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 (2 2 (:REWRITE |(equal x (/ y))|))
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 )
(NOT-IN-SORTED-LIST
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 (648 36 (:REWRITE NTH-IN-NUMBER-LISTP))
 (630 42 (:DEFINITION NUMBER-LISTP))
 (557 81 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (496 64 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (428 305 (:REWRITE DEFAULT-PLUS-2))
 (426 3 (:REWRITE NON-EMPTY-LEN))
 (363 363 (:REWRITE THE-FLOOR-BELOW))
 (363 363 (:REWRITE THE-FLOOR-ABOVE))
 (318 305 (:REWRITE DEFAULT-PLUS-1))
 (294 6 (:REWRITE LITERAL-LISTP-TRUE-LISTP))
 (292 284 (:REWRITE DEFAULT-CDR))
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 (265 265 (:REWRITE REDUCE-INTEGERP-+))
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 (81 81 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
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 (67 67 (:REWRITE |(equal (/ x) (/ y))|))
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 (64 64 (:REWRITE |(equal c (- x))|))
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 (43 43 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
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(SLICE-BOUNDS
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 (126 14 (:REWRITE ACL2-NUMBERP-X))
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 (98 2 (:REWRITE LITERAL-LISTP-TRUE-LISTP))
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 (60 6 (:DEFINITION LITERALP))
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 (56 14 (:REWRITE RATIONALP-X))
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 (36 2 (:REWRITE NUMBER-LISTP-TRUE-LISTP))
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 (8 8 (:TYPE-PRESCRIPTION VALUEP))
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 (1 1 (:REWRITE DEFAULT-PLUS-1))
 (1 1 (:REWRITE |(< 0 (/ x))|))
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(SLICE-LEN-LOW
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 (163 10 (:REWRITE NUMBER-LISTP-TRUE-LISTP))
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 (77 1 (:REWRITE NON-EMPTY-LEN))
 (66 13 (:REWRITE DEFAULT-LESS-THAN-2))
 (45 45 (:TYPE-PRESCRIPTION NUMBER-LISTP))
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 (2 2 (:REWRITE |(< 0 (/ x))|))
 (2 2 (:REWRITE |(< 0 (* x y))|))
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(CAR-SLICE
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(SLICE-APPEND1
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 (270 270 (:TYPE-PRESCRIPTION NUMBER-LISTP))
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 (110 22 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 2))
 (110 22 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 3))
 (110 22 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 2))
 (68 17 (:REWRITE |(* y x)|))
 (50 2 (:LINEAR LINEAR-FLOOR-BOUNDS-3))
 (32 32 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (31 31 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (31 31 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (31 31 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (31 31 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (10 2 (:REWRITE |(+ y x)|))
 (7 7 (:REWRITE DEFAULT-FLOOR-2))
 (7 7 (:REWRITE DEFAULT-FLOOR-1))
 (7 7 (:REWRITE |(floor x 2)| . 2))
 (4 4 (:REWRITE DEFAULT-PLUS-2))
 (4 4 (:REWRITE DEFAULT-PLUS-1))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2 2 (:REWRITE NORMALIZE-ADDENDS))
 (1 1 (:REWRITE REDUCE-INTEGERP-+))
 (1 1 (:REWRITE INTEGERP-MINUS-X))
 (1 1 (:META META-INTEGERP-CORRECT))
 )
(HIGH-LOW-KLUDGE4
 (34168 183 (:REWRITE HIGH-LOW-KLUDGE2))
 (14286 183 (:REWRITE THE-FLOOR-BELOW))
 (12400 40 (:LINEAR MOD-BOUNDS-1))
 (12195 5 (:REWRITE |(floor (+ x y) z) where (< 0 z)| . 3))
 (10710 5 (:REWRITE |(floor (+ x y) z) where (< 0 z)| . 2))
 (4156 4156 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (4156 4156 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (4156 4156 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (3180 60 (:REWRITE CANCEL-MOD-+))
 (2076 351 (:REWRITE INTEGERP-MINUS-X))
 (1709 1709 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (1709 1709 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (1709 1709 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (1709 1709 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (1660 60 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (1610 60 (:REWRITE MOD-X-Y-=-X . 3))
 (1317 162 (:REWRITE |(* (- x) y)|))
 (1225 245 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (1225 245 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (1225 245 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (1225 245 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (1129 93 (:TYPE-PRESCRIPTION FLOOR-ZERO . 2))
 (1118 170 (:REWRITE DEFAULT-PLUS-2))
 (1110 60 (:REWRITE MOD-ZERO . 3))
 (1080 60 (:REWRITE MOD-X-Y-=-X . 4))
 (1034 986 (:REWRITE DEFAULT-TIMES-2))
 (986 986 (:REWRITE DEFAULT-TIMES-1))
 (960 60 (:REWRITE |(mod x 2)| . 2))
 (872 10 (:REWRITE FLOOR-ZERO . 3))
 (866 170 (:REWRITE DEFAULT-PLUS-1))
 (847 183 (:REWRITE DEFAULT-LESS-THAN-1))
 (805 93 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 1))
 (805 93 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 1))
 (805 93 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 1))
 (776 182 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (771 155 (:REWRITE DEFAULT-MINUS))
 (770 10 (:REWRITE CANCEL-FLOOR-+))
 (745 245 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (693 154 (:REWRITE |(- (* c x))|))
 (660 60 (:REWRITE DEFAULT-MOD-RATIO))
 (640 35 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (626 626 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (580 60 (:REWRITE MOD-ZERO . 4))
 (465 93 (:TYPE-PRESCRIPTION FLOOR-ZERO . 3))
 (465 93 (:TYPE-PRESCRIPTION FLOOR-ZERO . 1))
 (465 93 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 3))
 (465 93 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 2))
 (465 93 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 3))
 (465 93 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 2))
 (465 93 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 3))
 (465 93 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 3))
 (465 93 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 2))
 (441 183 (:REWRITE DEFAULT-LESS-THAN-2))
 (440 20 (:LINEAR MOD-BOUNDS-3))
 (437 2 (:REWRITE FLOOR-=-X/Y . 4))
 (433 13 (:REWRITE |(floor x 2)| . 2))
 (400 36 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (390 10 (:REWRITE FLOOR-=-X/Y . 2))
 (370 10 (:REWRITE FLOOR-=-X/Y . 3))
 (349 13 (:REWRITE DEFAULT-FLOOR-RATIO))
 (340 10 (:REWRITE FLOOR-X-Y-=-1 . 2))
 (316 28 (:REWRITE SUM-IS-EVEN . 2))
 (300 60 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (300 60 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (300 60 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (300 60 (:REWRITE MOD-X-Y-=-X . 2))
 (300 60 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (300 60 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (300 60 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (300 60 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (299 10 (:REWRITE FLOOR-ZERO . 4))
 (285 5 (:LINEAR LINEAR-FLOOR-BOUNDS-3))
 (276 276 (:REWRITE REDUCE-INTEGERP-+))
 (276 276 (:META META-INTEGERP-CORRECT))
 (265 5 (:LINEAR LINEAR-FLOOR-BOUNDS-2))
