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 (232 232 (:REWRITE DEFAULT-IMAGPART))
 (232 232 (:REWRITE DEFAULT-DENOMINATOR))
 (232 232 (:REWRITE DEFAULT-COERCE-2))
 (232 232 (:REWRITE DEFAULT-COERCE-1))
 (49 9 (:REWRITE AC-<))
 (32 4 (:REWRITE O-FIRST-EXPT-<))
 (27 9 (:REWRITE O-INFP-O-FINP-O<=))
 (27 9 (:REWRITE DEFUNG::BOOLEAN-EQUAL-REDUCTION))
 (24 8 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (18 18 (:TYPE-PRESCRIPTION BOOLEANP))
 (12 4 (:REWRITE O-FIRST-COEFF-<))
 (9 9 (:REWRITE |a < b & b < c  =>  a < c|))
 )
(T-ENV-P-IMPLIES-REGION-P-GENERALIZE-INEQ
 (3459 3459 (:REWRITE DEFAULT-CDR))
 (2208 736 (:REWRITE DEFUNG::BOOLEAN-EQUAL-REDUCTION))
 (1472 1472 (:TYPE-PRESCRIPTION BOOLEANP))
 (1332 1332 (:REWRITE DEFAULT-CAR))
 (123 123 (:REWRITE ENV-P-WHEN-NOT-CONSP))
 (112 12 (:REWRITE ALT-EVAL-REGION))
 (83 6 (:REWRITE SIMPLIFY-AND-REGIONS-2))
 (83 6 (:REWRITE SIMPLIFY-AND-REGIONS))
 (56 10 (:DEFINITION EVAL-INEQ-LIST))
 (54 18 (:REWRITE POLY-FIX-WHEN-POLY-P))
 (46 6 (:REWRITE EVAL-REGION-NOT-REGION))
 (24 24 (:TYPE-PRESCRIPTION EVAL-INEQ-LIST))
 (20 20 (:TYPE-PRESCRIPTION EVAL-REGION))
 (14 14 (:TYPE-PRESCRIPTION EVAL-INEQ))
 (6 6 (:TYPE-PRESCRIPTION NEGATED-REGION-P))
 )
(GENERALIZE-INEQ)
(INV1-GENERALIZE-INEQ
 (99695 2467 (:DEFINITION GET-BINDING))
 (98979 10345 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (93832 18776 (:REWRITE ACL2-NUMBERP-X))
 (79959 2467 (:REWRITE VARID-FIX-VARID))
 (77492 2467 (:REWRITE VARID-P-OF-CAR-WHEN-VARID-LISTP))
 (67624 2467 (:REWRITE VARID-LISTP-OF-CDR-WHEN-VARID-LISTP))
 (56940 14235 (:REWRITE RATIONALP-X))
 (32380 10332 (:REWRITE DEFUNG::BOOLEAN-EQUAL-REDUCTION))
 (22364 5591 (:REWRITE O-P-O-INFP-CAR))
 (18758 18758 (:TYPE-PRESCRIPTION BOOLEANP))
 (15451 5153 (:REWRITE POLY-EVAL-CONST-POLY))
 (14478 10332 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (14295 14295 (:REWRITE REDUCE-INTEGERP-+))
 (14295 14295 (:REWRITE INTEGERP-MINUS-X))
 (14295 14295 (:META META-INTEGERP-CORRECT))
 (14235 14235 (:REWRITE REDUCE-RATIONALP-+))
 (14235 14235 (:REWRITE REDUCE-RATIONALP-*))
 (14235 14235 (:REWRITE RATIONALP-MINUS-X))
 (14235 14235 (:META META-RATIONALP-CORRECT))
 (12335 2467 (:REWRITE WF-BINDING-FIX-WF-BINDING))
 (10357 10351 (:REWRITE |(equal (- x) (- y))|))
 (10355 10351 (:REWRITE |(equal (/ x) (/ y))|))
 (10354 10345 (:REWRITE |(equal c (- x))|))
 (10351 10351 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (10351 10351 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (10351 10351 (:REWRITE |(equal c (/ x))|))
 (10351 10345 (:REWRITE |(equal (- x) c)|))
 (10345 10345 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (10298 10298 (:TYPE-PRESCRIPTION NOT-CONSTP))
 (9951 1844 (:REWRITE SIMPLIFY-SUMS-<))
 (7611 7611 (:REWRITE EVAL-POLY-CONST-DIFFERENCE))
