(COMMUTATIVITY-OF-LOGAND
 (54 36 (:REWRITE DEFAULT-+-2))
 (54 36 (:REWRITE DEFAULT-+-1))
 (36 30 (:REWRITE DEFAULT-*-2))
 (36 12 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (32 8 (:REWRITE FLOOR-WHEN-<))
 (30 30 (:REWRITE DEFAULT-*-1))
 (17 17 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (16 16 (:REWRITE ZIP-OPEN))
 (12 12 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (12 12 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-OF-2))
 (12 12 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (12 12 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (12 12 (:REWRITE INTEGERP-OF-*))
 (12 12 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (12 12 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (8 8 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (8 8 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (8 8 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (8 8 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (8 8 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (8 8 (:REWRITE DEFAULT-<-2))
 (8 8 (:REWRITE DEFAULT-<-1))
 (8 8 (:META CANCEL_PLUS-LESSP-CORRECT))
 )
(LOGAND-OF-0)
(LOGAND-OF--1
 (1 1 (:REWRITE ZIP-OPEN))
 (1 1 (:META CANCEL_PLUS-EQUAL-CORRECT))
 )
(LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP)
(LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP
 (1 1 (:REWRITE ZIP-OPEN))
 (1 1 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 )
(LOGAND-WHEN-NOT-INTEGERP-ARG1)
(LOGAND-WHEN-NOT-INTEGERP-ARG2)
(<-OF-LOGAND-AND-0-HELPER
 (5864 212 (:DEFINITION NONNEGATIVE-INTEGER-QUOTIENT))
 (3792 16 (:REWRITE FLOOR-MINUS-ARG1-HACK))
 (2688 32 (:REWRITE FLOOR-PEEL-OFF-CONSTANT))
 (2147 2147 (:META CANCEL_PLUS-LESSP-CORRECT))
 (1900 1383 (:REWRITE DEFAULT-+-2))
 (1668 1383 (:REWRITE DEFAULT-+-1))
 (1588 136 (:REWRITE <-OF-NUMERATOR-AND-DENOMINATOR-SAME))
 (1299 1220 (:REWRITE DEFAULT-*-2))
 (1246 1125 (:REWRITE DEFAULT-<-1))
 (1220 1220 (:REWRITE DEFAULT-*-1))
 (1134 330 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (1133 361 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (1129 1125 (:REWRITE DEFAULT-<-2))
 (884 158 (:REWRITE FLOOR-WHEN-<))
 (848 212 (:DEFINITION NFIX))
 (836 76 (:REWRITE <-OF---OF-NUMERATOR-AND-DENOMINATOR-SAME))
 (832 208 (:REWRITE <-OF-*-OF-/-ARG2-ARG1-GEN))
 (728 180 (:REWRITE NUMERATOR-WHEN-INTEGERP))
 (580 408 (:REWRITE DEFAULT-UNARY-MINUS))
 (442 442 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (354 350 (:REWRITE DEFAULT-DENOMINATOR))
 (336 112 (:REWRITE *-OF-*-COMBINE-CONSTANTS))
 (330 330 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-OF-2))
 (330 330 (:REWRITE INTEGERP-OF-*))
 (288 32 (:REWRITE INTEGERP-OF-+-OF-1/2-AND-*-OF-1/2))
 (281 91 (:REWRITE ZIP-OPEN))
 (280 126 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (218 218 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (218 126 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (203 107 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (192 32 (:REWRITE MOD-WHEN-INTEGERP-OF-QUOTIENT))
 (192 32 (:REWRITE DISTRIBUTIVITY))
 (192 16 (:REWRITE INTEGERP-OF-+-OF---AND--))
 (184 180 (:REWRITE DEFAULT-NUMERATOR))
 (180 30 (:REWRITE EQUAL-OF-*-OF-/))
 (174 174 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (174 174 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (174 174 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (174 174 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (126 126 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (116 116 (:TYPE-PRESCRIPTION RATIONALP-OF-MOD))
 (116 116 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-TYPE))
 (91 91 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (91 91 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (80 16 (:REWRITE MOD-WHEN-<))
 (68 68 (:LINEAR <=-OF-*-AND-*-SAME-ALT-LINEAR))
 (68 68 (:LINEAR <-OF-*-AND-*-LINEAR))
 (64 16 (:REWRITE *-OF---ARG2))
 (37 37 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (34 34 (:LINEAR <-OF-*-SAME-LINEAR-SPECIAL))
 (34 34 (:LINEAR <-OF-*-SAME-LINEAR-2))
 (34 34 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-4))
 (34 34 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-3))
 (34 34 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-2))
 (32 32 (:REWRITE MOD-WHEN-EQUAL-OF-MOD-AND-0-FREE-CHEAP))
 (32 32 (:REWRITE MOD-WHEN-<-OF-0))
 (20 20 (:REWRITE RATIONALP-*))
 (16 16 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (16 16 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (16 16 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (16 16 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (16 16 (:REWRITE MOD-OF-2-WHEN-EVEN-CHEAP))
 (16 16 (:REWRITE FLOOR-OF-ONE-LESS-GEN))
 (12 12 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE))
 (12 12 (:TYPE-PRESCRIPTION MOD))
 (10 10 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (4 4 (:REWRITE <-OF-*-OF-/-ARG1-ARG1))
 (2 2 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (2 2 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (2 2 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (2 2 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (2 2 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (2 2 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (2 2 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 )
(<-OF-LOGAND-AND-0
 (21 12 (:REWRITE DEFAULT-<-1))
 (12 12 (:REWRITE DEFAULT-<-2))
 (12 12 (:META CANCEL_PLUS-LESSP-CORRECT))
 (8 8 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(LOGAND-NON-NEGATIVE-TYPE)
(LOGAND-NEGATIVE-TYPE
 (31 31 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (4 4 (:META CANCEL_PLUS-LESSP-CORRECT))
 (1 1 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (1 1 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 )
(LOGAND-NON-POSITIVE-TYPE
 (196 6 (:REWRITE COMMUTATIVITY-OF-+))
 (118 118 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (114 12 (:REWRITE DEFAULT-+-2))
 (114 12 (:REWRITE DEFAULT-+-1))
 (76 4 (:REWRITE UNICITY-OF-0))
 (72 4 (:DEFINITION FIX))
 (48 48 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (48 48 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (48 48 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (48 48 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (48 48 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (48 48 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (44 10 (:REWRITE DEFAULT-*-2))
 (44 4 (:DEFINITION EVENP))
 (23 10 (:REWRITE DEFAULT-<-2))
 (20 6 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (20 6 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (12 4 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (12 4 (:REWRITE COMMUTATIVITY-OF-*))
 (10 10 (:REWRITE DEFAULT-<-1))