 (260 60 (:REWRITE MOD-CANCEL-*-CONST))
 (245 245 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (245 245 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (245 245 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (245 245 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (245 245 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (245 245 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (245 245 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (200 40 (:LINEAR MOD-BOUNDS-2))
 (197 2 (:REWRITE |(equal (floor (+ x y) z) x)|))
 (186 182 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (186 182 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (183 183 (:REWRITE THE-FLOOR-ABOVE))
 (182 182 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (182 182 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (182 182 (:REWRITE INTEGERP-<-CONSTANT))
 (182 182 (:REWRITE CONSTANT-<-INTEGERP))
 (182 182 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (182 182 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (182 182 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (182 182 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (182 182 (:REWRITE |(< c (- x))|))
 (182 182 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (182 182 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (182 182 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (182 182 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (182 182 (:REWRITE |(< (/ x) (/ y))|))
 (182 182 (:REWRITE |(< (- x) c)|))
 (182 182 (:REWRITE |(< (- x) (- y))|))
 (174 10 (:REWRITE FLOOR-ZERO . 5))
 (171 2 (:REWRITE EVEN-AND-ODD-ALTERNATE))
 (127 31 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (120 39 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (104 104 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (89 8 (:REWRITE |(floor (+ x r) i)|))
 (87 87 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (76 12 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 1))
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 (60 60 (:REWRITE DEFAULT-MOD-2))
 (60 60 (:REWRITE DEFAULT-MOD-1))
 (60 60 (:REWRITE |(mod x 2)| . 1))
 (60 60 (:REWRITE |(mod x (- y))| . 3))
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 (60 60 (:REWRITE |(mod x (- y))| . 1))
 (60 60 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (60 60 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
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 (60 60 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
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 (50 10 (:REWRITE FLOOR-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (50 10 (:REWRITE |(floor (* x (/ y)) z) not rewriting-goal-literal|))
 (46 10 (:REWRITE FLOOR-CANCEL-*-CONST))
 (45 5 (:REWRITE |(floor (+ x y) z) where (< z 0)| . 3))
 (45 5 (:REWRITE |(floor (+ x y) z) where (< z 0)| . 2))
 (36 36 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (36 36 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (36 36 (:REWRITE |(equal c (/ x))|))
 (36 36 (:REWRITE |(equal c (- x))|))
 (36 36 (:REWRITE |(equal (/ x) c)|))
 (36 36 (:REWRITE |(equal (/ x) (/ y))|))
 (36 36 (:REWRITE |(equal (- x) c)|))
 (36 36 (:REWRITE |(equal (- x) (- y))|))
 (32 16 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
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 (31 31 (:REWRITE |(< 0 (/ x))|))
 (31 31 (:REWRITE |(< 0 (* x y))|))
 (29 29 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (29 29 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (27 27 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (25 25 (:REWRITE |(< (+ c/d x) y)|))
 (25 25 (:REWRITE |(< (+ (- c) x) y)|))
 (18 18 (:TYPE-PRESCRIPTION NATP))
 (13 13 (:REWRITE DEFAULT-FLOOR-2))
 (13 13 (:REWRITE DEFAULT-FLOOR-1))
 (12 1 (:REWRITE HIGH-LOW-KLUDGE3))
 (11 11 (:TYPE-PRESCRIPTION ABS))
 (10 10 (:REWRITE FOLD-CONSTS-IN-+))
 (10 10 (:REWRITE FLOOR-CANCEL-*-REWRITING-GOAL-LITERAL))
 (10 10 (:REWRITE |(floor x (- y))| . 2))
 (10 10 (:REWRITE |(floor x (- y))| . 1))
 (10 10 (:REWRITE |(floor x (* y (/ z))) rewriting-goal-literal|))
 (10 10 (:REWRITE |(floor x (* y (/ z))) not rewriting-goal-literal|))
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 (10 10 (:REWRITE |(floor (* x (/ y)) z) rewriting-goal-literal|))
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 (4 4 (:REWRITE |(< (* (/ x) y) 1) with (< 0 x)|))
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 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (3 3 (:REWRITE |(< (/ x) 0)|))
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(HIGH-LOW-KLUDGE4-COROLLARY
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 (750 6 (:LINEAR FLR-HALF-LEMMA))
 (157 49 (:REWRITE SIMPLIFY-SUMS-<))
 (143 6 (:LINEAR FLR-LESSP))
 (116 49 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (103 8 (:REWRITE HIGH-LOW-KLUDGE3))
 (88 2 (:REWRITE FLR-POSP))
 (70 49 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (68 20 (:REWRITE NORMALIZE-ADDENDS))
 (63 50 (:REWRITE DEFAULT-LESS-THAN-1))
 (58 50 (:REWRITE DEFAULT-LESS-THAN-2))
 (56 46 (:REWRITE DEFAULT-PLUS-1))
 (54 54 (:TYPE-PRESCRIPTION NATP))
 (53 46 (:REWRITE DEFAULT-PLUS-2))
 (50 50 (:REWRITE THE-FLOOR-BELOW))
 (50 50 (:REWRITE THE-FLOOR-ABOVE))
 (50 50 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (50 50 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (50 50 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (50 50 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (50 50 (:REWRITE INTEGERP-<-CONSTANT))
 (50 50 (:REWRITE CONSTANT-<-INTEGERP))
 (50 50 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (50 50 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (50 50 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (50 50 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (50 50 (:REWRITE |(< c (- x))|))
 (50 50 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (50 50 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (50 50 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (50 50 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (50 50 (:REWRITE |(< (/ x) (/ y))|))
 (50 50 (:REWRITE |(< (- x) c)|))
 (50 50 (:REWRITE |(< (- x) (- y))|))
 (38 12 (:REWRITE |(equal (/ x) c)|))
 (17 3 (:REWRITE FLR-NATP))
 (17 1 (:REWRITE |(+ (+ x y) z)|))
 (16 8 (:REWRITE BUBBLE-DOWN-+-MATCH-1))
 (14 14 (:DEFINITION FIX))
 (13 1 (:REWRITE |(+ y (+ x z))|))
 (12 12 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (12 12 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (12 12 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (12 12 (:REWRITE |(equal c (/ x))|))
 (12 12 (:REWRITE |(equal (/ x) (/ y))|))
 (12 12 (:REWRITE |(equal (- x) (- y))|))
 (12 10 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (12 1 (:REWRITE HIGH-LOW-KLUDGE1))
 (10 10 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (10 10 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (10 10 (:REWRITE |(equal c (- x))|))
 (10 10 (:REWRITE |(equal (- x) c)|))
 (10 10 (:REWRITE |(< (+ c/d x) y)|))
 (10 10 (:REWRITE |(< (+ (- c) x) y)|))
 (8 8 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (8 8 (:REWRITE |(+ x (- x))|))
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 (6 6 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (6 6 (:REWRITE |(< (/ x) 0)|))
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 (3 3 (:REWRITE |(< y (+ (- c) x))|))
 (3 3 (:REWRITE |(< x (+ c/d y))|))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (2 2 (:REWRITE REDUCE-INTEGERP-+))
