11 11 (:REWRITE CONSISTENT-P-EQUATION-MEMBERP-REDUCTION))
 )
(EQUATION-EQUAL-P-TO-CONSISTENT-EQUATION
 (52 52 (:REWRITE DEFAULT-CAR))
 (32 32 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (32 32 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (32 32 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (28 28 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (28 28 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (28 28 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (28 28 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (14 14 (:REWRITE DEFAULT-CDR))
 (13 13 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (13 13 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (13 13 (:META CANCEL-ADDENDS-EQUAL-THM))
 )
(CONSISTENT-P-EQUATIONS-TO-CONSISTENT-P-EQUATIONS
 (576 144 (:REWRITE <<-TRICHOTOMY))
 (445 445 (:REWRITE DEFAULT-CAR))
 (420 73 (:REWRITE EQUATION-EQUAL-P-TO-CONSISTENT-EQUATION))
 (384 384 (:TYPE-PRESCRIPTION <<))
 (288 48 (:REWRITE <<-ASYMMETRIC))
 (207 6 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (201 26 (:REWRITE S-SAME-G-BACK-CHAINING))
 (186 186 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (186 186 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (186 186 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (186 186 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (186 186 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (186 186 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (186 186 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (162 2 (:DEFINITION SUBSET))
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 (144 144 (:REWRITE <<-TRANSITIVE))
 (132 132 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (132 132 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (122 17 (:DEFINITION LEN))
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 (44 22 (:REWRITE |Non-numeric y in (+ x y)|))
 (33 9 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (24 6 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (22 22 (:REWRITE |Non-numeric x in (+ x y)|))
 (22 22 (:META COLLECT-ADDENDS-THM))
 (12 12 (:REWRITE SUBSET-FROM-UNION-2))
 (10 10 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (6 6 (:REWRITE SUBSET-IS-TRANSITIVE))
 (6 6 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (2 2 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 (2 2 (:REWRITE G-DIFF-S))
 (2 2 (:REWRITE COLLECT-PLUS-1C))
 (1 1 (:REWRITE UN-HIDE-PLUS))
 )
(CLOSED-EQN-RECORD-P)
(CLOSED-EQN-RECORD-P-FROM-CONSISTENT-EQUATION-RECORD-P
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 (1000 66 (:DEFINITION MEMBERP))
 (707 21 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (428 76 (:DEFINITION LEN))
 (378 14 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (336 336 (:TYPE-PRESCRIPTION LEN))
 (336 14 (:DEFINITION ORDEREDP))
 (322 7 (:DEFINITION UNIQUEP))
 (272 272 (:REWRITE DEFAULT-CDR))
 (256 256 (:REWRITE DEFAULT-CAR))
 (240 10 (:DEFINITION SET-UNION))
 (168 42 (:REWRITE <<-TRICHOTOMY))
 (137 137 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (137 137 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (137 137 (:META CANCEL-ADDENDS-EQUAL-THM))
 (136 68 (:REWRITE |Non-numeric y in (+ x y)|))
 (122 122 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (122 122 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (122 122 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (122 122 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (112 112 (:TYPE-PRESCRIPTION <<))
 (104 61 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (100 100 (:TYPE-PRESCRIPTION FIND-VARIABLES))
 (84 21 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (84 14 (:REWRITE <<-ASYMMETRIC))
 (70 70 (:TYPE-PRESCRIPTION ORDEREDP))
 (68 68 (:REWRITE |Non-numeric x in (+ x y)|))
 (68 68 (:META COLLECT-ADDENDS-THM))
 (62 62 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (62 62 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (62 62 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (62 62 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (42 42 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (42 42 (:REWRITE SUBSET-FROM-UNION-2))
 (42 42 (:REWRITE <<-TRANSITIVE))
 (21 21 (:REWRITE SUBSET-IS-TRANSITIVE))
 (21 21 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (8 8 (:REWRITE EQUATION-EQUAL-P-TO-CONSISTENT-EQUATION))
 (7 7 (:REWRITE EQUATION-EQUAL-P-TO-CONSISTENT))
 (6 6 (:REWRITE CONSISTENT-P-EQUATION-MEMBERP-REDUCTION))
 )
(CLOSED-EQN-RECORD-P-TRUE-CONCRETIZED
 (54 2 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (48 2 (:DEFINITION ORDEREDP))
 (46 1 (:DEFINITION UNIQUEP))
 (29 1 (:DEFINITION CONSISTENT-P-EQUATIONS))
 (24 6 (:REWRITE <<-TRICHOTOMY))
 (20 2 (:DEFINITION MEMBERP))
 (16 16 (:TYPE-PRESCRIPTION <<))
 (12 2 (:REWRITE <<-ASYMMETRIC))
 (11 11 (:REWRITE DEFAULT-CDR))
 (10 10 (:TYPE-PRESCRIPTION ORDEREDP))
 (9 9 (:REWRITE DEFAULT-CAR))
 (6 6 (:REWRITE <<-TRANSITIVE))
 (4 4 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (4 4 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (4 4 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (4 4 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (4 1 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (2 2 (:TYPE-PRESCRIPTION MEMBERP))
 (2 2 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (2 2 (:REWRITE SUBSET-FROM-UNION-2))
 (2 2 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (2 2 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (2 2 (:REWRITE EQUATION-EQUAL-P-TO-CONSISTENT-EQUATION))
 (2 2 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (2 2 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (2 2 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (2 2 (:META CANCEL-ADDENDS-EQUAL-THM))
 (2 1 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (1 1 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (1 1 (:REWRITE SUBSET-IS-TRANSITIVE))
 (1 1 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (1 1 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 (1 1 (:REWRITE EQUATION-EQUAL-P-TO-CONSISTENT))
 (1 1 (:REWRITE CONSISTENT-P-EQUATION-MEMBERP-REDUCTION))
 )
(APPLY-EQUATION-PRODUCES-EQUAL
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 (4419 4419 (:REWRITE DEFAULT-CDR))
 (3461 3461 (:REWRITE DEFAULT-CAR))
 (2348 1312 (:REWRITE |Non-numeric y in (+ x y)|))
 (2247 2247 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (2247 2247 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (1596 114 (:DEFINITION EVALUATION-P))
 (1319 1319 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (1319 1319 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (1319 1319 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (1319 1319 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (1312 1312 (:REWRITE |Non-numeric x in (+ x y)|))
 (1312 1312 (:META COLLECT-ADDENDS-THM))
 (1134 63 (:DEFINITION EVALUATION-EQ))
 (972 36 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (954 18 (:DEFINITION UNIQUEP))
 (864 36 (:DEFINITION ORDEREDP))
 (849 219 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (744 16 (:LINEAR LEN-SET-UNION-MORE-THAN-Y))
 (464 8 (:REWRITE SUBSET-FROM-UNION))
 (453 453 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (453 453 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (432 108 (:REWRITE <<-TRICHOTOMY))
 (402 402 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (395 395 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (304 152 (:TYPE-PRESCRIPTION SET-UNION))
 (288 288 (:TYPE-PRESCRIPTION <<))
 (246 246 (:REWRITE EVALUATION-P-ONLY-EVALUATIONS-REDUCTION))
 (219 219 (:REWRITE SUBSET-IS-TRANSITIVE))
 (216 36 (:REWRITE <<-ASYMMETRIC))
 (210 210 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (180 180 (:TYPE-PRESCRIPTION ORDEREDP))
 (144 144 (:REWRITE THUS-R-IS-EVALUATION-EQ-TO-S))
 (126 126 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (108 108 (:REWRITE <<-TRANSITIVE))
 (92 92 (:REWRITE CONSISTENT-EQN-RECORD-P-EXPANDED))
 (18 18 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 )
(PRODUCE-NEXT-STATE-NOT-MEMBERP-VARS-REDUCTION
 (150 3 (:DEFINITION APPLY-EQUATION))
 (36 6 (:DEFINITION LEN))
 (34 34 (:REWRITE DEFAULT-CAR))
 (28 28 (:REWRITE DEFAULT-CDR))
 (25 25 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (25 25 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (25 25 (:META CANCEL-ADDENDS-EQUAL-THM))
 (24 3 (:REWRITE S-SAME-G-BACK-CHAINING))
 (20 20 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (20 20 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (20 20 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (20 20 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (18 18 (:TYPE-PRESCRIPTION LEN))
 (12 6 (:REWRITE |Non-numeric y in (+ x y)|))
 (7 7 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (7 7 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (7 7 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (7 7 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (6 6 (:REWRITE |Non-numeric x in (+ x y)|))
 (6 6 (:META COLLECT-ADDENDS-THM))
 (3 3 (:REWRITE APPLY-EQUATION-PRODUCES-EQUAL))
 )
(PRODUCE-NEXT-STATE-VARS-REDUCTION
 (1950 39 (:DEFINITION APPLY-EQUATION))
 (1126 26 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (1058 36 (:DEFINITION ORDEREDP))
 (553 553 (:REWRITE DEFAULT-CDR))
 (552 138 (:REWRITE <<-TRICHOTOMY))
 (523 523 (:REWRITE DEFAULT-CAR))
 (468 78 (:DEFINITION LEN))
 (368 368 (:TYPE-PRESCRIPTION <<))
 (305 305 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (305 305 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (305 305 (:META CANCEL-ADDENDS-EQUAL-THM))
 (276 46 (:REWRITE <<-ASYMMETRIC))
 (234 234 (:TYPE-PRESCRIPTION LEN))
 (156 78 (:REWRITE |Non-numeric y in (+ x y)|))
 (150 150 (:TYPE-PRESCRIPTION ORDEREDP))
 (138 138 (:REWRITE <<-TRANSITIVE))
 (126 126 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (126 126 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (126 126 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (126 126 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (114 114 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (114 114 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (114 114 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (114 114 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (78 78 (:REWRITE |Non-numeric x in (+ x y)|))
 (78 78 (:META COLLECT-ADDENDS-THM))
 (39 39 (:REWRITE APPLY-EQUATION-PRODUCES-EQUAL))
 )
(EVALUATION-EQ-SET-REDUCTION
 (176 62 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (160 20 (:REWRITE S-SAME-G-BACK-CHAINING))