 (10 10 (:REWRITE DEFAULT-*-1))
 (10 10 (:META CANCEL_PLUS-LESSP-CORRECT))
 (8 8 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (7 7 (:REWRITE ZIP-OPEN))
 (7 7 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (4 4 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (4 4 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-OF-2))
 (4 4 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (4 4 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (4 4 (:REWRITE INTEGERP-OF-*))
 (4 4 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (4 4 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (4 4 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (4 4 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (4 4 (:REWRITE FLOOR-WHEN-<))
 (4 4 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (4 4 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (4 4 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (4 4 (:META CANCEL_PLUS-EQUAL-CORRECT))
 )
(LOGAND-SAME
 (855 66 (:REWRITE FLOOR-WHEN-<))
 (632 632 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (632 632 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (632 632 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (632 632 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (632 632 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (632 632 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (632 632 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (583 11 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (500 164 (:REWRITE DEFAULT-*-2))
 (443 443 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (383 71 (:REWRITE DEFAULT-+-2))
 (339 71 (:REWRITE DEFAULT-+-1))
 (316 4 (:REWRITE <-OF-*-OF-/-ARG1-ARG1))
 (276 164 (:REWRITE DEFAULT-*-1))
 (239 7 (:LINEAR MY-FLOOR-LOWER-BOUND-LINEAR))
 (225 7 (:LINEAR FLOOR-UPPER-BOUND-LINEAR))
 (178 66 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (178 66 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (178 66 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (173 125 (:REWRITE DEFAULT-<-2))
 (158 22 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (158 22 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (143 143 (:META CANCEL_PLUS-LESSP-CORRECT))
 (125 125 (:REWRITE DEFAULT-<-1))
 (119 14 (:REWRITE FLOOR-OF-FLOOR))
 (112 14 (:REWRITE EQUAL-OF-0-AND-FLOOR-GEN))
 (68 17 (:REWRITE MOD-WHEN-<-OF-0))
 (66 66 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (64 4 (:LINEAR MOD-BOUND-LINEAR-ARG2))
 (52 52 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (50 50 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (40 10 (:REWRITE MOD-WHEN-<))
 (39 11 (:REWRITE <-OF-*-OF-CONSTANT-AND-CONSTANT-GEN))
 (28 7 (:REWRITE <-OF-FLOOR-OF-CONSTANT-AND-CONSTANT-GEN))
 (28 7 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (28 7 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (21 21 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (21 21 (:REWRITE INTEGERP-OF-*))
 (20 20 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (20 20 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (20 20 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (16 4 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 (14 14 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (10 10 (:TYPE-PRESCRIPTION RATIONALP-OF-MOD))
 (10 10 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE))
 (10 10 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-TYPE))
 (10 10 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (10 10 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (10 10 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (10 10 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (10 10 (:REWRITE MOD-OF-2-WHEN-EVEN-CHEAP))
 (9 9 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (9 9 (:REWRITE EQUAL-OF-+-COMBINE-CONSTANTS))
 (7 7 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (7 7 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (4 4 (:REWRITE <-OF-CONSTANT-AND-*-OF-CONSTANT))
 (2 2 (:REWRITE EQUAL-OF-+-AND-+-CANCEL-CONSTANTS))
 (2 2 (:LINEAR <=-OF-*-AND-*-SAME-LINEAR))
 (2 2 (:LINEAR <=-OF-*-AND-*-SAME-ALT-LINEAR))
 (2 2 (:LINEAR <-OF-*-AND-*-LINEAR))
 (1 1 (:LINEAR <-OF-*-SAME-LINEAR-SPECIAL))
 (1 1 (:LINEAR <-OF-*-SAME-LINEAR-2))
 (1 1 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-4))
 (1 1 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-3))
 (1 1 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-2))
 (1 1 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-1))
 )
(<=-OF-LOGAND-SAME-ARG1
 (862 862 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (862 862 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (862 862 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (862 862 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (862 862 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (862 862 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (496 496 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (202 22 (:REWRITE DEFAULT-+-2))
 (202 22 (:REWRITE DEFAULT-+-1))
 (139 51 (:REWRITE DEFAULT-<-2))
 (132 33 (:REWRITE FLOOR-WHEN-<))
 (116 48 (:REWRITE DEFAULT-*-2))
 (115 1 (:REWRITE *-OF-FLOOR-OF-SAME-WHEN-MULTIPLE))
 (65 51 (:REWRITE DEFAULT-<-1))
 (51 51 (:META CANCEL_PLUS-LESSP-CORRECT))
 (48 48 (:REWRITE DEFAULT-*-1))
 (33 33 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (33 33 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (33 33 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (33 33 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (33 33 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (30 5 (:REWRITE MOD-WHEN-INTEGERP-OF-QUOTIENT))
 (25 9 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (25 9 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (22 1 (:LINEAR MOD-OF-2-UPPER-BOUND))
 (22 1 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 (20 5 (:REWRITE MOD-WHEN-<))
 (20 1 (:LINEAR MOD-BOUND-LINEAR-ARG2-STRONG))
 (20 1 (:LINEAR MOD-BOUND-LINEAR-ARG2))
 (18 18 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (18 18 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-OF-2))
 (18 6 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (10 10 (:REWRITE ZIP-OPEN))
 (6 6 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (6 6 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (6 6 (:REWRITE INTEGERP-OF-*))
 (5 5 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (5 5 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (5 5 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (5 5 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (5 5 (:REWRITE MOD-WHEN-EQUAL-OF-MOD-AND-0-FREE-CHEAP))
 (5 5 (:REWRITE MOD-WHEN-<-OF-0))
 (5 5 (:REWRITE MOD-OF-2-WHEN-EVEN-CHEAP))