 (2 2 (:REWRITE INTEGERP-MINUS-X))
 (2 2 (:REWRITE FOLD-CONSTS-IN-+))
 (2 2 (:REWRITE DEFAULT-DIVIDE))
 (2 2 (:REWRITE |(not (equal x (/ y)))|))
 (2 2 (:REWRITE |(equal x (/ y))|))
 (2 2 (:REWRITE |(equal (+ (- c) x) y)|))
 (2 2 (:REWRITE |(/ (/ x))|))
 (2 2 (:REWRITE |(+ c (+ d x))|))
 (2 2 (:META META-INTEGERP-CORRECT))
 (1 1 (:REWRITE |(+ 0 x)|))
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(HIGH-LOW-KLUDGE5
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 (53454 659 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (53198 110 (:REWRITE |(< (+ c/d x) y)|))
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 (44108 18 (:REWRITE |(floor (+ x y) z) where (< 0 z)| . 3))
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 (35180 1 (:REWRITE |(< x (if a b c))|))
 (29783 660 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (15825 1 (:REWRITE |(floor (+ 1 x) y)|))
 (12185 229 (:REWRITE CANCEL-MOD-+))
 (11265 11265 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (11265 11265 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (11265 11265 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (7420 1164 (:REWRITE INTEGERP-MINUS-X))
 (6333 229 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (6152 229 (:REWRITE MOD-X-Y-=-X . 3))
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 (4818 4818 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (4818 4818 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (4818 4818 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
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 (2142 1 (:REWRITE |(mod (+ x y) z) where (<= 0 z)| . 2))
 (2131 23 (:REWRITE CANCEL-FLOOR-+))
 (2055 2055 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
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 (953 953 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
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(NATP-LESS-KLUDGE)
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(FLR-LOW-HIGH-EQUAL
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(FLR-NATP-COROLLARY
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(FLR-BOUNDS
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(FLR-X-X-PLUS-1
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 (2880 9 (:REWRITE ZP-OPEN))
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 (2118 876 (:REWRITE |(equal (/ x) c)|))
 (1946 14 (:REWRITE NTH-IN-NUMBER-LISTP))
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 (1752 772 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
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 (1462 14 (:REWRITE |(equal (+ (- c) x) y)|))
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 (1158 1158 (:REWRITE THE-FLOOR-ABOVE))
 (1100 116 (:REWRITE ACL2-NUMBERP-X))
 (1083 15 (:REWRITE VARP-EXEVAL-EXPANDER))
 (1071 772 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1050 1050 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (1050 1050 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (1036 220 (:REWRITE |(* a (/ a))|))
 (1020 1020 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
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 (1020 1020 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
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 (1020 1020 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (1020 1020 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (1020 1020 (:REWRITE |(< (/ x) (/ y))|))
 (1020 1020 (:REWRITE |(< (- x) (- y))|))
 (1013 4 (:REWRITE BINARYSEARCH-WHILE-TEST-SUCCEEDS2-COROLLARY1))
 (989 3 (:DEFINITION RUN-ASSIGNMENT))
 (942 942 (:TYPE-PRESCRIPTION BINARYSEARCH-WHILE))
 (928 926 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (926 926 (:REWRITE INTEGERP-<-CONSTANT))
 (926 926 (:REWRITE CONSTANT-<-INTEGERP))
 (926 926 (:REWRITE |(< c (- x))|))
 (926 926 (:REWRITE |(< (- x) c)|))
 (880 5 (:REWRITE FLR-POSP))
 (878 878 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (878 878 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (876 876 (:REWRITE |(equal c (/ x))|))
 (876 876 (:REWRITE |(equal (/ x) (/ y))|))
 (876 876 (:REWRITE |(equal (- x) (- y))|))
 (776 2 (:DEFINITION SORTED))
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 (772 772 (:REWRITE |(equal c (- x))|))
 (772 772 (:REWRITE |(equal (- x) c)|))
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 (720 720 (:REWRITE DEFAULT-TIMES-1))
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 (705 4 (:REWRITE BINARYSEARCH-WHILE-TEST-SUCCEEDS2-COROLLARY2))
 (492 96 (:REWRITE RATIONALP-X))
 (465 3 (:DEFINITION RUN-RETURN))
 (464 224 (:REWRITE DEFAULT-CAR))
 (440 10 (:REWRITE LOW-HIGH-FLR-KLUDGE))
 (428 233 (:REWRITE DEFAULT-CDR))
 (423 27 (:REWRITE |(< y (+ (- c) x))|))
 (403 403 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (403 403 (:REWRITE NORMALIZE-ADDENDS))
 (391 1 (:REWRITE SORTED-LESSP3))
 (391 1 (:REWRITE SORTED-LESSP2))
 (369 369 (:REWRITE |(< 0 (* x y))|))
 (356 356 (:TYPE-PRESCRIPTION NATP))
 (350 75 (:REWRITE |(+ y x)|))
 (304 62 (:REWRITE LOOKUP-STORE))
 (274 4 (:REWRITE SLICE-BOUNDS))
 (262 4 (:REWRITE LITERAL-LISTP-TRUE-LISTP))
 (259 259 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (259 259 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (214 214 (:REWRITE REDUCE-INTEGERP-+))
 (214 214 (:REWRITE INTEGERP-MINUS-X))
 (214 214 (:META META-INTEGERP-CORRECT))
 (206 63 (:REWRITE |(+ c (+ d x))|))
 (204 6 (:REWRITE VALUEP-LIST-LITERAL-LISTP))
 (199 199 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (198 198 (:REWRITE DEFAULT-DIVIDE))
 (198 198 (:REWRITE |(/ (/ x))|))
 (198 14 (:REWRITE |(+ (+ x y) z)|))
 (180 9 (:REWRITE |(+ y (+ x z))|))
 (162 162 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (148 9 (:DEFINITION NUMBER-LISTP))
 (140 140 (:REWRITE |(* 0 x)|))
 (131 3 (:REWRITE BINARYSEARCH-WHILE-TEST-SUCCEEDS))
 (120 12 (:DEFINITION LITERALP))
 (114 3 (:REWRITE VAR-ALISTP-VAR-VALUEP))
 (110 110 (:REWRITE |(<= (/ x) y) with (< x 0)|))
 (110 110 (:REWRITE |(< x (/ y)) with (< y 0)|))
 (110 110 (:DEFINITION FIX))
 (108 9 (:REWRITE LITERALP-VALUEP))
 (105 105 (:TYPE-PRESCRIPTION EXEVAL-STEPS-NATP-COROLLARY1))
 (105 105 (:TYPE-PRESCRIPTION EXEVAL-STEPS-NATP))
 (105 15 (:DEFINITION LEN))
 (105 3 (:DEFINITION VAR-ALISTP))
 (104 104 (:REWRITE |(not (equal x (/ y)))|))
 (104 104 (:REWRITE |(equal x (/ y))|))
 (102 102 (:TYPE-PRESCRIPTION EXEVAL))
 (100 100 (:REWRITE INTEGERP-/))
 (96 96 (:REWRITE REDUCE-RATIONALP-+))
 (96 96 (:REWRITE REDUCE-RATIONALP-*))
 (96 96 (:REWRITE RATIONALP-MINUS-X))
 (96 96 (:META META-RATIONALP-CORRECT))
 (93 3 (:DEFINITION LITERAL-LISTP))
 (84 22 (:REWRITE VARP-NOT-RESULT))
 (84 3 (:DEFINITION VAR-ALIST-PAIRP))
 (75 75 (:REWRITE |(< (* x y) 0)|))
 (74 74 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (74 74 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (74 74 (:REWRITE |(< (/ x) 0)|))
 (68 68 (:REWRITE |(< x (if a b c))|))
 (68 68 (:REWRITE |(+ (if a b c) x)|))
 (62 56 (:REWRITE |(+ 0 x)|))
 (41 41 (:REWRITE FOLD-CONSTS-IN-+))
 (34 34 (:REWRITE |(< (+ c/d x) y)|))
 (27 27 (:REWRITE |(< x (+ c/d y))|))
 (24 9 (:REWRITE FLR-NATP))
 (18 18 (:TYPE-PRESCRIPTION VALUEP))
 (18 18 (:DEFINITION RUN-ERROR))
 (15 15 (:TYPE-PRESCRIPTION VAR-ALISTP))
 (15 15 (:TYPE-PRESCRIPTION LITERAL-LISTP))
 (12 1 (:REWRITE HIGH-LOW-KLUDGE1))
 (10 10 (:TYPE-PRESCRIPTION SORTED))
 (9 9 (:TYPE-PRESCRIPTION LITERALP))