 (6107 1949 (:REWRITE DEFAULT-LESS-THAN-2))
 (6052 1949 (:REWRITE DEFAULT-LESS-THAN-1))
 (5591 5591 (:REWRITE O-P-DEF-O-FINP-1))
 (4934 4934 (:REWRITE VARID-LISTP-WHEN-NOT-CONSP))
 (4286 60 (:REWRITE DEFUNG::NATP-FIX))
 (4074 60 (:DEFINITION NATP))
 (3924 1308 (:REWRITE POLY-FIX-WHEN-POLY-P))
 (3196 3196 (:TYPE-PRESCRIPTION BINDING-P))
 (2819 1907 (:REWRITE |(< (- x) c)|))
 (2467 2467 (:REWRITE WF-BINDING-P-OF-CAR-WHEN-ENV-P))
 (1949 1949 (:REWRITE THE-FLOOR-BELOW))
 (1949 1949 (:REWRITE THE-FLOOR-ABOVE))
 (1929 1907 (:REWRITE |(< c (- x))|))
 (1913 1913 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (1913 1913 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (1913 1913 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (1913 1913 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (1913 1913 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (1913 1913 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (1913 1913 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (1913 1913 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (1913 1913 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (1913 1913 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (1913 1913 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (1913 1913 (:REWRITE |(< (/ x) (/ y))|))
 (1913 1913 (:REWRITE |(< (- x) (- y))|))
 (1880 1880 (:REWRITE INTEGERP-<-CONSTANT))
 (1880 1880 (:REWRITE CONSTANT-<-INTEGERP))
 (1844 1844 (:REWRITE >-ALL-IS-GREATER-THAN-MEMBERS-HYPS))
 (1508 1508 (:REWRITE >=ALL-MEMBER-HYPS))
 (825 825 (:REWRITE ENV-P-WHEN-NOT-CONSP))
 (799 799 (:REWRITE |(equal x (if a b c))|))
 (799 799 (:REWRITE |(equal (if a b c) x)|))
 (676 2 (:REWRITE INV2B-NORMALIZE-EQUAL-0))
 (668 2 (:REWRITE INV2A-NORMALIZE-EQUAL-0))
 (495 193 (:REWRITE DEFAULT-PLUS-2))
 (354 193 (:REWRITE DEFAULT-PLUS-1))
 (340 110 (:REWRITE |(< (/ x) 0)|))
 (218 6 (:REWRITE |(<= x (/ y)) with (< y 0)|))
 (218 6 (:REWRITE |(<= x (/ y)) with (< 0 y)|))
 (218 6 (:REWRITE |(<= (/ x) y) with (< x 0)|))
 (218 6 (:REWRITE |(<= (/ x) y) with (< 0 x)|))
 (218 6 (:REWRITE |(< x (/ y)) with (< y 0)|))
 (218 6 (:REWRITE |(< x (/ y)) with (< 0 y)|))
 (218 6 (:REWRITE |(< (/ x) y) with (< x 0)|))
 (218 6 (:REWRITE |(< (/ x) y) with (< 0 x)|))
 (171 27 (:REWRITE |(integerp (- x))|))
 (138 75 (:REWRITE O-INFP->NEQ-0))
 (110 110 (:REWRITE |(< (* x y) 0)|))
 (106 2 (:REWRITE INV2A-AND-REGIONS))
 (98 94 (:REWRITE |(< 0 (/ x))|))
 (94 94 (:REWRITE |(< 0 (* x y))|))
 (78 78 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (78 78 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (78 52 (:REWRITE DEFAULT-MINUS))
 (75 75 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (75 75 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (75 75 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (72 2 (:REWRITE INV2B-AND-REGIONS))