 (5 5 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (4 4 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (3 3 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (3 3 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (3 3 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (1 1 (:REWRITE EQUAL-OF-*-AND-CONSTANT))
 (1 1 (:REWRITE <-OF-FLOOR-OF-CONSTANT-AND-CONSTANT-GEN))
 )
(<=-OF-LOGAND-SAME-ARG2
 (55 55 (:TYPE-PRESCRIPTION LOGAND-NON-POSITIVE-TYPE))
 (55 55 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (6 2 (:REWRITE DEFAULT-<-2))
 (3 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (2 2 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (2 2 (:META CANCEL_PLUS-LESSP-CORRECT))
 (1 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(EQUAL-OF-LOGAND-AND--1
 (392 392 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (392 392 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (392 392 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (392 392 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (392 392 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (392 392 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (392 392 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (366 366 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (366 366 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (360 60 (:REWRITE DEFAULT-+-2))
 (360 60 (:REWRITE DEFAULT-+-1))
 (268 128 (:REWRITE DEFAULT-*-2))
 (132 12 (:REWRITE MOD-WHEN-INTEGERP-OF-QUOTIENT))
 (128 128 (:REWRITE DEFAULT-*-1))
 (48 12 (:REWRITE MOD-WHEN-<-OF-0))
 (48 12 (:REWRITE MOD-WHEN-<))
 (42 42 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (40 32 (:REWRITE DEFAULT-<-1))
 (33 23 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (33 23 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (32 32 (:REWRITE DEFAULT-<-2))
 (32 32 (:META CANCEL_PLUS-LESSP-CORRECT))
 (30 30 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (30 30 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (30 30 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (29 29 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (29 29 (:REWRITE INTEGERP-OF-*))
 (20 4 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 (20 4 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (17 17 (:REWRITE ZIP-OPEN))
 (12 12 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (12 12 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (12 12 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (12 12 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (12 12 (:REWRITE MOD-WHEN-EQUAL-OF-MOD-AND-0-FREE-CHEAP))
 (12 12 (:REWRITE MOD-OF-2-WHEN-EVEN-CHEAP))
 (8 8 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(LOGAND-IS-ZERO-HELPER
 (21870 1222 (:REWRITE MOD-WHEN-<-OF-0))
 (21029 1152 (:REWRITE <-OF-*-OF-CONSTANT-AND-CONSTANT-GEN))
 (17450 428 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (12038 8216 (:REWRITE DEFAULT-*-2))
 (10780 69 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (9027 2415 (:REWRITE DEFAULT-+-2))
 (8504 8216 (:REWRITE DEFAULT-*-1))
 (8291 116 (:REWRITE <-OF-LOGAND-AND-0))
 (8115 2415 (:REWRITE DEFAULT-+-1))
 (5589 5589 (:META CANCEL_PLUS-LESSP-CORRECT))
 (5128 5128 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (5128 5128 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (5128 5128 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (5128 5128 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (5128 5128 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (5128 5128 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (5072 5072 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (4449 3829 (:REWRITE DEFAULT-<-1))
 (4358 871 (:REWRITE MOD-WHEN-<))
 (3835 3829 (:REWRITE DEFAULT-<-2))
 (3220 3220 (:TYPE-PRESCRIPTION RATIONALP-OF-MOD))
 (3220 3220 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-TYPE))
 (1493 1493 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (1464 244 (:REWRITE <-OF-+-OF---AND-0-ARG1))
 (1218 303 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (1218 303 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (1162 295 (:REWRITE <-OF-FLOOR-OF-CONSTANT-AND-CONSTANT-GEN))
 (1063 134 (:REWRITE INTEGERP-OF-+-OF--1/2))
 (903 903 (:REWRITE INTEGERP-OF-*))
 (871 871 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (871 871 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (871 871 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (871 871 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (871 871 (:REWRITE MOD-OF-2-WHEN-EVEN-CHEAP))
 (661 134 (:REWRITE INTEGERP-OF-+-OF-1/2-AND-*-OF-1/2))
 (506 506 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (494 494 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (494 494 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (494 494 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (477 92 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-2))
 (303 303 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (303 303 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (276 46 (:REWRITE EQUAL-OF-0-AND-+-OF---ALT))
 (266 266 (:REWRITE MOD-OF-*-SUBST-CONSTANT-ARG2))
 (266 266 (:REWRITE MOD-OF-*-SUBST-CONSTANT-ARG1))
 (225 55 (:REWRITE MOD-OF-+-OF-CONSTANT))
 (112 112 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE))
 (102 102 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (92 92 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-1-CHEAP))
 (92 92 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-1))
 (91 91 (:REWRITE EQUAL-OF-/))
 (91 7 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (84 21 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 (78 6 (:REWRITE <-OF-FLOOR-AND-0))
 (69 69 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (60 60 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (55 55 (:REWRITE MOD-OF-+-SUBST-CONSTANT))
 (55 55 (:REWRITE MOD-OF-+-REDUCE-POSITIVE-CONSTANT))
 (46 46 (:REWRITE MOD-OF-+-OF---WHEN-EQUAL-OF-MOD-ARG1))
 (30 6 (:REWRITE <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE))
 )
(LOGAND-IS-ZERO-HELPER-2
 (21870 1222 (:REWRITE MOD-WHEN-<-OF-0))
 (20933 1152 (:REWRITE <-OF-*-OF-CONSTANT-AND-CONSTANT-GEN))
 (17964 428 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (12040 8222 (:REWRITE DEFAULT-*-2))
 (10780 69 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (9027 2415 (:REWRITE DEFAULT-+-2))
 (8510 8222 (:REWRITE DEFAULT-*-1))
 (8291 116 (:REWRITE <-OF-LOGAND-AND-0))
 (8115 2415 (:REWRITE DEFAULT-+-1))
 (5589 5589 (:META CANCEL_PLUS-LESSP-CORRECT))