 (62 62 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (62 62 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (62 62 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (51 51 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (51 51 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (51 51 (:META CANCEL-ADDENDS-EQUAL-THM))
 (46 46 (:REWRITE DEFAULT-CAR))
 (20 20 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (20 20 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (20 20 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (20 20 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (16 16 (:REWRITE THUS-R-IS-EVALUATION-EQ-TO-S))
 (16 16 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (16 16 (:REWRITE EVALUATION-EQ-IS-TRANSITIVE))
 (12 12 (:REWRITE DEFAULT-CDR))
 )
(PRODUCE-NEXT-STATE-IS-EVALUATION-EQ
 (882 7 (:DEFINITION FIND-VARIABLES))
 (855 28 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (833 14 (:DEFINITION APPLY-EQUATION))
 (623 104 (:DEFINITION LEN))
 (540 135 (:REWRITE <<-TRICHOTOMY))
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 (8 8 (:REWRITE CONSISTENT-EQN-RECORD-P-EXPANDED))
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 (2 2 (:REWRITE G-DIFF-S))
 )
(PRODUCE-NEXT-STATE-IS-EVALUATION-EQ-CONCRETIZED
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 (242 9 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (188 34 (:DEFINITION LEN))
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 (96 4 (:DEFINITION SET-UNION))
 (96 2 (:REWRITE S-SAME-G-BACK-CHAINING))
 (72 18 (:LINEAR CONSP-TO-LEN-EXPANDED))
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 (67 67 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (67 67 (:META CANCEL-ADDENDS-EQUAL-THM))
 (60 31 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (60 30 (:REWRITE |Non-numeric y in (+ x y)|))
 (54 54 (:TYPE-PRESCRIPTION MEMBERP))
 (54 2 (:REWRITE ORDERED-IMPLIES-UNIQUE))
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 (53 53 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (53 53 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (53 53 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (53 33 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
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 (48 2 (:DEFINITION ORDEREDP))
 (46 1 (:DEFINITION UNIQUEP))
 (40 2 (:REWRITE PRODUCE-NEXT-STATE-VARS-REDUCTION))
 (40 2 (:REWRITE PRODUCE-NEXT-STATE-NOT-MEMBERP-VARS-REDUCTION))
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 (15 1 (:DEFINITION EQUATION-EQUAL-P))
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 (12 2 (:REWRITE <<-ASYMMETRIC))
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 (2 2 (:REWRITE EVALUATION-EQ-IS-TRANSITIVE))
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 (1 1 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 (1 1 (:REWRITE EQUATION-EQUAL-P-TO-CONSISTENT))
 (1 1 (:REWRITE CONSISTENT-P-EQUATION-MEMBERP-REDUCTION))
 )
(PRODUCE-NEXT-STATE-EVALUATION-EQ-REDUCTION
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 (2089 60 (:REWRITE S-SAME-G-BACK-CHAINING))
 (2065 118 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (1486 246 (:DEFINITION LEN))
 (1471 1471 (:REWRITE DEFAULT-CAR))
 (1400 76 (:REWRITE PRODUCE-NEXT-STATE-NOT-MEMBERP-VARS-REDUCTION))
 (969 118 (:REWRITE EVALUATION-EQ-IS-TRANSITIVE))
 (890 890 (:TYPE-PRESCRIPTION LEN))
 (888 222 (:REWRITE <<-TRICHOTOMY))
 (872 872 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (872 872 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (872 872 (:META CANCEL-ADDENDS-EQUAL-THM))
 (756 24 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (592 592 (:TYPE-PRESCRIPTION <<))
 (496 248 (:REWRITE |Non-numeric y in (+ x y)|))
 (465 465 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (465 465 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (465 465 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (465 465 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (444 74 (:REWRITE <<-ASYMMETRIC))
 (377 377 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (377 377 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (365 365 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (248 248 (:REWRITE |Non-numeric x in (+ x y)|))
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 (222 222 (:REWRITE <<-TRANSITIVE))
 (118 118 (:REWRITE THUS-R-IS-EVALUATION-EQ-TO-S))
 (96 96 (:REWRITE APPLY-EQUATION-PRODUCES-EQUAL))
 (96 24 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (82 68 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (48 48 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (48 48 (:REWRITE SUBSET-FROM-UNION-2))
 (24 24 (:REWRITE SUBSET-IS-TRANSITIVE))
 (24 24 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 )
(PRODUCE-NEXT-STATE-FULLY-CONCRETIZED
 (4621 8 (:DEFINITION PRODUCE-NEXT-STATE))
 (4557 10 (:REWRITE APPLY-EQUATION-PRODUCES-EQUAL))
 (2520 20 (:DEFINITION FIND-VARIABLES))
 (1666 24 (:DEFINITION SUBSET))
 (1385 52 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (982 177 (:DEFINITION LEN))
 (716 716 (:TYPE-PRESCRIPTION LEN))
 (629 8 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (614 10 (:DEFINITION APPLY-EQUATION))
 (536 536 (:REWRITE DEFAULT-CDR))
 (519 519 (:REWRITE DEFAULT-CAR))
 (480 20 (:DEFINITION SET-UNION))
 (448 52 (:REWRITE SUBSET-IS-TRANSITIVE))
 (384 8 (:REWRITE S-SAME-G-BACK-CHAINING))
 (332 332 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (332 332 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (332 332 (:META CANCEL-ADDENDS-EQUAL-THM))
 (321 114 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (314 157 (:REWRITE |Non-numeric y in (+ x y)|))
 (255 255 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (255 255 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (255 255 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (255 255 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (240 240 (:TYPE-PRESCRIPTION FIND-VARIABLES))
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 (178 52 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (157 157 (:REWRITE |Non-numeric x in (+ x y)|))
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 (20 20 (:REWRITE CONSISTENT-EQN-RECORD-P-EXPANDED))
 (16 16 (:TYPE-PRESCRIPTION <<))
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 (10 10 (:TYPE-PRESCRIPTION ORDEREDP))
 (8 8 (:REWRITE THUS-R-IS-EVALUATION-EQ-TO-S))
 (6 6 (:REWRITE <<-TRANSITIVE))
 (4 4 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 (2 2 (:REWRITE EVALUATION-P-ONLY-EVALUATIONS-REDUCTION))
 (2 2 (:REWRITE EQUATION-EQUAL-P-TO-CONSISTENT-EQUATION))
 (1 1 (:REWRITE EQUATION-EQUAL-P-TO-CONSISTENT))
 (1 1 (:REWRITE CONSISTENT-P-EQUATION-MEMBERP-REDUCTION))
 )
(PRODUCE-NEXT-STATE-FOR-EQUATION-OF-CHOICE
 (1582 2 (:DEFINITION PRODUCE-NEXT-STATE))
 (1351 2 (:REWRITE APPLY-EQUATION-PRODUCES-EQUAL))
 (952 4 (:DEFINITION FIND-VARIABLES))
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 (504 9 (:DEFINITION CREATE-CORRESPONDING-EQUATION))
 (395 6 (:DEFINITION SUBSET))
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 (240 20 (:REWRITE S-SAME-G-BACK-CHAINING))
 (218 39 (:DEFINITION LEN))
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 (163 163 (:REWRITE DEFAULT-CDR))
 (119 2 (:DEFINITION APPLY-EQUATION))
 (112 13 (:REWRITE SUBSET-IS-TRANSITIVE))
 (108 4 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (102 102 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (102 102 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (102 102 (:META CANCEL-ADDENDS-EQUAL-THM))
 (99 70 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (96 4 (:DEFINITION SET-UNION))
 (96 4 (:DEFINITION ORDEREDP))
 (92 2 (:DEFINITION UNIQUEP))
 (84 84 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (84 84 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (84 84 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
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 (1 1 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 (1 1 (:REWRITE CONSISTENT-P-EQUATION-MEMBERP-REDUCTION))
 )
(BOOLEAN-P-APPLY-EQUATION
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 (558 12 (:LINEAR LEN-SET-UNION-MORE-THAN-Y))
 (465 465 (:REWRITE |Non-numeric x in (+ x y)|))
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 (424 8 (:DEFINITION UNIQUEP))
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 (411 411 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (384 16 (:DEFINITION ORDEREDP))
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 (192 48 (:REWRITE <<-TRICHOTOMY))
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 (128 128 (:TYPE-PRESCRIPTION <<))
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 (84 84 (:REWRITE SUBSET-IS-TRANSITIVE))
 (84 84 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
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 (43 43 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (43 43 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (30 30 (:REWRITE CONSISTENT-EQN-RECORD-P-EXPANDED))
 (8 8 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 )
(EVALUATION-P-SET-REDUCTION
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 (139 2 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (132 1 (:DEFINITION SUBSET))
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 (53 1 (:DEFINITION UNIQUEP))
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 (39 3 (:DEFINITION MEMBERP))
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 (23 23 (:REWRITE DEFAULT-CAR))
 (21 21 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (21 21 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (21 21 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (21 21 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (18 18 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (18 18 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (16 16 (:TYPE-PRESCRIPTION <<))
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 (6 6 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (6 6 (:REWRITE <<-TRANSITIVE))
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 (2 2 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
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 (1 1 (:REWRITE UN-HIDE-PLUS))
 (1 1 (:REWRITE SUBSET-IS-REFLEXIVE))
 (1 1 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 )
(PRODUCE-NEXT-STATE-IS-EVALUATION-P
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 (504 4 (:DEFINITION FIND-VARIABLES))
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 (204 204 (:REWRITE DEFAULT-CAR))
 (184 184 (:TYPE-PRESCRIPTION <<))
 (150 3 (:DEFINITION APPLY-EQUATION))
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 (110 55 (:REWRITE |Non-numeric y in (+ x y)|))
 (106 3 (:REWRITE S-SAME-G-BACK-CHAINING))