 (9 9 (:REWRITE NOT-TIMED-OUTP-NOT-ZP-COUNT))
 (9 9 (:REWRITE LEN-LESSP-NOT-ZP))
 (4 4 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (4 4 (:REWRITE NUMBER-LISTP-TRUE-LISTP))
 (3 3 (:DEFINITION RUN-SKIP))
 )
(LESSP-TRANSITIVE-KLUDGE2)
(SORTED-LOWER-INDEX-LOWER-VALUE-LEMMA2
 (77 5 (:REWRITE HIGH-LOW-KLUDGE2))
 (40 4 (:DEFINITION NTH))
 (35 5 (:DEFINITION LEN))
 (33 5 (:REWRITE NTH-IN-NUMBER-LISTP))
 (14 9 (:REWRITE DEFAULT-PLUS-2))
 (13 4 (:REWRITE DEFAULT-LESS-THAN-1))
 (11 3 (:REWRITE SIMPLIFY-SUMS-<))
 (11 3 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (11 3 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (9 9 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (9 9 (:REWRITE NORMALIZE-ADDENDS))
 (9 9 (:REWRITE DEFAULT-PLUS-1))
 (9 9 (:REWRITE DEFAULT-CDR))
 (4 4 (:TYPE-PRESCRIPTION NATP))
 (4 4 (:REWRITE ZP-OPEN))
 (4 4 (:REWRITE THE-FLOOR-BELOW))
 (4 4 (:REWRITE THE-FLOOR-ABOVE))
 (4 4 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (4 4 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (4 4 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (4 4 (:REWRITE NOT-TIMED-OUTP-NOT-ZP-COUNT))
 (4 4 (:REWRITE LEN-LESSP-NOT-ZP))
 (4 4 (:REWRITE INTEGERP-<-CONSTANT))
 (4 4 (:REWRITE DEFAULT-LESS-THAN-2))
 (4 4 (:REWRITE DEFAULT-CAR))
 (4 4 (:REWRITE CONSTANT-<-INTEGERP))
 (4 4 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (4 4 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (4 4 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (4 4 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (4 4 (:REWRITE |(< c (- x))|))
 (4 4 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
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 (4 4 (:REWRITE |(< (/ x) (/ y))|))
 (4 4 (:REWRITE |(< (- x) c)|))
 (4 4 (:REWRITE |(< (- x) (- y))|))
 (3 3 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (2 2 (:REWRITE REDUCE-INTEGERP-+))
 (2 2 (:REWRITE INTEGERP-MINUS-X))
 (2 2 (:REWRITE |(< (/ x) 0)|))
 (2 2 (:REWRITE |(< (* x y) 0)|))
 (2 2 (:META META-INTEGERP-CORRECT))
 )
(BINARYSEARCH-WHILE-TEST-SUCCEEDS2-COROLLARY4
 (9034 266 (:REWRITE HIGH-LOW-KLUDGE2))
 (3878 8 (:LINEAR FLR-HALF-LEMMA))
 (3470 233 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (1684 28 (:REWRITE NTH-IN-NUMBER-LISTP))
 (1623 257 (:REWRITE DEFAULT-LESS-THAN-1))
 (1611 261 (:REWRITE DEFAULT-LESS-THAN-2))
 (1540 4 (:DEFINITION SORTED))
 (1444 23 (:LINEAR FLR-LESSP))
 (1244 2 (:DEFINITION RUN))
 (1242 13 (:REWRITE ZP-OPEN))
 (1238 7 (:DEFINITION NTH))
 (1175 76 (:REWRITE |(< 0 (/ x))|))
 (1096 16 (:REWRITE SLICE-BOUNDS))
 (1048 16 (:REWRITE LITERAL-LISTP-TRUE-LISTP))
 (816 24 (:REWRITE VALUEP-LIST-LITERAL-LISTP))
 (792 88 (:REWRITE ACL2-NUMBERP-X))
 (762 23 (:LINEAR FLR-POSP))
 (701 217 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (671 217 (:REWRITE SIMPLIFY-SUMS-<))
 (659 62 (:REWRITE HIGH-LOW-KLUDGE3))
 (655 62 (:REWRITE FLR-LOW-HIGH-EQUAL))
 (536 4 (:REWRITE LOW-HIGH-FLR-KLUDGE))
 (480 48 (:DEFINITION LITERALP))
 (456 12 (:REWRITE VAR-ALISTP-VAR-VALUEP))
 (432 36 (:REWRITE LITERALP-VALUEP))
 (420 12 (:DEFINITION VAR-ALISTP))
 (402 194 (:REWRITE |(equal (/ x) c)|))
 (372 12 (:DEFINITION LITERAL-LISTP))
 (354 209 (:REWRITE DEFAULT-PLUS-2))
 (352 88 (:REWRITE RATIONALP-X))
 (336 12 (:DEFINITION VAR-ALIST-PAIRP))
 (300 38 (:DEFINITION MV-NTH))
 (283 215 (:REWRITE DEFAULT-CDR))
 (272 178 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (264 16 (:REWRITE |(<= (/ x) y) with (< 0 x)|))
 (264 16 (:REWRITE |(< x (/ y)) with (< 0 y)|))
 (261 261 (:REWRITE THE-FLOOR-BELOW))
 (261 261 (:REWRITE THE-FLOOR-ABOVE))
 (256 64 (:REWRITE |(* y x)|))
 (249 249 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (249 249 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (249 249 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (249 249 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (249 249 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (249 249 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (249 249 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (249 249 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
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 (249 249 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (249 249 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (249 249 (:REWRITE |(< (/ x) (/ y))|))
 (249 249 (:REWRITE |(< (- x) (- y))|))
 (242 2 (:DEFINITION RUN-ASSIGNMENT))
 (241 233 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (240 209 (:REWRITE DEFAULT-PLUS-1))
 (233 233 (:REWRITE INTEGERP-<-CONSTANT))
 (233 233 (:REWRITE CONSTANT-<-INTEGERP))
 (233 233 (:REWRITE |(< c (- x))|))
 (233 233 (:REWRITE |(< (- x) c)|))
 (233 189 (:REWRITE DEFAULT-CAR))
 (194 194 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (194 194 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (194 194 (:REWRITE |(equal c (/ x))|))
 (194 194 (:REWRITE |(equal (/ x) (/ y))|))
 (194 194 (:REWRITE |(equal (- x) (- y))|))
 (186 178 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (178 178 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (178 178 (:REWRITE |(equal c (- x))|))
 (178 178 (:REWRITE |(equal (- x) c)|))
 (172 18 (:REWRITE VARP-NOT-RESULT))
 (143 143 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (143 143 (:REWRITE NORMALIZE-ADDENDS))
 (141 141 (:REWRITE REDUCE-INTEGERP-+))
 (141 141 (:REWRITE INTEGERP-MINUS-X))
 (141 141 (:META META-INTEGERP-CORRECT))
 (132 40 (:REWRITE |(+ c (+ d x))|))
 (132 25 (:REWRITE |(+ y x)|))
 (131 131 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (128 128 (:REWRITE DEFAULT-TIMES-2))
 (128 128 (:REWRITE DEFAULT-TIMES-1))
 (120 6 (:REWRITE |(+ y (+ x z))|))
 (120 2 (:DEFINITION RUN-RETURN))
 (112 16 (:DEFINITION LEN))
 (90 6 (:REWRITE |(+ (+ x y) z)|))
 (88 88 (:REWRITE REDUCE-RATIONALP-+))
 (88 88 (:REWRITE REDUCE-RATIONALP-*))
 (88 88 (:REWRITE RATIONALP-MINUS-X))
 (88 88 (:META META-RATIONALP-CORRECT))
 (76 76 (:REWRITE |(< 0 (* x y))|))
 (72 72 (:TYPE-PRESCRIPTION VALUEP))
 (70 70 (:TYPE-PRESCRIPTION EXEVAL-STEPS-NATP-COROLLARY1))
 (70 70 (:TYPE-PRESCRIPTION EXEVAL-STEPS-NATP))
 (68 68 (:TYPE-PRESCRIPTION EXEVAL))
 (67 67 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (67 67 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (67 67 (:REWRITE |(< (/ x) 0)|))
 (67 67 (:REWRITE |(< (* x y) 0)|))
 (60 60 (:TYPE-PRESCRIPTION VAR-ALISTP))
 (60 60 (:TYPE-PRESCRIPTION LITERAL-LISTP))
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 (60 60 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (48 4 (:DEFINITION NUMBER-LISTP))
 (36 36 (:TYPE-PRESCRIPTION LITERALP))
 (32 32 (:REWRITE DEFAULT-DIVIDE))
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 (32 32 (:REWRITE |(* a (/ a))|))
 (32 32 (:REWRITE |(* 0 x)|))
 (28 16 (:REWRITE LOOKUP-STORE-UNCHANGED))
 (26 26 (:REWRITE FOLD-CONSTS-IN-+))
 (20 10 (:REWRITE VARP-EXEVAL-EXPANDER))
 (18 15 (:REWRITE |(+ 0 x)|))
 (16 16 (:TYPE-PRESCRIPTION TRUE-LISTP))
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 (16 16 (:REWRITE NUMBER-LISTP-TRUE-LISTP))
 (16 16 (:REWRITE |(not (equal x (/ y)))|))
 (16 16 (:REWRITE |(equal x (/ y))|))
 (16 16 (:REWRITE |(<= (/ x) y) with (< x 0)|))
 (16 16 (:REWRITE |(< x (/ y)) with (< y 0)|))
 (16 16 (:DEFINITION FIX))
 (14 14 (:REWRITE SORTED-LOWER-INDEX-LOWER-VALUE-LEMMA2))
 (13 13 (:REWRITE NOT-TIMED-OUTP-NOT-ZP-COUNT))
 (13 13 (:REWRITE LEN-LESSP-NOT-ZP))
 (12 12 (:DEFINITION RUN-ERROR))
 (10 10 (:REWRITE INTEGERP-/))
 (4 4 (:REWRITE |(< (+ c/d x) y)|))