 (5128 5128 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (5128 5128 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (5128 5128 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (5128 5128 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (5128 5128 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (5128 5128 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (5072 5072 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (4449 3829 (:REWRITE DEFAULT-<-1))
 (4358 871 (:REWRITE MOD-WHEN-<))
 (3835 3829 (:REWRITE DEFAULT-<-2))
 (3220 3220 (:TYPE-PRESCRIPTION RATIONALP-OF-MOD))
 (3220 3220 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-TYPE))
 (1491 1491 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (1464 244 (:REWRITE <-OF-+-OF---AND-0-ARG1))
 (1218 303 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (1218 303 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (1162 295 (:REWRITE <-OF-FLOOR-OF-CONSTANT-AND-CONSTANT-GEN))
 (1063 134 (:REWRITE INTEGERP-OF-+-OF--1/2))
 (903 903 (:REWRITE INTEGERP-OF-*))
 (871 871 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (871 871 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (871 871 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (871 871 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (871 871 (:REWRITE MOD-OF-2-WHEN-EVEN-CHEAP))
 (661 134 (:REWRITE INTEGERP-OF-+-OF-1/2-AND-*-OF-1/2))
 (506 506 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (494 494 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (494 494 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (494 494 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (477 92 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-2))
 (303 303 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (303 303 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (276 46 (:REWRITE EQUAL-OF-0-AND-+-OF---ALT))
 (266 266 (:REWRITE MOD-OF-*-SUBST-CONSTANT-ARG2))
 (266 266 (:REWRITE MOD-OF-*-SUBST-CONSTANT-ARG1))
 (225 55 (:REWRITE MOD-OF-+-OF-CONSTANT))
 (112 112 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE))
 (102 102 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (92 92 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-1-CHEAP))
 (92 92 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-1))
 (91 91 (:REWRITE EQUAL-OF-/))
 (91 7 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (84 21 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 (78 6 (:REWRITE <-OF-FLOOR-AND-0))
 (69 69 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (60 60 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (55 55 (:REWRITE MOD-OF-+-SUBST-CONSTANT))
 (55 55 (:REWRITE MOD-OF-+-REDUCE-POSITIVE-CONSTANT))
 (46 46 (:REWRITE MOD-OF-+-OF---WHEN-EQUAL-OF-MOD-ARG1))
 (30 6 (:REWRITE <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE))
 )
(LOGAND-ASSOCIATIVE
 (77308 3196 (:REWRITE FLOOR-WHEN-<))
 (40690 40690 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (40690 40690 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (40690 40690 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (40690 40690 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (40690 40690 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (40660 40660 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (26744 3048 (:REWRITE DEFAULT-+-2))
 (25660 3048 (:REWRITE DEFAULT-+-1))
 (22277 6305 (:REWRITE DEFAULT-*-2))
 (11625 6305 (:REWRITE DEFAULT-*-1))
 (8835 3215 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (8835 3215 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (8636 3196 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (8216 612 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (8152 916 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (7736 916 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (7708 7708 (:META CANCEL_PLUS-LESSP-CORRECT))
 (7582 834 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (6810 6410 (:REWRITE DEFAULT-<-1))
 (6677 630 (:REWRITE <-OF-*-OF-CONSTANT-AND-CONSTANT-GEN))
 (6410 6410 (:REWRITE DEFAULT-<-2))
 (3196 3196 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (3040 695 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (3040 695 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (3016 19 (:REWRITE MOD-WHEN-<-OF-0))
 (2896 659 (:REWRITE <-OF-FLOOR-OF-CONSTANT-AND-CONSTANT-GEN))
 (2761 2541 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (2496 12 (:REWRITE <-OF-LOGAND-AND-0))
 (1745 1745 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (1314 9 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (1224 1224 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (834 834 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (834 834 (:REWRITE INTEGERP-OF-*))
 (824 824 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (824 824 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (824 824 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (695 695 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (695 695 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (36 36 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (33 9 (:REWRITE MOD-WHEN-<))
 (19 19 (:REWRITE MOD-WHEN-EQUAL-OF-MOD-AND-0-FREE-CHEAP))
 (9 9 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (9 9 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (9 9 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (9 9 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (9 9 (:REWRITE MOD-OF-2-WHEN-EVEN-CHEAP))
 (9 9 (:REWRITE MOD-OF-*-SUBST-CONSTANT-ARG2))
 (9 9 (:REWRITE MOD-OF-*-SUBST-CONSTANT-ARG1))
 (9 9 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (8 2 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 )
(LOGAND-COMMUTATIVE-2
 (246 246 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (246 246 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (84 8 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 (84 8 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (40 20 (:REWRITE DEFAULT-<-1))
 (36 4 (:REWRITE <-OF-LOGAND-AND-0))
 (27 11 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (20 20 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (20 20 (:REWRITE DEFAULT-<-2))
 (20 20 (:META CANCEL_PLUS-LESSP-CORRECT))
 (19 11 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (1 1 (:META CANCEL_PLUS-EQUAL-CORRECT))
 )
(LOGAND-SAME-2
 (213 213 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (213 213 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (40 4 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 (26 4 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (15 9 (:REWRITE DEFAULT-<-1))
 (9 9 (:REWRITE DEFAULT-<-2))
 (9 9 (:META CANCEL_PLUS-LESSP-CORRECT))
 (8 1 (:REWRITE <-OF-LOGAND-AND-0))
 (7 3 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (4 4 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (3 3 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 )