 (105 6 (:REWRITE PRODUCE-NEXT-STATE-NOT-MEMBERP-VARS-REDUCTION))
 (101 101 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (101 101 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (101 101 (:META CANCEL-ADDENDS-EQUAL-THM))
 (101 6 (:REWRITE PRODUCE-NEXT-STATE-VARS-REDUCTION))
 (96 4 (:DEFINITION SET-UNION))
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 (88 88 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (88 88 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (88 88 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (73 49 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (72 18 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (69 69 (:REWRITE <<-TRANSITIVE))
 (56 56 (:TYPE-PRESCRIPTION FIND-VARIABLES))
 (55 55 (:REWRITE |Non-numeric x in (+ x y)|))
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 (39 39 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
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 (4 4 (:REWRITE CONSISTENT-EQN-RECORD-P-EXPANDED))
 (1 1 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 )
(NEXT-STATE-IS-EVALUATION-P-CONCRETIZED
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 (54 2 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (50 1 (:DEFINITION APPLY-EQUATION))
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 (23 23 (:REWRITE DEFAULT-CDR))
 (22 22 (:REWRITE DEFAULT-CAR))
 (20 1 (:REWRITE PRODUCE-NEXT-STATE-VARS-REDUCTION))
 (20 1 (:REWRITE PRODUCE-NEXT-STATE-NOT-MEMBERP-VARS-REDUCTION))
 (16 16 (:TYPE-PRESCRIPTION <<))
 (12 12 (:TYPE-PRESCRIPTION MEMBERP))
 (12 2 (:REWRITE <<-ASYMMETRIC))
 (12 2 (:DEFINITION LEN))
 (10 10 (:TYPE-PRESCRIPTION ORDEREDP))
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 (10 10 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (10 10 (:META CANCEL-ADDENDS-EQUAL-THM))
 (9 1 (:DEFINITION EVALUATION-P))
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 (8 8 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (8 8 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
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 (6 6 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (6 6 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
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 (4 2 (:REWRITE |Non-numeric y in (+ x y)|))
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 (1 1 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 (1 1 (:REWRITE EQUATION-EQUAL-P-TO-CONSISTENT))
 (1 1 (:REWRITE CONSISTENT-P-EQUATION-MEMBERP-REDUCTION))
 )
(R-IS-EVALUATION-EQ-MEMBER-P-WITH-RESPECT-TO-STATES
 (731 6 (:DEFINITION PRODUCE-NEXT-STATE))
 (504 18 (:REWRITE S-SAME-G-BACK-CHAINING))
 (444 19 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (395 6 (:DEFINITION APPLY-EQUATION))
 (384 6 (:REWRITE EVALUATION-EQ-MEMBERP-OF-CORRESPONDING-STATES-2))
 (378 14 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (365 6 (:DEFINITION SUBSET))
 (336 14 (:DEFINITION ORDEREDP))
 (282 282 (:REWRITE DEFAULT-CDR))
 (281 281 (:REWRITE DEFAULT-CAR))
 (260 98 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (252 42 (:DEFINITION LEN))
 (240 6 (:DEFINITION CORRESPONDING-STATES))
 (222 222 (:TYPE-PRESCRIPTION LEN))
 (216 6 (:DEFINITION CORRESPONDING-STATE))
 (195 10 (:DEFINITION EVALUATION-EQ))
 (168 42 (:REWRITE <<-TRICHOTOMY))
 (168 3 (:DEFINITION CREATE-CORRESPONDING-EQUATION))
 (160 8 (:REWRITE PRODUCE-NEXT-STATE-VARS-REDUCTION))
 (160 8 (:REWRITE PRODUCE-NEXT-STATE-NOT-MEMBERP-VARS-REDUCTION))
 (140 140 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (140 140 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (140 140 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (140 140 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (140 140 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (140 140 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (140 140 (:META CANCEL-ADDENDS-EQUAL-THM))
 (140 20 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (120 6 (:REWRITE NOT-MEMBERP-TO-CORRESPONDING-STATE))
 (112 112 (:TYPE-PRESCRIPTION <<))
 (108 6 (:REWRITE ALL-EVALUATIONS-CONSIDERS-AN-EVALUATION-A-MEMBER))
 (98 98 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (97 97 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (89 15 (:REWRITE EQUATION-EQUAL-P-TO-CONSISTENT-EQUATION))
 (84 42 (:REWRITE |Non-numeric y in (+ x y)|))
 (84 14 (:REWRITE <<-ASYMMETRIC))
 (73 19 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (70 70 (:TYPE-PRESCRIPTION ORDEREDP))
 (60 3 (:REWRITE MEMBERP-OF-NEXT-STATE-FROM-CONSISTENT-EQUATION))
 (60 3 (:REWRITE MEMBERP-NOT-USING-NEXT-STATES))
 (56 42 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (54 6 (:DEFINITION CREATE-NEXT-STATES-OF-P))
 (54 3 (:REWRITE EVALUATION-EQ-MEMBERP-FROM-ALL-EVALUATIONS-P))
 (42 42 (:REWRITE |Non-numeric x in (+ x y)|))
 (42 42 (:REWRITE <<-TRANSITIVE))
 (42 42 (:META COLLECT-ADDENDS-THM))
 (38 38 (:REWRITE SUBSET-FROM-UNION-2))
 (38 38 (:REWRITE EVALUATION-P-ONLY-EVALUATIONS-REDUCTION))
 (32 32 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (24 24 (:TYPE-PRESCRIPTION CORRESPONDING-STATES))
 (20 20 (:REWRITE THUS-R-IS-EVALUATION-EQ-TO-S))
 (20 20 (:REWRITE EVALUATION-EQ-IS-TRANSITIVE))
 (18 18 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (16 2 (:DEFINITION CONS-LIST-P))
 (11 11 (:REWRITE NEXT-STATE-IS-OK-FROM-CONSISTENT-EQN))
 (11 7 (:REWRITE EQUATION-EQUAL-P-TO-CONSISTENT))
 (10 10 (:TYPE-PRESCRIPTION BOOLEANP))
 (6 6 (:REWRITE NEXT-STATE-IS-OK-SUFF))
 (6 6 (:REWRITE EVALUATION-EQ-SUBSET-TO-MEMBER))
 (6 6 (:REWRITE EVALUATION-EQ-MEMBER-SUBSET-REDUCTION))
 (6 6 (:REWRITE EVALUATION-EQ-AND-MEMBERP-TO-MEMBERP))
 (6 6 (:REWRITE EVALUATION-EQ-AND-MEMBERP-TO-EVALUATION-EQ-MEMBERP))
 (5 5 (:REWRITE CONSISTENT-P-EQUATION-MEMBERP-REDUCTION))
 (4 4 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 (2 2 (:REWRITE CONSISTENT-P-EQUATIONS-TO-CONSISTENT-P-EQUATIONS))
 )
(EVALUATION-EQ-SUBSET-P-ORIG->CONE
 (757 23 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (540 20 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (480 20 (:DEFINITION ORDEREDP))
 (460 10 (:DEFINITION UNIQUEP))
 (414 3 (:DEFINITION EVALUATION-EQ-MEMBER-P))
 (384 6 (:REWRITE EVALUATION-EQ-MEMBERP-OF-CORRESPONDING-STATES-2))
 (312 16 (:DEFINITION EVALUATION-EQ))
 (307 47 (:DEFINITION LEN))
 (302 19 (:DEFINITION EVALUATION-P))
 (290 290 (:REWRITE DEFAULT-CDR))
 (287 287 (:TYPE-PRESCRIPTION LEN))
 (246 246 (:REWRITE DEFAULT-CAR))
 (240 60 (:REWRITE <<-TRICHOTOMY))
 (240 6 (:DEFINITION CORRESPONDING-STATES))
 (224 32 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (216 6 (:DEFINITION CORRESPONDING-STATE))
 (180 9 (:REWRITE MEMBERP-OF-NEXT-STATE-FROM-CONSISTENT-EQUATION))
 (180 9 (:REWRITE MEMBERP-NOT-USING-NEXT-STATES))
 (173 78 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (168 6 (:REWRITE S-SAME-G-BACK-CHAINING))
 (160 160 (:TYPE-PRESCRIPTION <<))
 (135 15 (:DEFINITION CREATE-NEXT-STATES-OF-P))
 (128 64 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (122 23 (:REWRITE SUBSET-IS-TRANSITIVE))
 (120 120 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (120 120 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (120 120 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (120 120 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (120 20 (:REWRITE <<-ASYMMETRIC))
 (120 6 (:REWRITE NOT-MEMBERP-TO-CORRESPONDING-STATE))
 (109 109 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (109 109 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (109 109 (:META CANCEL-ADDENDS-EQUAL-THM))
 (108 6 (:REWRITE ALL-EVALUATIONS-CONSIDERS-AN-EVALUATION-A-MEMBER))
 (100 100 (:TYPE-PRESCRIPTION ORDEREDP))
 (96 48 (:REWRITE |Non-numeric y in (+ x y)|))
 (92 23 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (78 78 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (78 78 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (78 78 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (75 5 (:DEFINITION EQUATION-EQUAL-P))
 (60 60 (:REWRITE <<-TRANSITIVE))
 (54 3 (:REWRITE EVALUATION-EQ-MEMBERP-FROM-ALL-EVALUATIONS-P))
 (48 48 (:REWRITE |Non-numeric x in (+ x y)|))
 (48 48 (:META COLLECT-ADDENDS-THM))
 (46 46 (:REWRITE SUBSET-FROM-UNION-2))
 (45 45 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (40 40 (:REWRITE EVALUATION-P-ONLY-EVALUATIONS-REDUCTION))
 (40 5 (:DEFINITION CONS-LIST-P))
 (32 32 (:REWRITE THUS-R-IS-EVALUATION-EQ-TO-S))
 (32 32 (:REWRITE EVALUATION-EQ-IS-TRANSITIVE))
 (25 15 (:REWRITE EQUATION-EQUAL-P-TO-CONSISTENT))
 (24 24 (:TYPE-PRESCRIPTION CORRESPONDING-STATES))
 (23 23 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (15 15 (:TYPE-PRESCRIPTION NEXT-STATE-IS-OK))
 (15 15 (:REWRITE NEXT-STATE-MEMBER-IMPLIES-CONSISTENT-EQUATION))
 (15 15 (:REWRITE NEXT-STATE-IS-OK-SUFF))
 (15 15 (:REWRITE NEXT-STATE-IS-OK-FROM-CONSISTENT-EQN))
 (9 9 (:TYPE-PRESCRIPTION BOOLEANP))
 (8 8 (:REWRITE EVALUATION-EQ-SUBSET-SUBSET-REDUCTION))
 (6 6 (:REWRITE EVALUATION-EQ-SUBSET-TO-MEMBER))
 (6 6 (:REWRITE EVALUATION-EQ-MEMBER-SUBSET-REDUCTION))
 (6 6 (:REWRITE EVALUATION-EQ-AND-MEMBERP-TO-MEMBERP))
 (6 6 (:REWRITE EVALUATION-EQ-AND-MEMBERP-TO-EVALUATION-EQ-MEMBERP))
 (3 3 (:TYPE-PRESCRIPTION EVALUATION-EQ-MEMBER-P))
 (3 3 (:REWRITE NEXT-STATE-OF-ORIG-TO-EVALUATION-EQ-MEMBER-P))
 (1 1 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 )
(EVALUATION-EQ-SUBSET-ORIG->CONE-CONCRETIZED
 (218 11 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (186 3 (:DEFINITION SUBSET))
 (139 1 (:DEFINITION EVALUATION-EQ-MEMBER-P))
 (130 2 (:REWRITE EVALUATION-EQ-MEMBERP-OF-CORRESPONDING-STATES-2))
 (108 4 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (96 4 (:DEFINITION ORDEREDP))
 (91 91 (:TYPE-PRESCRIPTION LEN))
 (84 14 (:DEFINITION LEN))
 (80 2 (:DEFINITION CORRESPONDING-STATES))
 (72 2 (:DEFINITION CORRESPONDING-STATE))
 (58 58 (:REWRITE DEFAULT-CDR))
 (56 2 (:REWRITE S-SAME-G-BACK-CHAINING))
 (48 12 (:REWRITE <<-TRICHOTOMY))
 (44 44 (:REWRITE DEFAULT-CAR))
 (44 11 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (40 2 (:REWRITE NOT-MEMBERP-TO-CORRESPONDING-STATE))
 (39 3 (:DEFINITION EVALUATION-P))
 (39 2 (:DEFINITION EVALUATION-EQ))
 (36 2 (:REWRITE ALL-EVALUATIONS-CONSIDERS-AN-EVALUATION-A-MEMBER))
 (32 32 (:TYPE-PRESCRIPTION <<))
 (28 14 (:REWRITE |Non-numeric y in (+ x y)|))
 (28 4 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (24 4 (:REWRITE <<-ASYMMETRIC))
 (22 22 (:REWRITE SUBSET-FROM-UNION-2))
 (21 21 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (20 20 (:TYPE-PRESCRIPTION ORDEREDP))
 (20 20 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (20 20 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (20 20 (:META CANCEL-ADDENDS-EQUAL-THM))