 (4 4 (:REWRITE |(< (+ (- c) x) y)|))
 (4 2 (:REWRITE BINARYSEARCH-WHILE-TEST-FAILS))
 (2 2 (:REWRITE BINARYSEARCH-WHILE-TEST-SUCCEEDS2-COROLLARY3))
 (2 2 (:REWRITE BINARYSEARCH-WHILE-TEST-SUCCEEDS2-COROLLARY2))
 (2 2 (:REWRITE BINARYSEARCH-WHILE-TEST-SUCCEEDS2-COROLLARY1))
 (2 2 (:REWRITE BINARYSEARCH-WHILE-TEST-SUCCEEDS2))
 (2 2 (:REWRITE BINARYSEARCH-WHILE-TEST-SUCCEEDS))
 (2 2 (:REWRITE |(< y (+ (- c) x))|))
 (2 2 (:REWRITE |(< x (+ c/d y))|))
 (2 2 (:DEFINITION RUN-SKIP))
 )
(BINARYSEARCH-WHILE-LOW-HIGH-EQUAL
 (8481 269 (:REWRITE HIGH-LOW-KLUDGE2))
 (4520 12 (:LINEAR FLR-HALF-LEMMA))
 (2220 3 (:REWRITE BINARYSEARCH-WHILE-TEST-SUCCEEDS2-COROLLARY3))
 (1763 266 (:REWRITE DEFAULT-LESS-THAN-2))
 (1736 5 (:DEFINITION SORTED))
 (1327 261 (:REWRITE DEFAULT-LESS-THAN-1))
 (917 7 (:DEFINITION NTH))
 (828 231 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (782 94 (:REWRITE ACL2-NUMBERP-X))
 (740 13 (:REWRITE SLICE-BOUNDS))
 (728 213 (:REWRITE SIMPLIFY-SUMS-<))
 (701 13 (:REWRITE LITERAL-LISTP-TRUE-LISTP))
 (578 2 (:REWRITE SORTED-LOWER-INDEX-LOWER-VALUE-LEMMA2))
 (544 16 (:REWRITE VALUEP-LIST-LITERAL-LISTP))
 (542 62 (:REWRITE |(+ y x)|))
 (531 3 (:REWRITE BINARYSEARCH-WHILE-TEST-SUCCEEDS2-COROLLARY4))
 (418 14 (:LINEAR FLR-LESSP))
 (414 414 (:TYPE-PRESCRIPTION FLR))
 (394 3 (:REWRITE BINARYSEARCH-WHILE-TEST-SUCCEEDS2-COROLLARY1))
 (392 2 (:REWRITE SORTED-LESSP3))
 (392 2 (:REWRITE SORTED-LESSP2))
 (360 12 (:REWRITE LOOKUP-STORE-UNCHANGED))
 (344 86 (:REWRITE RATIONALP-X))
 (343 5 (:REWRITE LOW-HIGH-FLR-KLUDGE))
 (340 3 (:REWRITE BINARYSEARCH-WHILE-TEST-SUCCEEDS2-COROLLARY2))
 (320 32 (:DEFINITION LITERALP))
 (304 247 (:REWRITE DEFAULT-PLUS-1))
 (304 8 (:REWRITE VAR-ALISTP-VAR-VALUEP))
 (302 14 (:LINEAR FLR-LESS-EQUAL))
 (298 14 (:LINEAR FLR-POSP))
 (288 24 (:REWRITE LITERALP-VALUEP))
 (280 8 (:DEFINITION VAR-ALISTP))
 (266 266 (:REWRITE THE-FLOOR-BELOW))
 (266 266 (:REWRITE THE-FLOOR-ABOVE))
 (253 247 (:REWRITE DEFAULT-PLUS-2))
 (251 251 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (251 251 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (248 213 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (248 8 (:DEFINITION LITERAL-LISTP))
 (231 231 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (231 231 (:REWRITE INTEGERP-<-CONSTANT))
 (231 231 (:REWRITE CONSTANT-<-INTEGERP))
 (231 231 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (231 231 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (231 231 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (231 231 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (231 231 (:REWRITE |(< c (- x))|))
 (231 231 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (231 231 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (231 231 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (231 231 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (231 231 (:REWRITE |(< (/ x) (/ y))|))
 (231 231 (:REWRITE |(< (- x) c)|))
 (231 231 (:REWRITE |(< (- x) (- y))|))
 (224 8 (:DEFINITION VAR-ALIST-PAIRP))
 (195 70 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (192 13 (:DEFINITION NUMBER-LISTP))
 (180 180 (:REWRITE DEFAULT-CAR))
 (163 70 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (152 152 (:REWRITE DEFAULT-CDR))
 (144 36 (:REWRITE |(* y x)|))
 (128 4 (:REWRITE NATP-LESS-KLUDGE))
 (126 74 (:REWRITE |(equal (/ x) c)|))
 (124 2 (:REWRITE BINARYSEARCH-WHILE-TEST-SUCCEEDS))
 (116 116 (:REWRITE REDUCE-INTEGERP-+))
 (116 116 (:REWRITE INTEGERP-MINUS-X))
 (116 116 (:META META-INTEGERP-CORRECT))
 (92 6 (:REWRITE |(equal (+ (- c) x) y)|))
 (88 21 (:REWRITE HIGH-LOW-KLUDGE3))
 (87 21 (:REWRITE FLR-LOW-HIGH-EQUAL))
 (86 86 (:REWRITE REDUCE-RATIONALP-+))
 (86 86 (:REWRITE REDUCE-RATIONALP-*))
 (86 86 (:REWRITE RATIONALP-MINUS-X))
 (86 86 (:META META-RATIONALP-CORRECT))
 (83 83 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (80 80 (:REWRITE DEFAULT-TIMES-2))
 (80 80 (:REWRITE DEFAULT-TIMES-1))
 (76 76 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (76 76 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (74 74 (:REWRITE |(equal c (/ x))|))
 (74 74 (:REWRITE |(equal (/ x) (/ y))|))
 (74 74 (:REWRITE |(equal (- x) (- y))|))
 (70 70 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (70 70 (:REWRITE |(equal c (- x))|))
 (70 70 (:REWRITE |(equal (- x) c)|))
 (56 56 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (52 4 (:REWRITE |(+ y (+ x z))|))
 (51 51 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (48 48 (:TYPE-PRESCRIPTION VALUEP))
 (48 48 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (48 48 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (48 48 (:REWRITE |(< (/ x) 0)|))
 (48 48 (:REWRITE |(< (* x y) 0)|))
 (48 48 (:REWRITE |(+ x (- x))|))
 (45 45 (:REWRITE |(< 0 (* x y))|))
 (42 4 (:REWRITE VARP-NOT-RESULT))
 (40 40 (:TYPE-PRESCRIPTION VAR-ALISTP))
 (40 40 (:TYPE-PRESCRIPTION LITERAL-LISTP))
 (36 36 (:REWRITE |(* a (/ a))|))
 (35 5 (:DEFINITION LEN))
 (25 25 (:TYPE-PRESCRIPTION SORTED))
 (25 25 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (25 25 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (25 25 (:REWRITE |(< 0 (/ x))|))
 (24 24 (:TYPE-PRESCRIPTION LITERALP))
 (22 2 (:REWRITE |(+ (+ x y) z)|))
 (18 18 (:REWRITE NTH-IN-NUMBER-LISTP))
 (18 18 (:REWRITE |(<= (/ x) y) with (< x 0)|))
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(LOW-HIGH-DIFFER-BY-1-FLR
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 (3522 8 (:LINEAR LINEAR-FLOOR-BOUNDS-1))
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 (1286 53 (:REWRITE |(* y x)|))
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 (526 46 (:TYPE-PRESCRIPTION FLOOR-ZERO . 2))
 (518 12 (:REWRITE DEFAULT-FLOOR-RATIO))
 (382 46 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 1))
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 (370 5 (:REWRITE FLOOR-ZERO . 3))
 (360 360 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
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 (360 360 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (360 360 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
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 (265 5 (:REWRITE CANCEL-FLOOR-+))
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 (25 5 (:REWRITE |(floor (* x (/ y)) z) not rewriting-goal-literal|))
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 (8 8 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
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(LESSP-TRANSITIVE-KLUDGE)
(SORTED-LOWER-INDEX-LOWER-VALUE
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(SORTED-LOWER-INDEX-LOWER-VALUE-COROLLARY
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(BINARYSEARCH-WHILE-LOW-HIGH-DIFFER-BY-ONE-SUBCASE1
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 (21434 21434 (:REWRITE THE-FLOOR-BELOW))
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 (17302 358 (:REWRITE LITERAL-LISTP-TRUE-LISTP))
 (16383 16383 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
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 (15524 15524 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
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 (15524 15524 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
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 (15524 15524 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (15524 15524 (:REWRITE |(< (/ x) (/ y))|))
 (15524 15524 (:REWRITE |(< (- x) (- y))|))