 (64 48 (:REWRITE DEFAULT-TIMES-2))
 (64 48 (:REWRITE DEFAULT-TIMES-1))
 (60 60 (:TYPE-PRESCRIPTION NATP))
 (48 27 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (27 27 (:REWRITE |(- (- x))|))
 (27 27 (:REWRITE |(+ c (+ d x))|))
 (25 25 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (17 17 (:REWRITE |(< y (+ (- c) x))|))
 (17 17 (:REWRITE |(< x (+ c/d y))|))
 (17 17 (:REWRITE |(+ x (if a b c))|))
 (16 12 (:REWRITE DEFAULT-DIVIDE))
 (14 14 (:REWRITE |(equal (+ (- c) x) y)|))
 (14 6 (:REWRITE |(equal x (/ y))|))
 (10 6 (:REWRITE |(not (equal x (/ y)))|))
 (8 8 (:REWRITE |(+ (if a b c) x)|))
 (6 6 (:TYPE-PRESCRIPTION O-FINP))
 (6 6 (:REWRITE INTEGERP-/))
 (6 2 (:REWRITE O-FIRST-EXPT-O-INFP))
 (4 4 (:REWRITE-QUOTED-CONSTANT VARID-LIST-FIX-UNDER-VARID-LIST-EQUIV))
 (4 4 (:REWRITE-QUOTED-CONSTANT PAIR-LIST-FIX-UNDER-PAIR-LIST-EQUIV))
 (4 4 (:REWRITE-QUOTED-CONSTANT ENV-FIX-TYPE-UNDER-ENV-FIX-EQUIV))
 (4 2 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (2 2 (:REWRITE |(- (if a b c))|))
 )
(T-ENV-P-IMPLIES-WF-REGION-P-GENERALIZE-INEQ
 (378 1 (:DEFINITION GENERALIZE-INEQ))
 (90 18 (:REWRITE ACL2-NUMBERP-X))
 (90 9 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (76 76 (:REWRITE DEFAULT-CDR))
 (36 9 (:REWRITE RATIONALP-X))
 (27 9 (:REWRITE DEFUNG::BOOLEAN-EQUAL-REDUCTION))
 (26 26 (:REWRITE DEFAULT-CAR))
 (24 6 (:DEFINITION POLY-FIX!))
 (18 18 (:TYPE-PRESCRIPTION BOOLEANP))
 (18 9 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (18 6 (:REWRITE POLY-FIX-WHEN-POLY-P))
 (14 2 (:REWRITE EVAL-REGION-NOT-REGION))
 (13 2 (:REWRITE SIMPLIFY-AND-REGIONS-2))
 (13 2 (:REWRITE SIMPLIFY-AND-REGIONS))
 (12 12 (:TYPE-PRESCRIPTION POLY-P))
 (9 9 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (9 9 (:REWRITE REDUCE-RATIONALP-+))
 (9 9 (:REWRITE REDUCE-RATIONALP-*))
 (9 9 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (9 9 (:REWRITE REDUCE-INTEGERP-+))
 (9 9 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (9 9 (:REWRITE RATIONALP-MINUS-X))
 (9 9 (:REWRITE INTEGERP-MINUS-X))
 (9 9 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (9 9 (:REWRITE |(equal c (/ x))|))
 (9 9 (:REWRITE |(equal c (- x))|))
 (9 9 (:REWRITE |(equal (/ x) c)|))
 (9 9 (:REWRITE |(equal (/ x) (/ y))|))
 (9 9 (:REWRITE |(equal (- x) c)|))
 (9 9 (:REWRITE |(equal (- x) (- y))|))
 (9 9 (:META META-RATIONALP-CORRECT))
 (9 9 (:META META-INTEGERP-CORRECT))
 (6 6 (:TYPE-PRESCRIPTION EVAL-INEQ))
 (4 4 (:TYPE-PRESCRIPTION EVAL-REGION))
 (2 2 (:REWRITE T-ENV-P-IMPLIES-REGION-P-GENERALIZE-INEQ))
 (1 1 (:REWRITE ENV-P-WHEN-NOT-CONSP))
 )
(INV2-GENERALIZE-INEQ
 (147884 15488 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (138634 27730 (:REWRITE ACL2-NUMBERP-X))