 (19 19 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (19 19 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (19 19 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (19 19 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (18 18 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (18 2 (:DEFINITION CREATE-NEXT-STATES-OF-P))
 (18 1 (:REWRITE EVALUATION-EQ-MEMBERP-FROM-ALL-EVALUATIONS-P))
 (14 14 (:REWRITE |Non-numeric x in (+ x y)|))
 (14 14 (:META COLLECT-ADDENDS-THM))
 (13 13 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (13 13 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (13 13 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (12 12 (:REWRITE <<-TRANSITIVE))
 (11 11 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (8 8 (:TYPE-PRESCRIPTION CORRESPONDING-STATES))
 (6 6 (:REWRITE THUS-R-IS-EVALUATION-EQ-TO-S))
 (5 3 (:REWRITE EQUATION-EQUAL-P-TO-CONSISTENT))
 (4 4 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 (3 3 (:TYPE-PRESCRIPTION BOOLEANP))
 (2 2 (:TYPE-PRESCRIPTION NEXT-STATE-IS-OK))
 (2 2 (:REWRITE NEXT-STATE-MEMBER-IMPLIES-CONSISTENT-EQUATION))
 (2 2 (:REWRITE NEXT-STATE-IS-OK-SUFF))
 (2 2 (:REWRITE NEXT-STATE-IS-OK-FROM-CONSISTENT-EQN))
 (2 2 (:REWRITE EVALUATION-EQ-SUBSET-TO-MEMBER))
 (2 2 (:REWRITE EVALUATION-EQ-SUBSET-SUBSET-REDUCTION))
 (2 2 (:REWRITE EVALUATION-EQ-MEMBER-SUBSET-REDUCTION))
 (2 2 (:REWRITE EVALUATION-EQ-AND-MEMBERP-TO-MEMBERP))
 (2 2 (:REWRITE EVALUATION-EQ-AND-MEMBERP-TO-EVALUATION-EQ-MEMBERP))
 (1 1 (:REWRITE R-IS-EVALUATION-EQ-MEMBER-P-WITH-RESPECT-TO-STATES))
 (1 1 (:REWRITE NEXT-STATE-OF-ORIG-TO-EVALUATION-EQ-MEMBER-P))
 )
(EQUATION-EQUAL-IS-SYMMETRIC
 (20 20 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (20 20 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (20 20 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (20 20 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (20 20 (:REWRITE DEFAULT-CAR))
 (9 9 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (9 9 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (9 9 (:META CANCEL-ADDENDS-EQUAL-THM))
 (4 4 (:REWRITE DEFAULT-CDR))
 )
(EQUATION-EQUAL-TO-SET-REDUCTION-2
 (40 5 (:REWRITE S-SAME-G-BACK-CHAINING))
 (29 29 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (29 29 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (29 29 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (29 29 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (28 28 (:REWRITE DEFAULT-CAR))
 (23 23 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (23 23 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (23 23 (:META CANCEL-ADDENDS-EQUAL-THM))
 (8 8 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (8 8 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (8 8 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (8 8 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (6 6 (:REWRITE DEFAULT-CDR))
 )
(MEMBERP-TO-CREATE-EQUATION-REDUCTION
 (202 202 (:REWRITE DEFAULT-CAR))
 (132 132 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (132 132 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (132 132 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (132 132 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (130 130 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (130 130 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (130 130 (:META CANCEL-ADDENDS-EQUAL-THM))
 (120 120 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (120 120 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (120 120 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (120 120 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (98 98 (:REWRITE DEFAULT-CDR))
 )
(NOT-MEMBERP-TO-CREATE-EQUATION
 (308 23 (:REWRITE MEMBERP-TO-CREATE-EQUATION-REDUCTION))
 (296 16 (:REWRITE S-SAME-G-BACK-CHAINING))
 (81 81 (:REWRITE DEFAULT-CAR))
 (59 59 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (59 59 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (59 59 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (59 59 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (54 54 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (54 54 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (54 54 (:META CANCEL-ADDENDS-EQUAL-THM))
 (52 52 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (52 52 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (52 52 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (52 52 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (46 46 (:REWRITE DEFAULT-CDR))
 )
(MEMBERP-EQUATION-REDUCTION-2
 (374 26 (:REWRITE NOT-MEMBERP-TO-CREATE-EQUATION))
 (177 25 (:REWRITE MEMBERP-TO-CREATE-EQUATION-REDUCTION))
 (129 129 (:REWRITE DEFAULT-CAR))
 (102 102 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (102 102 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (102 102 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (102 102 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (78 78 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (78 78 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (78 78 (:META CANCEL-ADDENDS-EQUAL-THM))
 (67 67 (:REWRITE DEFAULT-CDR))
 (59 59 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (59 59 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (59 59 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (59 59 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 )
(CREATE-CORRESPONDING-EQUATION-IS-EQUATION-EQUAL-2
 (1208 9 (:DEFINITION CREATE-CORRESPONDING-EQUATION))
 (1077 90 (:DEFINITION MEMBERP))
 (882 18 (:REWRITE S-SAME-G-BACK-CHAINING))
 (618 20 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (540 20 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (501 26 (:REWRITE NOT-MEMBERP-TO-CREATE-EQUATION))
 (480 20 (:DEFINITION ORDEREDP))
 (460 10 (:DEFINITION UNIQUEP))
 (292 26 (:REWRITE MEMBERP-EQUATION-REDUCTION-2))
 (263 43 (:DEFINITION LEN))
 (261 261 (:TYPE-PRESCRIPTION LEN))
 (242 242 (:REWRITE DEFAULT-CDR))
 (240 60 (:REWRITE <<-TRICHOTOMY))
 (222 222 (:REWRITE DEFAULT-CAR))
 (180 180 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (180 180 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (180 180 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (180 180 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (160 160 (:TYPE-PRESCRIPTION <<))
 (133 133 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (133 133 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (133 133 (:META CANCEL-ADDENDS-EQUAL-THM))
 (128 52 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (120 20 (:REWRITE <<-ASYMMETRIC))
 (100 100 (:TYPE-PRESCRIPTION ORDEREDP))
 (88 44 (:REWRITE |Non-numeric y in (+ x y)|))
 (80 20 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (65 58 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (60 60 (:REWRITE <<-TRANSITIVE))
 (52 52 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (52 52 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (52 52 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (44 44 (:REWRITE |Non-numeric x in (+ x y)|))
 (44 44 (:META COLLECT-ADDENDS-THM))
 (40 40 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (40 40 (:REWRITE SUBSET-FROM-UNION-2))
 (20 20 (:REWRITE SUBSET-IS-TRANSITIVE))
 (20 20 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 )
(PRODUCE-NEXT-STATE-FOR-EQUATION-OF-CHOICE-2
 (279 2 (:DEFINITION PRODUCE-NEXT-STATE))
 (225 21 (:DEFINITION MEMBERP))
 (194 4 (:REWRITE S-SAME-G-BACK-CHAINING))
 (130 1 (:DEFINITION CREATE-CORRESPONDING-EQUATION))
 (122 5 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (119 2 (:DEFINITION APPLY-EQUATION))
 (117 2 (:DEFINITION SUBSET))
 (108 4 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (104 5 (:REWRITE SUBSET-IS-TRANSITIVE))
 (96 4 (:DEFINITION ORDEREDP))
 (92 2 (:DEFINITION UNIQUEP))
 (73 73 (:TYPE-PRESCRIPTION MEMBERP))
 (73 2 (:DEFINITION CONSISTENT-P-EQUATIONS))
 (72 72 (:REWRITE DEFAULT-CDR))
 (72 72 (:REWRITE DEFAULT-CAR))
 (72 12 (:DEFINITION LEN))
 (64 64 (:TYPE-PRESCRIPTION LEN))
 (53 24 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (48 12 (:REWRITE <<-TRICHOTOMY))
 (48 3 (:REWRITE NOT-MEMBERP-TO-CREATE-EQUATION))
 (41 4 (:REWRITE EQUATION-EQUAL-P-TO-CONSISTENT-EQUATION))
 (41 3 (:REWRITE MEMBERP-TO-CREATE-EQUATION-REDUCTION))
 (41 3 (:REWRITE MEMBERP-EQUATION-REDUCTION-2))
 (40 2 (:REWRITE PRODUCE-NEXT-STATE-VARS-REDUCTION))
 (40 2 (:REWRITE PRODUCE-NEXT-STATE-NOT-MEMBERP-VARS-REDUCTION))
 (39 39 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (39 39 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (39 39 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (39 39 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (39 39 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (39 39 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (39 39 (:META CANCEL-ADDENDS-EQUAL-THM))
 (39 2 (:DEFINITION EVALUATION-EQ))
 (35 25 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (32 32 (:TYPE-PRESCRIPTION <<))
 (28 4 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (28 2 (:DEFINITION EVALUATION-P))
 (24 24 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (24 12 (:REWRITE |Non-numeric y in (+ x y)|))
 (24 4 (:REWRITE <<-ASYMMETRIC))
 (23 23 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (20 20 (:TYPE-PRESCRIPTION ORDEREDP))
 (20 5 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (15 1 (:DEFINITION EQUATION-EQUAL-P))
 (12 12 (:REWRITE |Non-numeric x in (+ x y)|))
 (12 12 (:REWRITE <<-TRANSITIVE))
 (12 12 (:META COLLECT-ADDENDS-THM))
 (12 12 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (10 10 (:REWRITE SUBSET-FROM-UNION-2))
 (9 9 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (8 1 (:DEFINITION CONS-LIST-P))
 (5 5 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (5 3 (:REWRITE EQUATION-EQUAL-P-TO-CONSISTENT))
 (4 4 (:REWRITE THUS-R-IS-EVALUATION-EQ-TO-S))
 (4 4 (:REWRITE EVALUATIONP-FOR-SUBSET))
 (4 4 (:REWRITE EVALUATION-P-ONLY-EVALUATIONS-REDUCTION))
 (4 4 (:REWRITE EVALUATION-EQ-IS-TRANSITIVE))
 (2 2 (:REWRITE CONSISTENT-P-EQUATION-MEMBERP-REDUCTION))
 (2 2 (:REWRITE CONS-LIST-P-SUBSET-REDUCTION))
 (1 1 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 (1 1 (:REWRITE CONS-LIST-P-EQUATION-EQUAL-REDUCTION))
 )
(AND-THUS-FOR-VARS-CONE
 (980 14 (:REWRITE PRODUCE-NEXT-STATE-VARS-REDUCTION))
 (938 2 (:DEFINITION CREATE-NEXT-STATES-OF-P))
 (880 8 (:DEFINITION EVALUATION-EQ))
 (795 15 (:DEFINITION UNIQUEP))
 (784 30 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (752 5 (:REWRITE EVALUATION-EQ-AND-MEMBERP-TO-MEMBERP))
 (696 29 (:DEFINITION ORDEREDP))
 (462 2 (:REWRITE NEXT-STATE-IS-OK-SUFF))
 (462 2 (:REWRITE NEXT-STATE-IS-OK-FROM-CONSISTENT-EQN))