 (15483 13207 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (14373 14373 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (14373 14373 (:REWRITE INTEGERP-<-CONSTANT))
 (14373 14373 (:REWRITE CONSTANT-<-INTEGERP))
 (14373 14373 (:REWRITE |(< c (- x))|))
 (14373 14373 (:REWRITE |(< (- x) c)|))
 (14164 44 (:REWRITE CAR-SLICE))
 (12888 179 (:DEFINITION TRUE-LISTP))
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 (11164 3700 (:REWRITE NORMALIZE-ADDENDS))
 (10943 353 (:DEFINITION LITERAL-LISTP))
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 (4701 4701 (:REWRITE |(equal c (- x))|))
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 (2476 688 (:REWRITE |(+ c (+ d x))|))
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 (2003 2003 (:REWRITE DEFAULT-CAR))
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 (1765 1765 (:TYPE-PRESCRIPTION NUMBER-LISTP))
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 (1470 1470 (:REWRITE |(not (equal x (/ y)))|))
 (1470 1470 (:REWRITE |(equal x (/ y))|))
 (1412 1412 (:TYPE-PRESCRIPTION VALUEP))
 (1389 1389 (:REWRITE |(< (+ c/d x) y)|))
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 (1180 1052 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (1103 1103 (:TYPE-PRESCRIPTION LEN))
 (1052 1052 (:REWRITE |(+ x (- x))|))
 (1022 146 (:DEFINITION LEN))
 (920 920 (:REWRITE |(< x (+ c/d y))|))
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 (895 895 (:TYPE-PRESCRIPTION TRUE-LISTP))
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 (748 44 (:REWRITE |(+ (+ x y) z)|))
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 (393 393 (:REWRITE |(equal (+ (- c) x) y)|))
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 (391 391 (:REWRITE LEN-LESSP-NOT-ZP))
 (385 5 (:REWRITE NON-EMPTY-LEN))
 (264 66 (:REWRITE FLR-NATP-COROLLARY))
 (226 226 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (224 28 (:REWRITE |(+ x (if a b c))|))
 (176 176 (:TYPE-PRESCRIPTION SLICE))
 (172 172 (:TYPE-PRESCRIPTION RECURSIVEBS-HELPER))
 (132 132 (:REWRITE FOLD-CONSTS-IN-+))
 (22 22 (:REWRITE SORTED-IN-UPPER))
 (22 22 (:REWRITE |(equal x (if a b c))|))
 (22 22 (:REWRITE |(equal (if a b c) x)|))
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 )
(RECURSIVEBS-HELPER-CALLS2
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 (67667 431 (:DEFINITION SORTED))
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 (38903 4410 (:REWRITE ACL2-NUMBERP-X))
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 (29116 1066 (:LINEAR FLR-POSP))
 (28432 391 (:DEFINITION NTH))
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 (20672 94 (:REWRITE SLICE-LEN-LOW))
 (18676 1066 (:LINEAR FLR-LESS-EQUAL))
 (18464 50 (:DEFINITION MEMBER-EQUAL))
 (18284 391 (:REWRITE ZP-OPEN))
 (17760 111 (:REWRITE SORTED-LESSP3))
 (17760 111 (:REWRITE SORTED-LESSP2))
 (17221 4312 (:REWRITE RATIONALP-X))
 (14950 310 (:REWRITE LITERAL-LISTP-TRUE-LISTP))
 (14827 326 (:REWRITE NATP-LESS-KLUDGE))
 (13596 13596 (:TYPE-PRESCRIPTION FLR))
 (13485 357 (:REWRITE LOW-HIGH-DIFFER-BY-1-FLR))
 (12584 357 (:REWRITE HIGH-LOW-KLUDGE3))
 (12516 357 (:REWRITE FLR-LOW-HIGH-EQUAL))
 (11248 302 (:REWRITE FLR-POSP))
 (11160 155 (:DEFINITION TRUE-LISTP))
 (10116 94 (:REWRITE SLICE-NIL))
 (9598 4864 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (9455 305 (:DEFINITION LITERAL-LISTP))
 (9150 915 (:DEFINITION LITERALP))
 (9150 610 (:REWRITE VALUEP-LIST-LITERAL-LISTP))
 (7974 44 (:REWRITE CAR-SLICE))
 (7320 610 (:REWRITE LITERALP-VALUEP))
 (7051 1066 (:LINEAR FLR-LESSP))
 (6522 920 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (6435 6435 (:REWRITE THE-FLOOR-BELOW))
 (6435 6435 (:REWRITE THE-FLOOR-ABOVE))
 (5980 4744 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (5526 5526 (:TYPE-PRESCRIPTION NATP))
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 (4864 4864 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (4864 4864 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
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 (920 920 (:REWRITE |(equal c (/ x))|))
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 (920 920 (:REWRITE |(equal (/ x) (/ y))|))
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 (825 825 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
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 (226 226 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
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 (22 22 (:REWRITE |(equal x (if a b c))|))
 (22 22 (:REWRITE |(equal (if a b c) x)|))
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 )
(RECURSIVEBS-HELPER-CALLS3
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 (18676 1066 (:LINEAR FLR-LESS-EQUAL))
 (18464 50 (:DEFINITION MEMBER-EQUAL))
 (18284 391 (:REWRITE ZP-OPEN))
 (17760 111 (:REWRITE SORTED-LESSP3))
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 (14950 310 (:REWRITE LITERAL-LISTP-TRUE-LISTP))
 (14827 326 (:REWRITE NATP-LESS-KLUDGE))
 (13596 13596 (:TYPE-PRESCRIPTION FLR))
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 (12514 355 (:REWRITE FLR-LOW-HIGH-EQUAL))
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 (11160 155 (:DEFINITION TRUE-LISTP))
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 (9598 4864 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
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 (7974 44 (:REWRITE CAR-SLICE))
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 (7051 1066 (:LINEAR FLR-LESSP))
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 (6435 6435 (:REWRITE THE-FLOOR-BELOW))
 (6435 6435 (:REWRITE THE-FLOOR-ABOVE))
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 (4864 4864 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
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 (4750 4750 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (4750 4750 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (4750 4750 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
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 (4750 4750 (:REWRITE |(< c (- x))|))
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 (4750 4750 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (4750 4750 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (4750 4750 (:REWRITE |(< (/ x) (/ y))|))
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 (4750 4750 (:REWRITE |(< (- x) (- y))|))
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 (920 920 (:REWRITE |(equal c (/ x))|))
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 (22 22 (:REWRITE |(equal (if a b c) x)|))
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 )
(RECURSIVEBS-HELPER-CALLS)
(RECURSIVEBS-HELPER-CALLS4
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(BS-IND2
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(BINARYSEARCH-WHILE-TEST-INDUCTION)
(BINARYSEARCH-WHILE-TEST-INDUCTION-COROLLARY1
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(BINARYSEARCH-WHILE-TEST-INDUCTION-COROLLARY2
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(BINARYSEARCH-WHILE-TEST-INDUCTION-COROLLARY2-VERSION2
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(BINARYSEARCH-WHILE-TEST-INDUCTION-COROLLARY2-VERSION2-STATUS
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(BINARYSEARCH-WHILE-TEST-INDUCTION-COROLLARY3
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(FLR-NATP2-COROLLARY1)
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 (326 2 (:REWRITE SORTED-LESSP2))