 (100236 4479 (:DEFINITION GET-BINDING))
 (91080 22770 (:REWRITE RATIONALP-X))
 (58257 4479 (:REWRITE VARID-FIX-VARID))
 (53778 4479 (:REWRITE VARID-P-OF-CAR-WHEN-VARID-LISTP))
 (49171 15444 (:REWRITE DEFUNG::BOOLEAN-EQUAL-REDUCTION))
 (40224 10056 (:REWRITE O-P-O-INFP-CAR))
 (35862 4479 (:REWRITE VARID-LISTP-OF-CDR-WHEN-VARID-LISTP))
 (28542 4479 (:REWRITE WF-BINDING-FIX-WF-BINDING))
 (27722 27722 (:TYPE-PRESCRIPTION BOOLEANP))
 (27393 9159 (:REWRITE POLY-EVAL-CONST-POLY))
 (22956 15444 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (22914 22914 (:REWRITE REDUCE-INTEGERP-+))
 (22914 22914 (:REWRITE INTEGERP-MINUS-X))
 (22914 22914 (:META META-INTEGERP-CORRECT))
 (22770 22770 (:REWRITE REDUCE-RATIONALP-+))
 (22770 22770 (:REWRITE REDUCE-RATIONALP-*))
 (22770 22770 (:REWRITE RATIONALP-MINUS-X))
 (22770 22770 (:META META-RATIONALP-CORRECT))
 (18234 18234 (:TYPE-PRESCRIPTION NOT-CONSTP))
 (18110 3295 (:REWRITE SIMPLIFY-SUMS-<))
 (15530 15494 (:REWRITE |(equal (- x) (- y))|))
 (15524 15488 (:REWRITE |(equal (- x) c)|))
 (15506 15488 (:REWRITE |(equal c (- x))|))
 (15498 15494 (:REWRITE |(equal (/ x) (/ y))|))
 (15494 15494 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (15494 15494 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (15494 15494 (:REWRITE |(equal c (/ x))|))
 (15488 15488 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (13783 13783 (:REWRITE EVAL-POLY-CONST-DIFFERENCE))
 (11111 81 (:REWRITE INV2B-AND-REGIONS))
 (10983 3437 (:REWRITE DEFAULT-LESS-THAN-2))
 (10881 3437 (:REWRITE DEFAULT-LESS-THAN-1))
 (10056 10056 (:REWRITE O-P-DEF-O-FINP-1))
 (9308 144 (:REWRITE DEFUNG::NATP-FIX))
 (8958 8958 (:REWRITE VARID-LISTP-WHEN-NOT-CONSP))
 (8760 144 (:DEFINITION NATP))
 (7055 7055 (:TYPE-PRESCRIPTION BINDING-P))
 (6528 4479 (:REWRITE WF-BINDING-P-OF-CAR-WHEN-ENV-P))
 (6390 2130 (:REWRITE POLY-FIX-WHEN-POLY-P))
 (6041 3395 (:REWRITE |(< (- x) c)|))
 (3439 3395 (:REWRITE |(< c (- x))|))
 (3437 3437 (:REWRITE THE-FLOOR-BELOW))
 (3437 3437 (:REWRITE THE-FLOOR-ABOVE))
 (3401 3401 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (3401 3401 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (3401 3401 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (3401 3401 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (3401 3401 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (3401 3401 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (3401 3401 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (3401 3401 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (3401 3401 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (3401 3401 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (3401 3401 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (3401 3401 (:REWRITE |(< (/ x) (/ y))|))