(LOGAND-COMBINE-CONSTANTS
 (12 12 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (12 12 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 )
(INTEGERP-OF-*-1/2-OF-LOGAND
 (2780 146 (:REWRITE FLOOR-WHEN-<))
 (1937 1937 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (1937 1937 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (1937 1937 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (1937 1937 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (1937 1937 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (1937 1937 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (1937 1937 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (1508 304 (:REWRITE DEFAULT-*-2))
 (856 96 (:REWRITE DEFAULT-+-2))
 (792 24 (:LINEAR MY-FLOOR-LOWER-BOUND-LINEAR))
 (776 776 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (776 96 (:REWRITE DEFAULT-+-1))
 (744 24 (:LINEAR FLOOR-UPPER-BOUND-LINEAR))
 (703 73 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (655 55 (:REWRITE ZIP-OPEN))
 (557 73 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-OF-2))
 (448 304 (:REWRITE DEFAULT-*-1))
 (338 146 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (338 146 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (338 146 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (312 24 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (310 310 (:META CANCEL_PLUS-LESSP-CORRECT))
 (284 44 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (284 44 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (262 262 (:REWRITE DEFAULT-<-2))
 (262 262 (:REWRITE DEFAULT-<-1))
 (240 24 (:REWRITE FLOOR-OF-FLOOR))
 (192 24 (:REWRITE EQUAL-OF-0-AND-FLOOR-GEN))
 (146 146 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (122 122 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (120 24 (:REWRITE <-OF-*-OF-CONSTANT-AND-CONSTANT-GEN))
 (96 24 (:REWRITE <-OF-FLOOR-OF-CONSTANT-AND-CONSTANT-GEN))
 (96 24 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (96 24 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (84 84 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (73 73 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (73 73 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (73 73 (:REWRITE INTEGERP-OF-*))
 (51 51 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (51 51 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (51 51 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (48 48 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (24 24 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (24 24 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 )
(FLOOR-FLOOR-SUB1-INDUCT
 (6 6 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (6 6 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (6 6 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (6 6 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (6 6 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (6 6 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (6 6 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 )
(FLOOR-OF-LOGAND-AND-EXPT
 (19092 51 (:REWRITE <-OF-*-OF-/-ARG2-ARG1-GEN))
 (18776 5 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (14700 5 (:REWRITE <-OF-*-OF-/-ARG1-ARG1))
 (12942 12942 (:TYPE-PRESCRIPTION EVENP))
 (9077 46 (:LINEAR <-OF-*-SAME-LINEAR-SPECIAL))
 (9077 46 (:LINEAR <-OF-*-SAME-LINEAR-2))
 (8628 4314 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (8628 4314 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (8628 4314 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (6493 222 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (5732 5732 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (5732 5732 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (5525 5525 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (4314 4314 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (4282 946 (:REWRITE DEFAULT-*-2))
 (3771 27 (:REWRITE <-OF-FLOOR-AND-0))
 (3653 1350 (:REWRITE DEFAULT-<-2))
 (3143 127 (:LINEAR <-OF-EXPT2-SAME-LINEAR))
 (3141 152 (:LINEAR <=-OF-2-AND-EXPT2-LINEAR))
 (3097 1350 (:REWRITE DEFAULT-<-1))
 (2561 512 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (2001 87 (:REWRITE DEFAULT-UNARY-/))
 (1996 946 (:REWRITE DEFAULT-*-1))
 (1896 1896 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (1669 1669 (:META CANCEL_PLUS-LESSP-CORRECT))
 (1460 8 (:REWRITE <-OF-LOGAND-AND-0))
 (1318 512 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (1318 512 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (1278 510 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (1277 256 (:REWRITE DEFAULT-+-2))
 (1128 2 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (1084 2 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (751 208 (:REWRITE <-OF-FLOOR-OF-CONSTANT-AND-CONSTANT-GEN))
 (670 46 (:REWRITE <-OF-*-OF-CONSTANT-AND-CONSTANT-GEN))
 (589 7 (:REWRITE <-OF-CONSTANT-AND-*-OF-CONSTANT))
 (512 512 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (480 256 (:REWRITE DEFAULT-+-1))
 (448 4 (:REWRITE ASSOCIATIVITY-OF-*))
 (435 127 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-4))
 (430 254 (:LINEAR EXPT-BOUND-LINEAR-WEAK))
 (430 254 (:LINEAR <=-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (424 4 (:REWRITE <-OF-*-AND-*))
 (337 32 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (318 32 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (301 301 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (301 301 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (264 7 (:LINEAR FLOOR-UPPER-BOUND-STRONG-LINEAR-CHEAP))
 (254 254 (:LINEAR EXPT-BOUND-LINEAR))
 (254 254 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR-NEGATIVE-EXPONENT))
 (254 254 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR))
 (254 254 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (222 222 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (222 222 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (127 127 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-3))
 (127 127 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-2))
 (127 127 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-1))
 (127 127 (:LINEAR EXPT-BOUND-LINEAR-2))
 (108 27 (:REWRITE <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE))
 (92 92 (:LINEAR <=-OF-*-AND-*-SAME-LINEAR))
 (92 92 (:LINEAR <=-OF-*-AND-*-SAME-ALT-LINEAR))
 (92 92 (:LINEAR <-OF-*-AND-*-LINEAR))
 (64 16 (:REWRITE <-OF-2-AND-EXPT2))
 (46 46 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-4))
 (46 46 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-3))
 (46 46 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-2))