 (312 312 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (312 312 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (312 312 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (282 282 (:REWRITE REDUCE-RATIONALP-+))
 (282 282 (:REWRITE REDUCE-RATIONALP-*))
 (282 282 (:REWRITE RATIONALP-MINUS-X))
 (282 282 (:META META-RATIONALP-CORRECT))
 (210 210 (:REWRITE |(* (- x) y)|))
 (180 180 (:TYPE-PRESCRIPTION SORTED))
 (126 126 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (125 125 (:REWRITE |(< 0 (/ x))|))
 (125 125 (:REWRITE |(< 0 (* x y))|))
 (118 118 (:REWRITE DEFAULT-CDR))
 (102 102 (:TYPE-PRESCRIPTION ABS))
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 (58 58 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
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 (38 38 (:REWRITE DEFAULT-FLOOR-1))
 (38 38 (:REWRITE |(floor x 2)| . 2))
 (20 2 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (10 10 (:REWRITE NOT-TIMED-OUTP-NOT-ZP-COUNT))
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 (4 4 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
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 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (2 2 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
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 (2 2 (:REWRITE |(equal (/ x) (/ y))|))
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 (2 2 (:REWRITE |(equal (- x) (- y))|))
 )
(FLR-HIGH-LOW-KLUDGE
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 (282 282 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (282 282 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (282 282 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (282 282 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (220 61 (:REWRITE DEFAULT-PLUS-1))
 (195 39 (:TYPE-PRESCRIPTION FLOOR-ZERO . 3))
 (195 39 (:TYPE-PRESCRIPTION FLOOR-ZERO . 1))
 (195 39 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 3))
 (195 39 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 2))
 (195 39 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 3))
 (195 39 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 2))
 (195 39 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 3))
 (195 39 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 3))
 (195 39 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 2))
 (102 3 (:REWRITE DEFAULT-FLOOR-RATIO))
 (95 5 (:REWRITE SUM-IS-EVEN . 2))
 (82 14 (:REWRITE DEFAULT-LESS-THAN-1))
 (78 3 (:REWRITE |(floor (+ x r) i)|))
 (76 12 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 1))
 (75 75 (:REWRITE DEFAULT-TIMES-2))
 (75 75 (:REWRITE DEFAULT-TIMES-1))
 (74 1 (:LINEAR LINEAR-FLOOR-BOUNDS-3))
 (70 1 (:LINEAR LINEAR-FLOOR-BOUNDS-2))
 (66 66 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
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 (30 14 (:REWRITE DEFAULT-LESS-THAN-2))
 (29 29 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (28 4 (:REWRITE DEFAULT-MINUS))
 (19 7 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (18 18 (:REWRITE REDUCE-INTEGERP-+))
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 (14 14 (:REWRITE THE-FLOOR-BELOW))
 (14 14 (:REWRITE THE-FLOOR-ABOVE))
 (14 13 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (14 13 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
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 (13 13 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
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 (13 13 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
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 (12 12 (:REWRITE INTEGERP-<-CONSTANT))
 (12 12 (:REWRITE CONSTANT-<-INTEGERP))
 (9 9 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (9 9 (:REWRITE |(+ c (+ d x))|))
 (6 6 (:REWRITE FOLD-CONSTS-IN-+))
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 (4 4 (:REWRITE |(< (+ c/d x) y)|))
 (4 4 (:REWRITE |(< (+ (- c) x) y)|))
 (4 4 (:REWRITE |(< (* x y) 0)|))
 (3 3 (:REWRITE DEFAULT-FLOOR-2))
 (3 3 (:REWRITE DEFAULT-FLOOR-1))
 (3 3 (:REWRITE |(floor x 2)| . 2))
 (3 3 (:REWRITE |(* (- x) y)|))
 (2 2 (:TYPE-PRESCRIPTION ABS))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (2 2 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (2 2 (:REWRITE |(< y (+ (- c) x))|))
 (2 2 (:REWRITE |(< x (+ c/d y))|))
 (1 1 (:REWRITE |(< 0 (/ x))|))
 (1 1 (:REWRITE |(< 0 (* x y))|))
 )
(NTH-MID-ACL2-NUMBERP
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 (52 2 (:LINEAR FLR-HIGH-LOW-KLUDGE))
 (52 1 (:REWRITE SLICE-BOUNDS))
 (50 1 (:DEFINITION NTH))
 (49 1 (:REWRITE LITERAL-LISTP-TRUE-LISTP))
 (48 4 (:REWRITE HIGH-LOW-KLUDGE3))
 (48 4 (:REWRITE FLR-LOW-HIGH-EQUAL))
 (38 1 (:REWRITE ZP-OPEN))
 (36 4 (:REWRITE ACL2-NUMBERP-X))
 (31 1 (:DEFINITION LITERAL-LISTP))
 (30 3 (:DEFINITION LITERALP))
 (30 2 (:REWRITE VALUEP-LIST-LITERAL-LISTP))
 (27 1 (:LINEAR FLR-POSP))
 (27 1 (:LINEAR FLR-LESS-EQUAL))
 (24 2 (:REWRITE LITERALP-VALUEP))
 (16 4 (:REWRITE RATIONALP-X))
 (14 2 (:DEFINITION LEN))
 (12 12 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (12 12 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (12 12 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (12 12 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (12 12 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (12 12 (:REWRITE |(equal c (/ x))|))
 (12 12 (:REWRITE |(equal c (- x))|))
 (12 12 (:REWRITE |(equal (/ x) c)|))
 (12 12 (:REWRITE |(equal (/ x) (/ y))|))
 (12 12 (:REWRITE |(equal (- x) c)|))
 (12 12 (:REWRITE |(equal (- x) (- y))|))
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 (9 9 (:REWRITE THE-FLOOR-ABOVE))
 (9 9 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
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 (9 9 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
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 (9 9 (:REWRITE DEFAULT-LESS-THAN-1))
 (9 9 (:REWRITE CONSTANT-<-INTEGERP))
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 (9 9 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
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 (9 9 (:REWRITE |(< (/ x) (/ y))|))
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 (9 9 (:REWRITE |(< (- x) (- y))|))
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 (4 4 (:REWRITE |(equal (+ (- c) x) y)|))
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 (2 2 (:TYPE-PRESCRIPTION LITERALP))
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 (2 2 (:REWRITE |(< (/ x) 0)|))
 (2 2 (:REWRITE |(< (* x y) 0)|))
 (1 1 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (1 1 (:REWRITE NUMBER-LISTP-TRUE-LISTP))
 (1 1 (:REWRITE NOT-TIMED-OUTP-NOT-ZP-COUNT))
 (1 1 (:REWRITE LEN-LESSP-NOT-ZP))
 (1 1 (:REWRITE |(< 0 (/ x))|))
 (1 1 (:REWRITE |(< 0 (* x y))|))
 (1 1 (:LINEAR FLR-LESSP))
 )
(HIGH-LOW-KLUDGE
 (1828 1828 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (1828 1828 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
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 (719 87 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 1))
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 (549 549 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (549 549 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (549 549 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (549 549 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (449 57 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 1))