 (3401 3401 (:REWRITE |(< (- x) (- y))|))
 (3317 3317 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (3317 3317 (:REWRITE INTEGERP-<-CONSTANT))
 (3317 3317 (:REWRITE CONSTANT-<-INTEGERP))
 (3295 3295 (:REWRITE >-ALL-IS-GREATER-THAN-MEMBERS-HYPS))
 (2630 2595 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (2573 2573 (:REWRITE >=ALL-MEMBER-HYPS))
 (2049 683 (:REWRITE BODY-IMPLIES-WF-BINDING-P))
 (1628 1628 (:REWRITE ENV-P-WHEN-NOT-CONSP))
 (1486 1486 (:REWRITE |(equal x (if a b c))|))
 (1486 1486 (:REWRITE |(equal (if a b c) x)|))
 (1321 472 (:REWRITE DEFAULT-PLUS-2))
 (953 472 (:REWRITE DEFAULT-PLUS-1))
 (706 706 (:REWRITE T-ENV-P-IMPLIES-REGION-P-GENERALIZE-INEQ))
 (528 78 (:REWRITE |(integerp (- x))|))
 (426 196 (:REWRITE |(< (/ x) 0)|))
 (243 159 (:REWRITE DEFAULT-MINUS))
 (218 6 (:REWRITE |(<= x (/ y)) with (< y 0)|))
 (218 6 (:REWRITE |(<= x (/ y)) with (< 0 y)|))
 (218 6 (:REWRITE |(<= (/ x) y) with (< x 0)|))
 (218 6 (:REWRITE |(<= (/ x) y) with (< 0 x)|))
 (218 6 (:REWRITE |(< x (/ y)) with (< y 0)|))
 (218 6 (:REWRITE |(< x (/ y)) with (< 0 y)|))
 (218 6 (:REWRITE |(< (/ x) y) with (< x 0)|))
 (218 6 (:REWRITE |(< (/ x) y) with (< 0 x)|))
 (196 196 (:REWRITE |(< (* x y) 0)|))
 (158 154 (:REWRITE |(< 0 (/ x))|))
 (154 154 (:REWRITE |(< 0 (* x y))|))
 (150 78 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (144 144 (:TYPE-PRESCRIPTION NATP))
 (138 138 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (138 138 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (112 112 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (112 112 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (98 55 (:REWRITE O-INFP->NEQ-0))
 (78 78 (:REWRITE |(- (- x))|))
 (64 48 (:REWRITE DEFAULT-TIMES-2))
 (64 48 (:REWRITE DEFAULT-TIMES-1))
 (59 59 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (58 58 (:REWRITE |(+ x (if a b c))|))
 (55 55 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (52 52 (:REWRITE |(+ c (+ d x))|))
 (47 47 (:REWRITE |(equal (+ (- c) x) y)|))
 (32 32 (:REWRITE WF-REGION-P-IMPLIES-WF-REGION-P-NOT-REGION))
 (28 28 (:REWRITE |(+ (if a b c) x)|))
 (24 24 (:REWRITE |(< y (+ (- c) x))|))
 (24 24 (:REWRITE |(< x (+ c/d y))|))
 (16 12 (:REWRITE DEFAULT-DIVIDE))
 (14 6 (:REWRITE |(equal x (/ y))|))
 (10 6 (:REWRITE |(not (equal x (/ y)))|))
 (6 6 (:TYPE-PRESCRIPTION O-FINP))
 (6 6 (:REWRITE INTEGERP-/))
 (6 2 (:REWRITE O-FIRST-EXPT-O-INFP))
 (4 4 (:REWRITE-QUOTED-CONSTANT VARID-LIST-FIX-UNDER-VARID-LIST-EQUIV))
 (4 4 (:REWRITE-QUOTED-CONSTANT PAIR-LIST-FIX-UNDER-PAIR-LIST-EQUIV))
 (4 4 (:REWRITE-QUOTED-CONSTANT ENV-FIX-TYPE-UNDER-ENV-FIX-EQUIV))
 (4 4 (:REWRITE |(- (if a b c))|))
 (4 2 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 )