 (46 46 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-1))
 (39 39 (:REWRITE <-OF-*-OF-CONSTANT-AND-CONSTANT))
 (30 10 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (27 27 (:REWRITE <-OF-0-AND-EXPT))
 (18 18 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (14 14 (:REWRITE ZIP-OPEN))
 (13 13 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (13 13 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (13 13 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (12 12 (:REWRITE *-OF-*-COMBINE-CONSTANTS))
 (10 10 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (10 10 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-OF-2))
 (10 10 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (10 10 (:REWRITE INTEGERP-OF-*))
 (6 6 (:REWRITE ZP-OPEN))
 (4 4 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (4 4 (:REWRITE <-OF-1-AND-EXPT-GEN))
 (2 2 (:REWRITE FOLD-CONSTS-IN-+))
 (2 2 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (2 2 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (2 2 (:REWRITE +-COMBINE-CONSTANTS))
 )
(FLOOR-OF-LOGAND-AND-2
 (40 40 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (30 30 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (30 30 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NON-POSITIVE-EXPONENT))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 )
(FLOOR-OF-LOGAND-AND-2-BACK
 (208 2 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 (208 2 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (132 4 (:LINEAR MY-FLOOR-LOWER-BOUND-LINEAR))
 (124 4 (:LINEAR FLOOR-UPPER-BOUND-LINEAR))
 (107 107 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (107 107 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (107 107 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (107 107 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (107 107 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (107 107 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (52 52 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (52 52 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (42 12 (:REWRITE FLOOR-WHEN-<))
 (26 26 (:META CANCEL_PLUS-LESSP-CORRECT))
 (24 8 (:REWRITE COMMUTATIVITY-OF-*))
 (22 22 (:REWRITE DEFAULT-<-2))
 (22 22 (:REWRITE DEFAULT-<-1))
 (19 3 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (19 3 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (16 16 (:REWRITE DEFAULT-*-2))
 (16 16 (:REWRITE DEFAULT-*-1))
 (16 4 (:REWRITE <-OF-FLOOR-OF-CONSTANT-AND-CONSTANT-GEN))
 (16 4 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (16 4 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (12 12 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (12 12 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (12 12 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (12 12 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (12 12 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (4 4 (:REWRITE DEFAULT-+-2))
 (4 4 (:REWRITE DEFAULT-+-1))
 (4 4 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (4 4 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 )
(LOGAND-OF-FLOOR-ARG2
 (94 94 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (94 94 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (70 2 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (68 2 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (59 59 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (59 59 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (59 59 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (59 59 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (59 59 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (59 59 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (57 9 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (45 29 (:REWRITE DEFAULT-*-2))
 (45 29 (:REWRITE DEFAULT-*-1))
 (41 11 (:REWRITE FLOOR-WHEN-<))
 (38 38 (:META CANCEL_PLUS-LESSP-CORRECT))
 (38 30 (:REWRITE DEFAULT-<-2))
 (36 6 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (32 8 (:REWRITE <-OF-*-OF-CONSTANT-AND-CONSTANT-GEN))
 (30 30 (:REWRITE DEFAULT-<-1))
 (24 6 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 (24 2 (:REWRITE <-OF-LOGAND-AND-0))
 (17 9 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (16 16 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (16 16 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (15 5 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (11 11 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (11 11 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (11 11 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (10 2 (:REWRITE DEFAULT-+-2))
 (5 5 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (5 5 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-OF-2))
 (5 5 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (5 5 (:REWRITE INTEGERP-OF-*))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (2 2 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 )
(<=-OF-LOGAND-SAME-WHEN-NEGATIVE
 (953 953 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (953 953 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (953 953 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (953 953 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (191 191 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (94 1 (:REWRITE *-OF-FLOOR-OF-SAME-WHEN-MULTIPLE))
 (84 12 (:REWRITE DEFAULT-<-2))
 (63 9 (:REWRITE DEFAULT-+-2))
 (63 9 (:REWRITE DEFAULT-+-1))
 (57 32 (:REWRITE DEFAULT-*-2))
 (32 32 (:REWRITE DEFAULT-*-1))
 (26 5 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 (26 5 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (24 4 (:REWRITE MOD-WHEN-INTEGERP-OF-QUOTIENT))
 (22 1 (:LINEAR MOD-OF-2-UPPER-BOUND))
 (20 1 (:LINEAR MOD-BOUND-LINEAR-ARG2-STRONG))
 (20 1 (:LINEAR MOD-BOUND-LINEAR-ARG2))
 (19 12 (:REWRITE DEFAULT-<-1))
 (18 18 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (18 18 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (18 18 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (18 18 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (18 18 (:REWRITE FLOOR-WHEN-<))
 (18 18 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (16 4 (:REWRITE MOD-WHEN-<-OF-0))
 (14 14 (:META CANCEL_PLUS-LESSP-CORRECT))
 (12 12 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (12 12 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-OF-2))
 (8 1 (:REWRITE <=-OF-LOGAND-SAME-ARG1))