 (424 4 (:DEFINITION PRODUCE-NEXT-STATE))
 (403 7 (:DEFINITION EVALUATION-P))
 (354 45 (:DEFINITION MEMBERP))
 (348 87 (:REWRITE <<-TRICHOTOMY))
 (332 4 (:REWRITE EVALUATION-EQ-MEMBERP-OF-CORRESPONDING-STATES-2))
 (294 4 (:REWRITE ALL-EVALUATIONS-CONSIDERS-AN-EVALUATION-A-MEMBER))
 (270 16 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (232 232 (:TYPE-PRESCRIPTION <<))
 (200 200 (:REWRITE DEFAULT-CDR))
 (200 4 (:DEFINITION APPLY-EQUATION))
 (192 4 (:REWRITE S-SAME-G-BACK-CHAINING))
 (187 187 (:REWRITE DEFAULT-CAR))
 (174 29 (:REWRITE <<-ASYMMETRIC))
 (163 36 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (160 14 (:REWRITE PRODUCE-NEXT-STATE-NOT-MEMBERP-VARS-REDUCTION))
 (145 145 (:TYPE-PRESCRIPTION ORDEREDP))
 (141 141 (:TYPE-PRESCRIPTION MEMBERP))
 (138 16 (:REWRITE EVALUATION-EQ-IS-TRANSITIVE))
 (87 87 (:REWRITE <<-TRANSITIVE))
 (87 2 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (75 75 (:TYPE-PRESCRIPTION UNIQUEP))
 (69 69 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (69 69 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (69 69 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (69 69 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (60 10 (:DEFINITION LEN))
 (57 57 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (57 57 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (57 57 (:META CANCEL-ADDENDS-EQUAL-THM))
 (55 6 (:REWRITE PRODUCE-NEXT-STATE-IS-EVALUATION-P))
 (37 37 (:TYPE-PRESCRIPTION LEN))
 (37 3 (:REWRITE NEXT-STATE-IS-EVALUATION-P-CONCRETIZED))
 (36 36 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (36 36 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (35 35 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (20 10 (:REWRITE |Non-numeric y in (+ x y)|))
 (19 19 (:REWRITE EVALUATIONP-FOR-SUBSET))
 (19 19 (:REWRITE EVALUATION-P-ONLY-EVALUATIONS-REDUCTION))
 (16 16 (:REWRITE THUS-R-IS-EVALUATION-EQ-TO-S))
 (10 10 (:REWRITE |Non-numeric x in (+ x y)|))
 (10 10 (:META COLLECT-ADDENDS-THM))
 (8 2 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (7 7 (:TYPE-PRESCRIPTION BOOLEANP))
 (4 4 (:REWRITE SUBSET-FROM-UNION-2))
 (4 4 (:REWRITE EVALUATION-EQ-SUBSET-TO-MEMBER))
 (4 4 (:REWRITE EVALUATION-EQ-AND-MEMBERP-TO-EVALUATION-EQ-MEMBERP))
 (3 3 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (3 3 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (2 2 (:TYPE-PRESCRIPTION NEXT-STATE-IS-OK))
 (2 2 (:REWRITE R-IS-EVALUATION-EQ-MEMBER-P-WITH-RESPECT-TO-STATES))
 (2 2 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (2 2 (:REWRITE NEXT-STATE-OF-ORIG-TO-EVALUATION-EQ-MEMBER-P))
 (2 2 (:REWRITE NEXT-STATE-MEMBER-IMPLIES-CONSISTENT-EQUATION))
 (1 1 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 )
(THUS-R-IS-EVALUATION-EQ-TO-S-2
 (116 1 (:DEFINITION EVALUATION-EQ))
 (110 2 (:REWRITE PRODUCE-NEXT-STATE-VARS-REDUCTION))
 (108 4 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (106 2 (:DEFINITION UNIQUEP))
 (106 1 (:DEFINITION PRODUCE-NEXT-STATE))
 (96 4 (:DEFINITION ORDEREDP))
 (83 1 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (56 6 (:DEFINITION MEMBERP))
 (50 1 (:DEFINITION APPLY-EQUATION))
 (48 12 (:REWRITE <<-TRICHOTOMY))
 (48 1 (:REWRITE S-SAME-G-BACK-CHAINING))
 (32 32 (:TYPE-PRESCRIPTION <<))
 (30 30 (:REWRITE DEFAULT-CDR))
 (28 28 (:REWRITE DEFAULT-CAR))
 (28 2 (:REWRITE PRODUCE-NEXT-STATE-NOT-MEMBERP-VARS-REDUCTION))
 (24 4 (:REWRITE <<-ASYMMETRIC))
 (22 22 (:TYPE-PRESCRIPTION MEMBERP))
 (20 20 (:TYPE-PRESCRIPTION ORDEREDP))
 (12 12 (:REWRITE <<-TRANSITIVE))
 (12 2 (:DEFINITION LEN))
 (11 11 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (11 11 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (11 11 (:META CANCEL-ADDENDS-EQUAL-THM))
 (10 10 (:TYPE-PRESCRIPTION UNIQUEP))
 (10 10 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (10 10 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (10 10 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (10 10 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (6 6 (:TYPE-PRESCRIPTION LEN))
 (5 5 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (5 5 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (5 5 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (5 5 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (4 2 (:REWRITE |Non-numeric y in (+ x y)|))
 (4 1 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (2 2 (:REWRITE SUBSET-FROM-UNION-2))
 (2 2 (:REWRITE |Non-numeric x in (+ x y)|))
 (2 2 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (2 2 (:REWRITE EVALUATION-EQ-IS-TRANSITIVE))
 (2 2 (:META COLLECT-ADDENDS-THM))
 (1 1 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (1 1 (:REWRITE SUBSET-IS-TRANSITIVE))
 (1 1 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (1 1 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 (1 1 (:REWRITE NEXT-STATE-MEMBER-IMPLIES-CONSISTENT-EQUATION))
 (1 1 (:REWRITE NEXT-STATE-IS-OK-SUFF))
 (1 1 (:REWRITE NEXT-STATE-IS-OK-FROM-CONSISTENT-EQN))
 )
(THUS-POLISHED-R-IS-EVALUATION-EQ-TO-S-2
 (20 1 (:REWRITE MEMBERP-OF-NEXT-STATE-FROM-CONSISTENT-EQUATION))
 (20 1 (:REWRITE MEMBERP-NOT-USING-NEXT-STATES))
 (8 1 (:DEFINITION CREATE-NEXT-STATES-OF-P))
 (6 6 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (6 6 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (6 6 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (6 6 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (5 5 (:REWRITE DEFAULT-CDR))
 (5 5 (:REWRITE DEFAULT-CAR))
 (3 3 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (3 3 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (3 3 (:META CANCEL-ADDENDS-EQUAL-THM))
 (2 2 (:REWRITE NEXT-STATE-IS-OK-SUFF))
 (2 2 (:REWRITE NEXT-STATE-IS-OK-FROM-CONSISTENT-EQN))
 )
(EVALUATION-EQ-MEMBER-P-FROM-MEMBERP
 (166 2 (:REWRITE EVALUATION-EQ-MEMBERP-OF-CORRESPONDING-STATES-2))
 (132 1 (:DEFINITION EVALUATION-EQ-MEMBER-P))
 (108 4 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (106 2 (:DEFINITION UNIQUEP))
 (96 4 (:DEFINITION ORDEREDP))
 (48 12 (:REWRITE <<-TRICHOTOMY))
 (38 2 (:DEFINITION EVALUATION-EQ))
 (36 2 (:REWRITE ALL-EVALUATIONS-CONSIDERS-AN-EVALUATION-A-MEMBER))
 (32 32 (:TYPE-PRESCRIPTION <<))
 (26 2 (:DEFINITION MEMBERP))
 (26 2 (:DEFINITION EVALUATION-P))
 (24 4 (:REWRITE <<-ASYMMETRIC))
 (23 23 (:REWRITE DEFAULT-CDR))
 (20 20 (:TYPE-PRESCRIPTION ORDEREDP))
 (19 19 (:REWRITE DEFAULT-CAR))
 (12 12 (:REWRITE <<-TRANSITIVE))
 (10 10 (:TYPE-PRESCRIPTION UNIQUEP))
 (10 10 (:TYPE-PRESCRIPTION MEMBERP))
 (10 10 (:TYPE-PRESCRIPTION EVALUATION-P))
 (6 6 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (6 6 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (6 6 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (6 6 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (4 4 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (4 4 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (4 4 (:REWRITE THUS-R-IS-EVALUATION-EQ-TO-S))
 (4 4 (:REWRITE THUS-POLISHED-R-IS-EVALUATION-EQ-TO-S-2))
 (4 4 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (4 4 (:REWRITE EVALUATIONP-FOR-SUBSET))
 (4 4 (:REWRITE EVALUATION-P-ONLY-EVALUATIONS-REDUCTION))
 (4 4 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (4 4 (:REWRITE EVALUATION-EQ-IS-TRANSITIVE))
 (4 4 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (4 4 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (4 4 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (4 4 (:META CANCEL-ADDENDS-EQUAL-THM))
 (2 2 (:TYPE-PRESCRIPTION BOOLEANP))
 (2 2 (:REWRITE EVALUATION-EQ-SUBSET-TO-MEMBER))
 (2 2 (:REWRITE EVALUATION-EQ-MEMBER-SUBSET-REDUCTION))
 (2 2 (:REWRITE EVALUATION-EQ-AND-MEMBERP-TO-EVALUATION-EQ-MEMBERP))
 )
(NEXT-STATE-OF-ORIG-TO-EVALUATION-EQ-MEMBER-P-2
 (2114 26 (:DEFINITION EVALUATION-EQ))
 (1810 38 (:REWRITE PRODUCE-NEXT-STATE-VARS-REDUCTION))
 (1686 3 (:DEFINITION EVALUATION-EQ-MEMBER-P))
 (1650 33 (:DEFINITION APPLY-EQUATION))
 (889 144 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (855 52 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (848 8 (:DEFINITION PRODUCE-NEXT-STATE))
 (796 4 (:DEFINITION CREATE-NEXT-STATES-OF-P))
 (580 15 (:REWRITE S-SAME-G-BACK-CHAINING))
 (520 15 (:DEFINITION EVALUATION-P))
 (494 12 (:REWRITE ALL-EVALUATIONS-CONSIDERS-AN-EVALUATION-A-MEMBER))
 (489 489 (:REWRITE DEFAULT-CAR))
 (474 12 (:REWRITE EVALUATION-EQ-AND-MEMBERP-TO-MEMBERP))
 (456 76 (:DEFINITION LEN))
 (450 12 (:REWRITE EVALUATION-EQ-MEMBERP-OF-CORRESPONDING-STATES-2))
 (426 426 (:REWRITE DEFAULT-CDR))
 (385 5 (:REWRITE NEXT-STATE-IS-OK-FROM-CONSISTENT-EQN))
 (384 4 (:REWRITE NEXT-STATE-IS-OK-SUFF))
 (277 7 (:DEFINITION CORRESPONDING-STATES))
 (269 269 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (269 269 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (269 269 (:META CANCEL-ADDENDS-EQUAL-THM))
 (263 263 (:TYPE-PRESCRIPTION LEN))
 (260 13 (:REWRITE PRODUCE-NEXT-STATE-NOT-MEMBERP-VARS-REDUCTION))
 (252 7 (:DEFINITION CORRESPONDING-STATE))
 (158 9 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (152 152 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (152 152 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (152 152 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (152 152 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (152 76 (:REWRITE |Non-numeric y in (+ x y)|))
 (144 144 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (144 144 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (140 7 (:REWRITE NOT-MEMBERP-TO-CORRESPONDING-STATE))
 (134 134 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (117 2 (:DEFINITION SUBSET))
 (108 4 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (96 8 (:REWRITE PRODUCE-NEXT-STATE-IS-EVALUATION-P))
 (96 4 (:DEFINITION ORDEREDP))
 (92 2 (:DEFINITION UNIQUEP))
 (76 76 (:REWRITE |Non-numeric x in (+ x y)|))
 (76 76 (:META COLLECT-ADDENDS-THM))
 (72 4 (:REWRITE NEXT-STATE-IS-EVALUATION-P-CONCRETIZED))
 (58 58 (:REWRITE THUS-R-IS-EVALUATION-EQ-TO-S))
 (48 12 (:REWRITE <<-TRICHOTOMY))
 (40 2 (:REWRITE MEMBERP-OF-NEXT-STATE-FROM-CONSISTENT-EQUATION))
 (40 2 (:REWRITE MEMBERP-NOT-USING-NEXT-STATES))
 (37 37 (:REWRITE EVALUATION-P-ONLY-EVALUATIONS-REDUCTION))
 (36 9 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (36 2 (:REWRITE PRODUCE-NEXT-STATE-FULLY-CONCRETIZED))
 (32 32 (:TYPE-PRESCRIPTION <<))
 (28 28 (:TYPE-PRESCRIPTION CORRESPONDING-STATES))
 (24 4 (:REWRITE <<-ASYMMETRIC))
 (20 20 (:TYPE-PRESCRIPTION ORDEREDP))
 (18 18 (:REWRITE SUBSET-FROM-UNION-2))
 (15 15 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (14 14 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (14 14 (:TYPE-PRESCRIPTION BOOLEANP))
 (12 12 (:REWRITE EVALUATION-EQ-SUBSET-TO-MEMBER))
 (12 12 (:REWRITE EVALUATION-EQ-MEMBER-SUBSET-REDUCTION))