 (435 87 (:TYPE-PRESCRIPTION FLOOR-ZERO . 3))
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 (435 87 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 3))
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 (435 87 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 2))
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 (435 87 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 2))
 (266 4 (:REWRITE |(floor (+ x r) i)|))
 (261 173 (:REWRITE DEFAULT-TIMES-2))
 (229 4 (:REWRITE DEFAULT-FLOOR-RATIO))
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 (150 1 (:LINEAR LINEAR-FLOOR-BOUNDS-3))
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 (25 25 (:REWRITE THE-FLOOR-BELOW))
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 (23 22 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
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 (21 21 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
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 (21 21 (:REWRITE |(< (- x) (- y))|))
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 (9 9 (:REWRITE |(< x (+ c/d y))|))
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 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
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 (4 4 (:REWRITE DEFAULT-FLOOR-1))
 (4 4 (:REWRITE |(floor x 2)| . 2))
 (4 4 (:REWRITE |(< (/ x) 0)|))
 (4 4 (:REWRITE |(< (* x y) 0)|))
 (3 3 (:REWRITE |(+ x (- x))|))
 (2 2 (:TYPE-PRESCRIPTION ABS))
 (1 1 (:REWRITE |(<= (/ x) y) with (< x 0)|))
 (1 1 (:REWRITE |(<= (/ x) y) with (< 0 x)|))
 (1 1 (:REWRITE |(< x (/ y)) with (< y 0)|))
 (1 1 (:REWRITE |(< 0 (* x y))|))
 )
(HIGH-LOW-KLUDGE9
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 (2820 2820 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (2820 2820 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
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 (1122 282 (:REWRITE DEFAULT-PLUS-2))
 (1119 135 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 1))
 (1119 135 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 1))
 (1119 135 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 1))
 (833 282 (:REWRITE DEFAULT-PLUS-1))
 (725 725 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (725 725 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (725 725 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (725 725 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (675 135 (:TYPE-PRESCRIPTION FLOOR-ZERO . 3))
 (675 135 (:TYPE-PRESCRIPTION FLOOR-ZERO . 1))
 (675 135 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 3))
 (675 135 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 2))
 (675 135 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 3))
 (675 135 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 2))
 (675 135 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 3))
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 (376 260 (:REWRITE DEFAULT-TIMES-2))
 (375 10 (:REWRITE DEFAULT-FLOOR-RATIO))
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 (171 35 (:REWRITE DEFAULT-LESS-THAN-2))
 (170 170 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (146 32 (:REWRITE REDUCE-INTEGERP-+))
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 (119 31 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
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 (101 25 (:REWRITE DEFAULT-MINUS))
 (98 98 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (35 35 (:REWRITE THE-FLOOR-BELOW))
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 (32 32 (:META META-INTEGERP-CORRECT))
 (31 2 (:REWRITE |(<= (/ x) y) with (< 0 x)|))
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 (25 25 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (25 25 (:REWRITE INTEGERP-<-CONSTANT))
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 (25 25 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
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 (25 25 (:REWRITE |(< (/ x) (/ y))|))
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 (25 25 (:REWRITE |(< (- x) (- y))|))
 (21 21 (:REWRITE |(* (- x) y)|))
 (19 1 (:REWRITE SUM-IS-EVEN . 2))
 (16 16 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (10 10 (:REWRITE DEFAULT-FLOOR-2))
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 (10 10 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (10 10 (:REWRITE |(floor x 2)| . 2))
 (10 10 (:REWRITE |(< y (+ (- c) x))|))
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 (5 5 (:REWRITE |(< 0 (* x y))|))
 (4 4 (:TYPE-PRESCRIPTION ABS))
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 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (4 4 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (4 4 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (4 4 (:REWRITE |(equal c (/ x))|))
 (4 4 (:REWRITE |(equal (/ x) (/ y))|))
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 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
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 (3 3 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (3 3 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (3 3 (:REWRITE |(equal c (- x))|))
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 (1 1 (:REWRITE |(equal x (/ y))|))
 )
(LOG2-BS-COUNT-CALLS-INDUCTION-SUBCASE1
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(LOG2-BS-COUNT-CALLS-INDUCTION-SUBCASE2
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(LOG2-BS-COUNT-CALLS-RELATION1
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(LOG2-BS-COUNT-CALLS-RELATION
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(LOG2-BS-COUNT-CALLS-RELATION-COROLLARY
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(RECURSIVEBS-HELPER-COUNT-CALLS-BS-COUNT-CALLS
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 (47085 134 (:REWRITE SLICE-NIL))
 (42985 4844 (:REWRITE ACL2-NUMBERP-X))
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 (35934 956 (:LINEAR FLR-POSP))
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(RECURSIVEBS-HELPER-COUNT-CALLS
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(RECURSIVEBS-HELPER-COUNT-CALLS-COROLLARY
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 (294 262 (:REWRITE |(<= (/ x) y) with (< 0 x)|))
 (294 262 (:REWRITE |(< x (/ y)) with (< y 0)|))
 (294 262 (:REWRITE |(< x (/ y)) with (< 0 y)|))
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 (228 19 (:DEFINITION NUMBER-LISTP))
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 (139 139 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
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 (93 93 (:LINEAR FLR-LESSP))
 (93 93 (:LINEAR FLR-LESS-EQUAL))
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 (71 71 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (71 71 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (71 71 (:REWRITE |(< 0 (/ x))|))
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 (40 40 (:REWRITE SORTED-LOWER-INDEX-LOWER-VALUE))
 (24 24 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (20 20 (:REWRITE NOT-MEMBER-NOT-IN-SLICE))
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 (12 12 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
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 (2 2 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (2 2 (:REWRITE DEFAULT-MINUS))
 (1 1 (:REWRITE |(< x (if a b c))|))
 (1 1 (:REWRITE |(< (if a b c) x)|))
 )