 (6 6 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (6 2 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (5 5 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (5 5 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (4 4 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (4 4 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (4 4 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (4 4 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (4 4 (:REWRITE MOD-WHEN-EQUAL-OF-MOD-AND-0-FREE-CHEAP))
 (4 4 (:REWRITE MOD-WHEN-<))
 (4 4 (:REWRITE MOD-OF-2-WHEN-EVEN-CHEAP))
 (3 3 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (3 3 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (3 3 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (3 3 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (3 3 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (3 3 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (2 2 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (2 2 (:REWRITE INTEGERP-OF-*))
 (1 1 (:REWRITE ZIP-OPEN))
 (1 1 (:REWRITE EQUAL-OF-*-AND-CONSTANT))
 (1 1 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 )
(LOGAND-OF-LOGNOT-SAME
 (1357 122 (:REWRITE FLOOR-WHEN-<))
 (1254 38 (:LINEAR MY-FLOOR-LOWER-BOUND-LINEAR))
 (1178 38 (:LINEAR FLOOR-UPPER-BOUND-LINEAR))
 (882 21 (:REWRITE <-OF-MINUS-AND-CONSTANT))
 (853 265 (:REWRITE DEFAULT-*-2))
 (774 18 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (750 750 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (750 750 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (750 750 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (750 750 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (750 750 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (750 750 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (750 750 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (710 146 (:REWRITE DEFAULT-+-2))
 (670 13 (:REWRITE <-OF-+-OF---AND-0-ARG1))
 (598 146 (:REWRITE DEFAULT-+-1))
 (359 359 (:META CANCEL_PLUS-LESSP-CORRECT))
 (315 289 (:REWRITE DEFAULT-<-2))
 (313 265 (:REWRITE DEFAULT-*-1))
 (311 289 (:REWRITE DEFAULT-<-1))
 (276 19 (:REWRITE MOD-WHEN-<-OF-0))
 (261 6 (:REWRITE FLOOR-OF-ONE-LESS-GEN))
 (237 237 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (235 35 (:REWRITE DEFAULT-UNARY-MINUS))
 (233 6 (:DEFINITION NATP))
 (232 12 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (222 14 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (192 128 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (192 128 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (192 128 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (152 38 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (152 38 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (140 10 (:REWRITE MOD-WHEN-<))
 (128 128 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (105 105 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (78 14 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (68 17 (:REWRITE <-OF-FLOOR-OF-CONSTANT-AND-CONSTANT-GEN))
 (50 5 (:REWRITE FLOOR-OF-FLOOR))
 (40 5 (:REWRITE <-OF-0-AND-FLOOR))
 (38 38 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (38 38 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (29 2 (:LINEAR MOD-OF-2-UPPER-BOUND))
 (29 2 (:LINEAR MOD-BOUND-LINEAR-ARG2))
 (27 3 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (24 3 (:REWRITE EQUAL-OF-0-AND-FLOOR-GEN))
 (18 10 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (18 10 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (18 10 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (16 16 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (16 16 (:REWRITE INTEGERP-OF-*))
 (16 16 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (16 16 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (12 12 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (10 10 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (10 10 (:REWRITE MOD-OF-2-WHEN-EVEN-CHEAP))
 (10 2 (:REWRITE <-OF-*-OF-CONSTANT-AND-CONSTANT-GEN))
 (8 2 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 (6 6 (:TYPE-PRESCRIPTION RATIONALP-OF-MOD))
 (6 6 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE))
 (6 6 (:TYPE-PRESCRIPTION NATP))
 (6 6 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-TYPE))
 (4 4 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(MOD-OF-LOGAND-AND-EXPT-ALT
 (49637 1275 (:REWRITE FLOOR-WHEN-<))
 (29832 29832 (:TYPE-PRESCRIPTION EVENP))
 (19888 9944 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (19888 9944 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (19888 9944 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (17216 98 (:REWRITE <-OF-LOGAND-AND-0))
 (13227 2936 (:REWRITE DEFAULT-*-2))
 (11542 11542 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (11542 11542 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (11542 11542 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (11542 11542 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (11378 11378 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (11063 47 (:REWRITE <-OF-*-OF-/-ARG2-ARG1-GEN))
 (10726 122 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 (9944 9944 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (8631 1045 (:REWRITE DEFAULT-+-2))
 (7464 156 (:REWRITE <-OF-*-OF-CONSTANT-AND-CONSTANT-GEN))
 (6928 306 (:REWRITE DEFAULT-UNARY-/))
 (6698 2936 (:REWRITE DEFAULT-*-1))
 (6549 3696 (:REWRITE DEFAULT-<-2))
 (6083 1045 (:REWRITE DEFAULT-+-1))
 (5487 3696 (:REWRITE DEFAULT-<-1))
 (4633 18 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (4389 4389 (:META CANCEL_PLUS-LESSP-CORRECT))
 (3879 265 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (3548 3548 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (2927 265 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (2659 17 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-2))
 (2465 1291 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (2273 1275 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (2273 1275 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (2185 62 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (1720 113 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (1553 1195 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (1275 1275 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (1217 265 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (1217 265 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (970 113 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (638 470 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (612 9 (:REWRITE COMMUTATIVITY-2-OF-*))
 (470 470 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (453 453 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE))
 (418 418 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (418 418 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (336 28 (:REWRITE DEFAULT-UNARY-MINUS))