 (12 12 (:REWRITE EVALUATION-EQ-AND-MEMBERP-TO-EVALUATION-EQ-MEMBERP))
 (12 12 (:REWRITE <<-TRANSITIVE))
 (9 9 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (5 5 (:REWRITE BOOLEAN-P-APPLY-EQUATION))
 (4 4 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 (4 4 (:REWRITE EQUATION-EQUAL-P-TO-CONSISTENT-EQUATION))
 )
(CONSISTENT-P-EQUATIONS-TO-CONSISTENT-P-EQUATIONS-2
 (945 27 (:REWRITE S-SAME-G-BACK-CHAINING))
 (883 35 (:REWRITE CONS-LIST-P-SUBSET-REDUCTION))
 (602 12 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (576 144 (:REWRITE <<-TRICHOTOMY))
 (563 82 (:REWRITE EQUATION-EQUAL-P-TO-CONSISTENT-EQUATION))
 (550 8 (:REWRITE CONSISTENT-P-EQUATIONS-TO-CONSISTENT-P-EQUATIONS))
 (528 528 (:REWRITE DEFAULT-CAR))
 (486 6 (:DEFINITION SUBSET))
 (454 32 (:REWRITE NOT-MEMBERP-TO-CREATE-EQUATION))
 (384 384 (:TYPE-PRESCRIPTION <<))
 (360 50 (:DEFINITION LEN))
 (355 32 (:REWRITE MEMBERP-EQUATION-REDUCTION-2))
 (349 26 (:REWRITE MEMBERP-TO-CREATE-EQUATION-REDUCTION))
 (319 319 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (319 319 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (319 319 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (319 319 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (288 48 (:REWRITE <<-ASYMMETRIC))
 (239 193 (:META CANCEL-ADDENDS-EQUAL-THM))
 (210 210 (:TYPE-PRESCRIPTION LEN))
 (193 193 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (193 193 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (191 191 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (191 191 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (191 191 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (144 144 (:REWRITE <<-TRANSITIVE))
 (128 64 (:REWRITE |Non-numeric y in (+ x y)|))
 (110 30 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (64 64 (:REWRITE |Non-numeric x in (+ x y)|))
 (64 64 (:META COLLECT-ADDENDS-THM))
 (48 12 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (30 30 (:TYPE-PRESCRIPTION SUBSET))
 (24 24 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (24 24 (:REWRITE SUBSET-FROM-UNION-2))
 (18 18 (:REWRITE CONS-LIST-P-EQUATION-EQUAL-REDUCTION))
 (12 12 (:REWRITE SUBSET-IS-TRANSITIVE))
 (12 12 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (4 4 (:REWRITE G-DIFF-S))
 (4 4 (:REWRITE COLLECT-PLUS-1C))
 (2 2 (:REWRITE UN-HIDE-PLUS))
 )
(NEXT-STATE-CONE->ORIG-THUS-SETTLED
 (4632 6 (:DEFINITION FIND-VARIABLES))
 (4160 32 (:DEFINITION CREATE-CORRESPONDING-EQUATION))
 (3574 2 (:REWRITE BOOLEAN-P-APPLY-EQUATION))
 (3384 70 (:REWRITE S-SAME-G-BACK-CHAINING))
 (2992 4 (:REWRITE PRODUCE-NEXT-STATE-IS-EVALUATION-P))
 (2148 2 (:DEFINITION CLOSED-EQN-RECORD-P))
 (1456 107 (:REWRITE NOT-MEMBERP-TO-CREATE-EQUATION))
 (1418 107 (:REWRITE MEMBERP-TO-CREATE-EQUATION-REDUCTION))
 (1418 107 (:REWRITE MEMBERP-EQUATION-REDUCTION-2))
 (928 34 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (824 12 (:DEFINITION SUBSET))
 (764 764 (:REWRITE DEFAULT-CAR))
 (660 660 (:REWRITE DEFAULT-CDR))
 (643 643 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (643 643 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (643 643 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (643 643 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (625 4 (:DEFINITION PRODUCE-NEXT-STATE))
 (558 96 (:DEFINITION LEN))
 (470 470 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (470 470 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (470 470 (:META CANCEL-ADDENDS-EQUAL-THM))
 (432 16 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (429 429 (:TYPE-PRESCRIPTION LEN))
 (426 4 (:REWRITE CLOSED-EQN-RECORD-P-FROM-CONSISTENT-EQUATION-RECORD-P))
 (395 6 (:DEFINITION APPLY-EQUATION))
 (384 16 (:DEFINITION ORDEREDP))
 (310 215 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (223 75 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (215 215 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (215 215 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (192 48 (:REWRITE <<-TRICHOTOMY))
 (180 90 (:REWRITE |Non-numeric y in (+ x y)|))
 (178 2 (:REWRITE NEXT-STATE-IS-EVALUATION-P-CONCRETIZED))
 (178 2 (:REWRITE CLOSED-EQN-RECORD-P-TRUE-CONCRETIZED))
 (144 33 (:REWRITE EQUATION-EQUAL-P-TO-CONSISTENT-EQUATION))
 (144 6 (:DEFINITION SET-UNION))
 (130 34 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (128 128 (:TYPE-PRESCRIPTION <<))
 (128 2 (:REWRITE EVALUATION-EQ-MEMBERP-OF-CORRESPONDING-STATES-2))
 (96 96 (:TYPE-PRESCRIPTION FIND-VARIABLES))
 (96 16 (:REWRITE <<-ASYMMETRIC))
 (90 90 (:REWRITE |Non-numeric x in (+ x y)|))
 (90 90 (:META COLLECT-ADDENDS-THM))
 (80 80 (:TYPE-PRESCRIPTION ORDEREDP))
 (80 4 (:REWRITE PRODUCE-NEXT-STATE-NOT-MEMBERP-VARS-REDUCTION))
 (80 2 (:DEFINITION CORRESPONDING-STATES))
 (72 2 (:DEFINITION CORRESPONDING-STATE))
 (68 68 (:REWRITE SUBSET-FROM-UNION-2))
 (57 57 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (48 48 (:REWRITE <<-TRANSITIVE))
 (41 2 (:DEFINITION EVALUATION-EQ))
 (40 2 (:REWRITE NOT-MEMBERP-TO-CORRESPONDING-STATE))
 (36 2 (:REWRITE ALL-EVALUATIONS-CONSIDERS-AN-EVALUATION-A-MEMBER))
 (32 32 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (30 4 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (20 1 (:REWRITE MEMBERP-OF-NEXT-STATE-FROM-CONSISTENT-EQUATION))
 (20 1 (:REWRITE MEMBERP-NOT-USING-NEXT-STATES))
 (18 2 (:DEFINITION CREATE-NEXT-STATES-OF-P))
 (18 1 (:REWRITE AND-THUS-FOR-VARS-CONE))
 (15 15 (:REWRITE CONSISTENT-P-EQUATION-MEMBERP-REDUCTION))
 (14 14 (:REWRITE EVALUATION-P-ONLY-EVALUATIONS-REDUCTION))
 (12 12 (:REWRITE CONSISTENT-P-EQUATIONS-TO-CONSISTENT-P-EQUATIONS))
 (10 10 (:TYPE-PRESCRIPTION CLOSED-EQN-RECORD-P))
 (8 8 (:TYPE-PRESCRIPTION CORRESPONDING-STATES))
 (7 7 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 (6 6 (:REWRITE CONSISTENT-EQN-RECORD-P-EXPANDED))
 (5 5 (:REWRITE THUS-POLISHED-R-IS-EVALUATION-EQ-TO-S-2))
 (5 5 (:REWRITE NEXT-STATE-IS-OK-FROM-CONSISTENT-EQN))
 (4 4 (:REWRITE THUS-R-IS-EVALUATION-EQ-TO-S))
 (4 4 (:REWRITE EVALUATION-EQ-IS-TRANSITIVE))
 (3 3 (:TYPE-PRESCRIPTION BOOLEANP))
 (2 2 (:REWRITE NEXT-STATE-IS-OK-SUFF))
 (2 2 (:REWRITE EVALUATION-EQ-SUBSET-TO-MEMBER))
 (2 2 (:REWRITE EVALUATION-EQ-MEMBER-SUBSET-REDUCTION))
 (2 2 (:REWRITE EVALUATION-EQ-MEMBER-P-FROM-MEMBERP))
 (2 2 (:REWRITE EVALUATION-EQ-AND-MEMBERP-TO-MEMBERP))
 (2 2 (:REWRITE EVALUATION-EQ-AND-MEMBERP-TO-EVALUATION-EQ-MEMBERP))
 (2 2 (:REWRITE EQUATION-EQUAL-P-TO-CONSISTENT))
 )
(NEXT-STATE-CONE->ORIG-CONCRETIZED
 (695 20 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (540 20 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (480 20 (:DEFINITION ORDEREDP))
 (460 10 (:DEFINITION UNIQUEP))
 (429 3 (:DEFINITION EVALUATION-EQ-MEMBER-P))
 (384 6 (:REWRITE EVALUATION-EQ-MEMBERP-OF-CORRESPONDING-STATES-2))
 (328 16 (:DEFINITION EVALUATION-EQ))
 (302 19 (:DEFINITION EVALUATION-P))
 (284 284 (:REWRITE DEFAULT-CDR))
 (283 43 (:DEFINITION LEN))
 (261 261 (:TYPE-PRESCRIPTION LEN))
 (244 244 (:REWRITE DEFAULT-CAR))
 (240 60 (:REWRITE <<-TRICHOTOMY))
 (240 32 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (240 6 (:DEFINITION CORRESPONDING-STATES))
 (216 6 (:DEFINITION CORRESPONDING-STATE))
 (180 9 (:REWRITE MEMBERP-OF-NEXT-STATE-FROM-CONSISTENT-EQUATION))
 (180 9 (:REWRITE MEMBERP-NOT-USING-NEXT-STATES))
 (173 78 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (168 6 (:REWRITE S-SAME-G-BACK-CHAINING))
 (160 160 (:TYPE-PRESCRIPTION <<))
 (135 15 (:DEFINITION CREATE-NEXT-STATES-OF-P))
 (122 58 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (120 20 (:REWRITE <<-ASYMMETRIC))
 (120 6 (:REWRITE NOT-MEMBERP-TO-CORRESPONDING-STATE))
 (118 118 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (118 118 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (118 118 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (118 118 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (108 6 (:REWRITE ALL-EVALUATIONS-CONSIDERS-AN-EVALUATION-A-MEMBER))
 (106 106 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (106 106 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (106 106 (:META CANCEL-ADDENDS-EQUAL-THM))
 (100 100 (:TYPE-PRESCRIPTION ORDEREDP))
 (88 44 (:REWRITE |Non-numeric y in (+ x y)|))
 (80 20 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (78 78 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (78 78 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (78 78 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (75 5 (:DEFINITION EQUATION-EQUAL-P))
 (60 60 (:REWRITE <<-TRANSITIVE))
 (54 3 (:REWRITE AND-THUS-FOR-VARS-CONE))
 (44 44 (:REWRITE |Non-numeric x in (+ x y)|))
 (44 44 (:META COLLECT-ADDENDS-THM))
 (40 40 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (40 40 (:REWRITE SUBSET-FROM-UNION-2))
 (40 40 (:REWRITE EVALUATION-P-ONLY-EVALUATIONS-REDUCTION))
 (40 5 (:DEFINITION CONS-LIST-P))
 (32 32 (:REWRITE THUS-R-IS-EVALUATION-EQ-TO-S))
 (32 32 (:REWRITE THUS-POLISHED-R-IS-EVALUATION-EQ-TO-S-2))
 (32 32 (:REWRITE EVALUATION-EQ-IS-TRANSITIVE))
 (25 15 (:REWRITE EQUATION-EQUAL-P-TO-CONSISTENT))
 (24 24 (:TYPE-PRESCRIPTION CORRESPONDING-STATES))
 (20 20 (:REWRITE SUBSET-IS-TRANSITIVE))
 (20 20 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (15 15 (:TYPE-PRESCRIPTION NEXT-STATE-IS-OK))
 (15 15 (:REWRITE NEXT-STATE-MEMBER-IMPLIES-CONSISTENT-EQUATION))
 (15 15 (:REWRITE NEXT-STATE-IS-OK-SUFF))
 (15 15 (:REWRITE NEXT-STATE-IS-OK-FROM-CONSISTENT-EQN))
 (10 10 (:REWRITE CONS-LIST-P-SUBSET-REDUCTION))
 (9 9 (:TYPE-PRESCRIPTION BOOLEANP))
 (8 8 (:REWRITE EVALUATION-EQ-SUBSET-SUBSET-REDUCTION))
 (6 6 (:REWRITE EVALUATION-EQ-SUBSET-TO-MEMBER))
 (6 6 (:REWRITE EVALUATION-EQ-MEMBER-SUBSET-REDUCTION))
 (6 6 (:REWRITE EVALUATION-EQ-MEMBER-P-FROM-MEMBERP))
 (6 6 (:REWRITE EVALUATION-EQ-AND-MEMBERP-TO-MEMBERP))
 (6 6 (:REWRITE EVALUATION-EQ-AND-MEMBERP-TO-EVALUATION-EQ-MEMBERP))
 (5 5 (:REWRITE CONS-LIST-P-EQUATION-EQUAL-REDUCTION))
 (3 3 (:TYPE-PRESCRIPTION EVALUATION-EQ-MEMBER-P))
 (3 3 (:REWRITE NEXT-STATE-OF-ORIG-TO-EVALUATION-EQ-MEMBER-P-2))
 )
(AND-FULLY-CONCRETIZED-CONE->ORIG
 (164 1 (:DEFINITION EVALUATION-EQ-MEMBER-P))
 (130 2 (:REWRITE EVALUATION-EQ-MEMBERP-OF-CORRESPONDING-STATES-2))
 (108 4 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (96 6 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (96 4 (:DEFINITION ORDEREDP))
 (80 2 (:DEFINITION CORRESPONDING-STATES))
 (76 2 (:REWRITE ALL-EVALUATIONS-CONSIDERS-AN-EVALUATION-A-MEMBER))
 (72 2 (:DEFINITION CORRESPONDING-STATE))
 (62 1 (:DEFINITION SUBSET))
 (56 2 (:REWRITE S-SAME-G-BACK-CHAINING))
 (50 50 (:REWRITE DEFAULT-CDR))
 (48 12 (:REWRITE <<-TRICHOTOMY))
 (44 44 (:REWRITE DEFAULT-CAR))
 (41 2 (:DEFINITION EVALUATION-EQ))
 (40 2 (:REWRITE NOT-MEMBERP-TO-CORRESPONDING-STATE))
 (39 39 (:TYPE-PRESCRIPTION LEN))
 (39 3 (:DEFINITION EVALUATION-P))
 (38 1 (:REWRITE AND-THUS-FOR-VARS-CONE))
 (36 6 (:DEFINITION LEN))
 (32 32 (:TYPE-PRESCRIPTION <<))
 (30 4 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (24 6 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (24 4 (:REWRITE <<-ASYMMETRIC))
 (23 23 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (23 23 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (23 23 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (23 23 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (20 20 (:TYPE-PRESCRIPTION ORDEREDP))
 (18 18 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (18 18 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (18 18 (:META CANCEL-ADDENDS-EQUAL-THM))
 (18 2 (:DEFINITION CREATE-NEXT-STATES-OF-P))
 (13 13 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (13 13 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (13 13 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (12 12 (:REWRITE SUBSET-FROM-UNION-2))
 (12 12 (:REWRITE <<-TRANSITIVE))
 (12 6 (:REWRITE |Non-numeric y in (+ x y)|))
 (9 9 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (9 9 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (8 8 (:TYPE-PRESCRIPTION CORRESPONDING-STATES))
 (6 6 (:REWRITE THUS-R-IS-EVALUATION-EQ-TO-S))
 (6 6 (:REWRITE THUS-POLISHED-R-IS-EVALUATION-EQ-TO-S-2))
 (6 6 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (6 6 (:REWRITE |Non-numeric x in (+ x y)|))
 (6 6 (:META COLLECT-ADDENDS-THM))
 (6 4 (:REWRITE EQUATION-EQUAL-P-TO-CONSISTENT))
 (3 3 (:TYPE-PRESCRIPTION BOOLEANP))
 (3 3 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 (2 2 (:TYPE-PRESCRIPTION NEXT-STATE-IS-OK))
 (2 2 (:REWRITE NEXT-STATE-MEMBER-IMPLIES-CONSISTENT-EQUATION))
 (2 2 (:REWRITE NEXT-STATE-IS-OK-SUFF))
 (2 2 (:REWRITE NEXT-STATE-IS-OK-FROM-CONSISTENT-EQN))
 (2 2 (:REWRITE EVALUATION-EQ-SUBSET-TO-MEMBER))
 (2 2 (:REWRITE EVALUATION-EQ-SUBSET-SUBSET-REDUCTION))
 (2 2 (:REWRITE EVALUATION-EQ-MEMBER-SUBSET-REDUCTION))
 (2 2 (:REWRITE EVALUATION-EQ-MEMBER-P-FROM-MEMBERP))
 (2 2 (:REWRITE EVALUATION-EQ-AND-MEMBERP-TO-MEMBERP))
 (2 2 (:REWRITE EVALUATION-EQ-AND-MEMBERP-TO-EVALUATION-EQ-MEMBERP))
 (1 1 (:REWRITE NEXT-STATE-OF-ORIG-TO-EVALUATION-EQ-MEMBER-P-2))
 (1 1 (:REWRITE NEXT-STATE-CONE->ORIG-THUS-SETTLED))
 )
(NOT-MEMBER-P-TO-NEXT-STATES
 (48 4 (:REWRITE S-SAME-G-BACK-CHAINING))
 (16 16 (:TYPE-PRESCRIPTION CREATE-NEXT-STATES-OF-P))
 (13 13 (:REWRITE DEFAULT-CAR))
 (11 11 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (11 11 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (11 11 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (11 11 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (9 9 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (9 9 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (9 9 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (9 9 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (9 9 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (9 9 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (9 9 (:META CANCEL-ADDENDS-EQUAL-THM))
 (6 6 (:REWRITE DEFAULT-CDR))
 )
(CREATE-NEXT-STATES-TO-NEXT-STATE-OF-P
 (107 10 (:REWRITE NOT-MEMBER-P-TO-NEXT-STATES))
 (26 26 (:REWRITE DEFAULT-CAR))
 (18 18 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (18 18 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (18 18 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (18 18 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (17 17 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (17 17 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (17 17 (:META CANCEL-ADDENDS-EQUAL-THM))
 (11 11 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (11 11 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (11 11 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (11 11 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (9 9 (:REWRITE DEFAULT-CDR))
 )
(WELL-FORMED-TRANSITION-P-AUX-ORIG->CONE
 (130 12 (:DEFINITION MEMBERP))
 (122 5 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (117 2 (:DEFINITION SUBSET))
 (112 2 (:DEFINITION CREATE-NEXT-STATES))
 (108 4 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (104 5 (:REWRITE SUBSET-IS-TRANSITIVE))
 (104 2 (:REWRITE S-SAME-G-BACK-CHAINING))
 (96 4 (:DEFINITION ORDEREDP))
 (92 2 (:DEFINITION UNIQUEP))
 (52 52 (:TYPE-PRESCRIPTION LEN))
 (48 48 (:REWRITE DEFAULT-CDR))
 (48 12 (:REWRITE <<-TRICHOTOMY))
 (48 8 (:DEFINITION LEN))
 (41 2 (:DEFINITION EVALUATION-EQ))
 (40 40 (:REWRITE DEFAULT-CAR))
 (40 2 (:REWRITE NOT-MEMBER-P-TO-NEXT-STATES))
 (37 3 (:DEFINITION EVALUATION-P))
 (32 32 (:TYPE-PRESCRIPTION <<))
 (30 4 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (30 2 (:DEFINITION ONLY-EVALUATIONS-P))
 (24 4 (:REWRITE <<-ASYMMETRIC))
 (23 23 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (23 23 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (23 23 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (23 23 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (23 13 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (20 20 (:TYPE-PRESCRIPTION ORDEREDP))
 (20 20 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (20 20 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (20 20 (:META CANCEL-ADDENDS-EQUAL-THM))
 (20 5 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (16 8 (:REWRITE |Non-numeric y in (+ x y)|))
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 (13 13 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (13 13 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (12 12 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (12 12 (:REWRITE <<-TRANSITIVE))
 (12 12 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (10 10 (:REWRITE SUBSET-FROM-UNION-2))
 (9 9 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (8 8 (:TYPE-PRESCRIPTION CREATE-NEXT-STATES-OF-P))
 (8 8 (:REWRITE |Non-numeric x in (+ x y)|))
 (8 8 (:META COLLECT-ADDENDS-THM))
 (8 1 (:DEFINITION CONS-LIST-P))
 (6 6 (:REWRITE EVALUATIONP-FOR-SUBSET))
 (5 5 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (5 3 (:REWRITE EQUATION-EQUAL-P-TO-CONSISTENT))
 (4 4 (:REWRITE THUS-R-IS-EVALUATION-EQ-TO-S))
 (4 4 (:REWRITE THUS-POLISHED-R-IS-EVALUATION-EQ-TO-S-2))
 (4 4 (:REWRITE EVALUATION-EQ-IS-TRANSITIVE))
 (1 1 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 (1 1 (:REWRITE NEXT-STATE-CONE->ORIG-CONCRETIZED))
 )
(WELL-FORMED-TRANSITION-P-AUX-CONE->ORIG
 (117 11 (:DEFINITION MEMBERP))
 (112 2 (:DEFINITION CREATE-NEXT-STATES))
 (108 4 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (104 2 (:REWRITE S-SAME-G-BACK-CHAINING))
 (96 4 (:DEFINITION ORDEREDP))
 (92 2 (:DEFINITION UNIQUEP))
 (60 2 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (55 1 (:DEFINITION SUBSET))
 (48 12 (:REWRITE <<-TRICHOTOMY))
 (42 42 (:REWRITE DEFAULT-CDR))
 (41 2 (:DEFINITION EVALUATION-EQ))
 (40 2 (:REWRITE NOT-MEMBER-P-TO-NEXT-STATES))
 (38 38 (:REWRITE DEFAULT-CAR))
 (37 3 (:DEFINITION EVALUATION-P))
 (32 32 (:TYPE-PRESCRIPTION <<))
 (30 4 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (30 2 (:DEFINITION ONLY-EVALUATIONS-P))
 (26 26 (:TYPE-PRESCRIPTION LEN))
 (24 4 (:REWRITE <<-ASYMMETRIC))
 (24 4 (:DEFINITION LEN))
 (23 13 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (21 21 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (21 21 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (21 21 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (21 21 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (20 20 (:TYPE-PRESCRIPTION ORDEREDP))
 (17 17 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (17 17 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (17 17 (:META CANCEL-ADDENDS-EQUAL-THM))
 (15 1 (:DEFINITION EQUATION-EQUAL-P))
 (13 13 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (13 13 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (12 12 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (12 12 (:REWRITE <<-TRANSITIVE))
 (8 8 (:TYPE-PRESCRIPTION CREATE-NEXT-STATES-OF-P))
 (8 4 (:REWRITE |Non-numeric y in (+ x y)|))
 (8 2 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (8 1 (:DEFINITION CONS-LIST-P))
 (6 6 (:REWRITE EVALUATIONP-FOR-SUBSET))
 (6 6 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (5 3 (:REWRITE EQUATION-EQUAL-P-TO-CONSISTENT))
 (4 4 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (4 4 (:REWRITE THUS-R-IS-EVALUATION-EQ-TO-S))
 (4 4 (:REWRITE THUS-POLISHED-R-IS-EVALUATION-EQ-TO-S-2))
 (4 4 (:REWRITE SUBSET-FROM-UNION-2))
 (4 4 (:REWRITE |Non-numeric x in (+ x y)|))
 (4 4 (:REWRITE EVALUATION-EQ-IS-TRANSITIVE))
 (4 4 (:META COLLECT-ADDENDS-THM))
 (2 2 (:REWRITE SUBSET-IS-TRANSITIVE))
 (2 2 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (2 2 (:REWRITE CONS-LIST-P-SUBSET-REDUCTION))
 (1 1 (:REWRITE CONS-LIST-P-EQUATION-EQUAL-REDUCTION))
 )
(WELL-FORMED-TRANSITION-P-AUX-CONE->ORIG-CONCRETIZED)
(ORIG-CONE-CONE-IS-WELL-FORMED-TRANSITION-P
 (40361 2892 (:REWRITE S-SAME-G-BACK-CHAINING))
 (11688 510 (:DEFINITION SET-UNION))
 (9273 9183 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (9183 9183 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (9183 9183 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (9174 9174 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (7676 115 (:DEFINITION CREATE-NEXT-STATES))
 (6904 165 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (6864 146 (:DEFINITION CORRESPONDING-STATES))
 (6424 146 (:DEFINITION CORRESPONDING-STATE))
 (4463 4463 (:REWRITE DEFAULT-CDR))
 (4440 222 (:DEFINITION SET-INTERSECT))
 (4232 4232 (:REWRITE DEFAULT-CAR))
 (3504 146 (:REWRITE NOT-MEMBERP-TO-CORRESPONDING-STATE))
 (3171 151 (:DEFINITION REMOVE-DUPLICATE-OCCURRENCES))
 (3080 1540 (:TYPE-PRESCRIPTION FIND-ALL-VARIABLES))
 (2852 117 (:REWRITE NOT-MEMBER-P-TO-NEXT-STATES))
 (2791 2791 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (2791 2791 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (2791 2791 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (2791 2791 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (2617 58 (:LINEAR LEN-SET-UNION-MORE-THAN-Y))
 (2520 316 (:DEFINITION LEN))
 (2108 2108 (:TYPE-PRESCRIPTION SET-INTERSECT))
 (2025 75 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (1800 75 (:DEFINITION ORDEREDP))
 (1793 1793 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (1793 1793 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (1793 1793 (:META CANCEL-ADDENDS-EQUAL-THM))
 (1619 1619 (:TYPE-PRESCRIPTION LEN))
 (1181 320 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (900 225 (:REWRITE <<-TRICHOTOMY))
 (660 165 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (657 2 (:DEFINITION EVALUATION-EQ-SUBSET-P))
 (632 316 (:REWRITE |Non-numeric y in (+ x y)|))
 (600 600 (:TYPE-PRESCRIPTION <<))
 (580 29 (:DEFINITION ONLY-TRUTH-P))
 (472 472 (:TYPE-PRESCRIPTION CREATE-NEXT-STATES-OF-P))
 (450 75 (:REWRITE <<-ASYMMETRIC))
 (375 375 (:TYPE-PRESCRIPTION ORDEREDP))
 (347 17 (:DEFINITION EVALUATION-P))
 (330 330 (:REWRITE SUBSET-FROM-UNION-2))
 (326 2 (:DEFINITION EVALUATION-EQ-MEMBER-P))
 (316 316 (:REWRITE |Non-numeric x in (+ x y)|))
 (316 316 (:META COLLECT-ADDENDS-THM))
 (312 4 (:REWRITE EVALUATION-EQ-MEMBERP-OF-CORRESPONDING-STATES-2))
 (290 29 (:DEFINITION TRUTHP-LABEL))
 (279 62 (:REWRITE |(equal (if x y z) w)|))
 (276 12 (:DEFINITION EVALUATION-EQ))
 (265 265 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (225 225 (:REWRITE <<-TRANSITIVE))
 (165 165 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (145 4 (:REWRITE ALL-EVALUATIONS-CONSIDERS-AN-EVALUATION-A-MEMBER))
 (121 121 (:REWRITE EQUATION-EQUAL-P-TO-CONSISTENT))
 (103 103 (:REWRITE STRICT-EVALUATION-P-NECC))
 (74 74 (:REWRITE CONS-LIST-P-EQUATION-EQUAL-REDUCTION))
 (73 1 (:REWRITE AND-THUS-FOR-VARS-CONE))
 (71 71 (:REWRITE TRUTHP-LABEL-IS-A-SUBSET))
 (65 65 (:REWRITE SUBSET-IS-TRANSITIVE))
 (65 65 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 (34 34 (:REWRITE EVALUATIONP-FOR-SUBSET))
 (29 29 (:TYPE-PRESCRIPTION TRUTHP-LABEL))
 (29 29 (:REWRITE TRUTHP-LABEL-FROM-ONLY-TRUTHP))
 (24 24 (:REWRITE THUS-R-IS-EVALUATION-EQ-TO-S))
 (24 24 (:REWRITE THUS-POLISHED-R-IS-EVALUATION-EQ-TO-S-2))
 (24 24 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (24 24 (:REWRITE EVALUATION-EQ-IS-TRANSITIVE))
 (24 1 (:REWRITE EVALUATION-EQ-MEMBERP-FROM-ALL-EVALUATIONS-P))
 (8 8 (:REWRITE NEXT-STATE-CONE->ORIG-CONCRETIZED))
 (6 6 (:TYPE-PRESCRIPTION BOOLEANP))
 (4 4 (:REWRITE EVALUATION-EQ-SUBSET-TO-MEMBER))
 (4 4 (:REWRITE EVALUATION-EQ-SUBSET-SUBSET-REDUCTION))
 (4 4 (:REWRITE EVALUATION-EQ-MEMBER-SUBSET-REDUCTION))
 (4 4 (:REWRITE EVALUATION-EQ-MEMBER-P-FROM-MEMBERP))
 (4 4 (:REWRITE EVALUATION-EQ-AND-MEMBERP-TO-MEMBERP))
 (4 4 (:REWRITE EVALUATION-EQ-AND-MEMBERP-TO-EVALUATION-EQ-MEMBERP))
 (2 2 (:TYPE-PRESCRIPTION EVALUATION-EQ-MEMBER-P))
 (2 2 (:REWRITE EVALUATION-EQ-SUBSET-P-ORIG->CONE))
 (1 1 (:REWRITE WELL-FORMED-TRANSITION-P-EXPANDED))
 (1 1 (:REWRITE R-IS-EVALUATION-EQ-MEMBER-P-WITH-RESPECT-TO-STATES))
 (1 1 (:REWRITE R-IS-EVALUATION-EQ-MEMBER-P))
 (1 1 (:REWRITE NEXT-STATE-OF-ORIG-TO-EVALUATION-EQ-MEMBER-P-2))
 (1 1 (:REWRITE NEXT-STATE-OF-ORIG-TO-EVALUATION-EQ-MEMBER-P))
 (1 1 (:REWRITE NEXT-STATE-CONE->ORIG-THUS-SETTLED))
 )
(CONE-ORIG-IS-WELL-FORMED-TRANSITION-P
 (69285 3782 (:REWRITE S-SAME-G-BACK-CHAINING))
 (29448 1282 (:DEFINITION SET-UNION))
 (28497 1357 (:DEFINITION REMOVE-DUPLICATE-OCCURRENCES))
 (28360 1418 (:DEFINITION SET-INTERSECT))
 (26898 572 (:DEFINITION CORRESPONDING-STATES))
 (25168 572 (:DEFINITION CORRESPONDING-STATE))
 (20484 315 (:DEFINITION CREATE-NEXT-STATES))
 (17258 17258 (:REWRITE DEFAULT-CDR))
 (16036 15866 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (15866 15866 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (15866 15866 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (15849 15849 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (13728 572 (:REWRITE NOT-MEMBERP-TO-CORRESPONDING-STATE))
 (11077 11077 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (11077 11077 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (11077 11077 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (11077 11077 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (7689 318 (:REWRITE NOT-MEMBER-P-TO-NEXT-STATES))
 (6481 6481 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (6481 6481 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (6481 6481 (:META CANCEL-ADDENDS-EQUAL-THM))
 (5956 145 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (3680 9 (:DEFINITION EVALUATION-EQ-SUBSET-P))
 (2261 50 (:LINEAR LEN-SET-UNION-MORE-THAN-Y))
 (2172 272 (:DEFINITION LEN))
 (2025 75 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (1800 75 (:DEFINITION ORDEREDP))
 (1647 9 (:DEFINITION EVALUATION-EQ-MEMBER-P))
 (1416 18 (:REWRITE EVALUATION-EQ-MEMBERP-OF-CORRESPONDING-STATES-2))
 (1393 1393 (:TYPE-PRESCRIPTION LEN))
 (1373 1373 (:TYPE-PRESCRIPTION CREATE-NEXT-STATES-OF-P))
 (1216 18 (:REWRITE ALL-EVALUATIONS-CONSIDERS-AN-EVALUATION-A-MEMBER))
 (1015 274 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (900 225 (:REWRITE <<-TRICHOTOMY))
 (763 29 (:DEFINITION EVALUATION-EQ))
 (724 39 (:DEFINITION ONLY-TRUTH-P))
 (600 600 (:TYPE-PRESCRIPTION <<))
 (581 7 (:REWRITE AND-THUS-FOR-VARS-CONE))
 (580 145 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (544 272 (:REWRITE |Non-numeric y in (+ x y)|))
 (450 75 (:REWRITE <<-ASYMMETRIC))
 (390 39 (:DEFINITION TRUTHP-LABEL))
 (375 375 (:TYPE-PRESCRIPTION ORDEREDP))
 (290 290 (:REWRITE SUBSET-FROM-UNION-2))
 (272 272 (:REWRITE |Non-numeric x in (+ x y)|))
 (272 272 (:META COLLECT-ADDENDS-THM))
 (232 50 (:REWRITE |(equal (if x y z) w)|))
 (231 231 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (225 225 (:REWRITE <<-TRANSITIVE))
 (145 145 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (125 125 (:REWRITE EQUATION-EQUAL-P-TO-CONSISTENT))
 (113 113 (:REWRITE STRICT-EVALUATION-P-NECC))
 (111 70 (:REWRITE EVALUATION-EQ-IS-TRANSITIVE))
 (92 92 (:REWRITE EVALUATIONP-FOR-SUBSET))
 (77 77 (:REWRITE CONS-LIST-P-EQUATION-EQUAL-REDUCTION))
 (70 70 (:REWRITE THUS-R-IS-EVALUATION-EQ-TO-S))
 (70 70 (:REWRITE THUS-POLISHED-R-IS-EVALUATION-EQ-TO-S-2))
 (61 61 (:REWRITE TRUTHP-LABEL-IS-A-SUBSET))
 (59 59 (:REWRITE SUBSET-IS-TRANSITIVE))
 (59 59 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 (58 58 (:REWRITE EVALUATION-EQ-SUBSET-REDUCTION))
 (39 39 (:TYPE-PRESCRIPTION TRUTHP-LABEL))
 (39 39 (:REWRITE TRUTHP-LABEL-FROM-ONLY-TRUTHP))
 (27 27 (:TYPE-PRESCRIPTION BOOLEANP))
 (24 1 (:REWRITE WELL-FORMED-TRANSITION-P-AUX-CONE->ORIG-CONCRETIZED))
 (24 1 (:REWRITE WELL-FORMED-TRANSITION-P-AUX-CONE->ORIG))
 (18 18 (:REWRITE EVALUATION-EQ-SUBSET-TO-MEMBER))
 (18 18 (:REWRITE EVALUATION-EQ-SUBSET-SUBSET-REDUCTION))
 (18 18 (:REWRITE EVALUATION-EQ-MEMBER-SUBSET-REDUCTION))
 (18 18 (:REWRITE EVALUATION-EQ-MEMBER-P-FROM-MEMBERP))
 (18 18 (:REWRITE EVALUATION-EQ-AND-MEMBERP-TO-MEMBERP))
 (18 18 (:REWRITE EVALUATION-EQ-AND-MEMBERP-TO-EVALUATION-EQ-MEMBERP))
 (14 14 (:REWRITE NEXT-STATE-CONE->ORIG-CONCRETIZED))
 (9 9 (:TYPE-PRESCRIPTION EVALUATION-EQ-MEMBER-P))
 (7 7 (:REWRITE NEXT-STATE-OF-ORIG-TO-EVALUATION-EQ-MEMBER-P-2))
 (7 7 (:REWRITE NEXT-STATE-CONE->ORIG-THUS-SETTLED))
 (2 2 (:REWRITE R-IS-EVALUATION-EQ-MEMBER-P))
 (1 1 (:REWRITE WELL-FORMED-TRANSITION-P-EXPANDED))
 )
(CONE-OF-INFLUENCE-IS-C-BISIMI-EQUIV
 (14 14 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (14 14 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (14 14 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (14 14 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 )
(RESTRICTED-FORMULA-OF-VARS-IS-ALSO-TRUE-FOR-SUBSET
 (1350 45 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (712 712 (:REWRITE DEFAULT-CDR))
 (690 472 (:REWRITE |Non-numeric y in (+ x y)|))
 (618 618 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (618 618 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (472 472 (:REWRITE |Non-numeric x in (+ x y)|))
 (472 472 (:META COLLECT-ADDENDS-THM))
 (429 429 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (429 429 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (429 429 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (429 429 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (415 415 (:REWRITE DEFAULT-CAR))
 (180 45 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (90 90 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (90 90 (:REWRITE SUBSET-FROM-UNION-2))
 (45 45 (:REWRITE SUBSET-IS-TRANSITIVE))
 (45 45 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 )
(CONE-OF-INFLUENCE-REDUCTION-IS-SOUND
 (88 2 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (42 1 (:REWRITE ORDERED-IMPLIES-UNIQUE))
 (39 1 (:DEFINITION ORDEREDP))
 (23 23 (:TYPE-PRESCRIPTION CONE-VARIABLES))
 (16 2 (:DEFINITION LEN))
 (14 5 (:REWRITE DEFAULT-CDR))
 (13 13 (:TYPE-PRESCRIPTION LEN))
 (12 3 (:REWRITE <<-TRICHOTOMY))
 (12 3 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (8 8 (:TYPE-PRESCRIPTION <<))
 (8 2 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (6 1 (:REWRITE <<-ASYMMETRIC))
 (5 5 (:TYPE-PRESCRIPTION ORDEREDP))
 (5 5 (:TYPE-PRESCRIPTION CREATE-RESTRICTED-VAR-SET))
 (5 2 (:REWRITE DEFAULT-CAR))
 (4 4 (:REWRITE SUBSET-FROM-UNION-2))
 (4 2 (:REWRITE |Non-numeric y in (+ x y)|))
 (3 3 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (3 3 (:REWRITE <<-TRANSITIVE))
 (2 2 (:TYPE-PRESCRIPTION UNIQUEP))
 (2 2 (:REWRITE SUBSET-IS-TRANSITIVE))
 (2 2 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (2 2 (:REWRITE |Non-numeric x in (+ x y)|))
 (2 2 (:META COLLECT-ADDENDS-THM))
 (1 1 (:REWRITE VARIABLES-IN-LABEL-ARE-T-IN-Q))
 (1 1 (:REWRITE STRICT-EVALUATION-P-EXPANDED))
 (1 1 (:REWRITE PROPER-SUBSET-IS-IRREFLEXIVE))
 (1 1 (:REWRITE EVALUATION-EQ-VARS-REDUCTION))
 (1 1 (:REWRITE EQUATION-EQUAL-P-MEMBER-REDUCTION))
 (1 1 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (1 1 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (1 1 (:META CANCEL-ADDENDS-EQUAL-THM))
 )
(CONE-OF-INFLUENCE-REDUCTION-IS-SOUND-GENERALIZED
 (331 1 (:DEFINITION RESTRICTED-FORMULAP))
 (271 19 (:DEFINITION MEMBERP))
 (114 1 (:DEFINITION LTL-VARIABLEP))
 (81 2 (:REWRITE LEN-EQUAL-TO-SET-EQUAL))
 (42 6 (:DEFINITION LEN))
 (40 40 (:META PREFER-POSITIVE-ADDENDS-EQUAL-THM))
 (40 40 (:META CANCEL-FACTORS-GATHER-EXPONENTS-EQUAL-THM))
 (40 40 (:META CANCEL-ADDENDS-EQUAL-THM))
 (35 35 (:REWRITE TRUTHP-LABEL-TO-SUBSET))
 (35 35 (:REWRITE TRANSITION-SUBSET-P-EXPANDED))
 (35 35 (:REWRITE ONLY-TRUTHSP-AND-SUBSET-TO-SUBSET))
 (35 35 (:REWRITE ALL-TRUTHSP-LABEL-EXPANDED))
 (32 32 (:TYPE-PRESCRIPTION LEN))
 (22 22 (:REWRITE DEFAULT-CAR))
 (21 6 (:LINEAR CONSP-TO-LEN-EXPANDED))
 (19 19 (:REWRITE DEFAULT-CDR))
 (16 16 (:TYPE-PRESCRIPTION CONE-VARIABLES))
 (12 6 (:REWRITE |Non-numeric y in (+ x y)|))
 (8 2 (:REWRITE PROPER-SUBSET-IS-STRONGER-THAN-SUBSET))
 (7 1 (:DEFINITION LTL-CONSTANTP))
 (6 6 (:REWRITE |Non-numeric x in (+ x y)|))
 (6 6 (:META COLLECT-ADDENDS-THM))
 (6 2 (:REWRITE CIRCUIT-BISIM-IMPLIES-SAME-LTL-SEMANTICS))
 (5 5 (:TYPE-PRESCRIPTION CREATE-RESTRICTED-VAR-SET))
 (4 4 (:TYPE-PRESCRIPTION PROPER-SUBSET))
 (4 4 (:REWRITE SUBSET-FROM-UNION-2))
 (2 2 (:TYPE-PRESCRIPTION CIRCUIT-MODELP))
 (2 2 (:REWRITE SUBSET-IS-TRANSITIVE))
 (2 2 (:REWRITE PROPER-SUBSET-IS-TRANSITIVE))
 (2 2 (:REWRITE CREATE-KRIPKE-PRODUCES-CIRCUIT-MODEL))
 )