 (260 17 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-1))
 (238 238 (:LINEAR EXPT-BOUND-LINEAR))
 (238 238 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR-NEGATIVE-EXPONENT))
 (238 238 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR))
 (238 238 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (234 18 (:REWRITE UNICITY-OF-1))
 (144 144 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (119 119 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-3))
 (119 119 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-2))
 (119 119 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-1))
 (119 119 (:LINEAR EXPT-BOUND-LINEAR-2))
 (106 18 (:REWRITE MOD-OF-2-WHEN-EVEN-CHEAP))
 (86 86 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (86 86 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (86 86 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (47 47 (:REWRITE <-OF-*-OF-CONSTANT-AND-CONSTANT))
 (11 11 (:REWRITE ZP-OPEN))
 (9 9 (:REWRITE MOD-OF-+-SUBST-CONSTANT))
 (9 9 (:REWRITE MOD-OF-+-REDUCE-POSITIVE-CONSTANT))
 (9 9 (:REWRITE MOD-OF-+-OF-CONSTANT))
 (8 8 (:REWRITE NATP-OF-*-WHEN-NATP-AND-NATP))
 (8 8 (:REWRITE MOD-OF-EXPT-WHEN-EQUAL-OF-MOD-SUBST-CONSTANT))
 (8 8 (:REWRITE MOD-OF-*-SUBST-CONSTANT-ARG2))
 (8 8 (:REWRITE MOD-OF-*-SUBST-CONSTANT-ARG1))
 (5 5 (:REWRITE FOLD-CONSTS-IN-+))
 (5 5 (:REWRITE +-COMBINE-CONSTANTS))
 (5 5 (:REWRITE *-OF---ARG1))
 (3 3 (:REWRITE <-OF-CONSTANT-AND-*-OF-CONSTANT))
 (3 3 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (3 3 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (2 2 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (2 2 (:REWRITE EQUAL-OF-+-COMBINE-CONSTANTS))
 )
(MOD-OF-LOGAND-AND-EXPT
 (68163 2078 (:REWRITE FLOOR-WHEN-<))
 (49824 49824 (:TYPE-PRESCRIPTION EVENP))
 (33216 16608 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (33216 16608 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (33216 16608 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (26806 139 (:REWRITE <-OF-LOGAND-AND-0))
 (22188 78 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (21212 4694 (:REWRITE DEFAULT-*-2))
 (17766 17766 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (17766 17766 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (17766 17766 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (17766 17766 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (16608 16608 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (15854 1730 (:REWRITE DEFAULT-+-2))
 (14922 183 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 (12338 765 (:REWRITE <-OF-FLOOR-OF-CONSTANT-AND-CONSTANT-GEN))
 (12099 263 (:REWRITE <-OF-*-OF-CONSTANT-AND-CONSTANT-GEN))
 (11340 1730 (:REWRITE DEFAULT-+-1))
 (10262 4694 (:REWRITE DEFAULT-*-1))
 (9857 5657 (:REWRITE DEFAULT-<-2))
 (9372 5657 (:REWRITE DEFAULT-<-1))
 (9050 404 (:REWRITE DEFAULT-UNARY-/))
 (6813 6813 (:META CANCEL_PLUS-LESSP-CORRECT))
 (6775 30 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (6421 413 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (5420 5420 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (4285 413 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (4163 31 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-2))
 (4062 2100 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (3798 2078 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (3798 2078 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (3514 203 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (2718 1958 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (2549 413 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (2549 413 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (2078 2078 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (1808 203 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (1199 765 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (972 81 (:REWRITE DEFAULT-UNARY-MINUS))
 (884 13 (:REWRITE COMMUTATIVITY-2-OF-*))
 (765 765 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (616 616 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE))
 (429 429 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (429 429 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (382 31 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-1))
 (338 26 (:REWRITE UNICITY-OF-1))
 (248 50 (:REWRITE MOD-OF-2-WHEN-EVEN-CHEAP))
 (182 182 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (132 132 (:LINEAR EXPT-BOUND-LINEAR))
 (132 132 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR-NEGATIVE-EXPONENT))
 (132 132 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR))
 (132 132 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (106 106 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (106 106 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (106 106 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (99 99 (:REWRITE <-OF-*-OF-CONSTANT-AND-CONSTANT))
 (66 66 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-3))
 (66 66 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-2))
 (66 66 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-1))
 (66 66 (:LINEAR EXPT-BOUND-LINEAR-2))
 (18 18 (:REWRITE ZP-OPEN))
 (18 18 (:REWRITE NATP-OF-*-WHEN-NATP-AND-NATP))
 (18 18 (:REWRITE MOD-OF-*-SUBST-CONSTANT-ARG2))
 (18 18 (:REWRITE MOD-OF-*-SUBST-CONSTANT-ARG1))
 (14 14 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (14 14 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (13 13 (:REWRITE MOD-OF-+-SUBST-CONSTANT))
 (13 13 (:REWRITE MOD-OF-+-REDUCE-POSITIVE-CONSTANT))
 (13 13 (:REWRITE MOD-OF-+-OF-CONSTANT))
 (11 11 (:REWRITE FOLD-CONSTS-IN-+))
 (11 11 (:REWRITE +-COMBINE-CONSTANTS))
 (11 11 (:REWRITE *-OF---ARG1))
 (6 6 (:REWRITE <-OF-CONSTANT-AND-*-OF-CONSTANT))
 (4 4 (:REWRITE MOD-OF-EXPT-WHEN-EQUAL-OF-MOD-SUBST-CONSTANT))
 (3 3 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (3 3 (:REWRITE EQUAL-OF-+-COMBINE-CONSTANTS))
 )
(MOD-OF-LOGAND-AND-2
 (27 27 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NON-POSITIVE-EXPONENT))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 )
(LOGAND-OF-NEGATIVE-AND-POSITIVE
 (32 32 (:TYPE-PRESCRIPTION LOGAND-NON-POSITIVE-TYPE))
 (32 32 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (5 1 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1 1 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (1 1 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:META CANCEL_PLUS-LESSP-CORRECT))
 )
(LOGAND-OF-NEGATIVE-AND-NEGATIVE
 (369 369 (:TYPE-PRESCRIPTION EVENP))
 (246 123 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (246 123 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (246 123 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (123 123 (:TYPE-PRESCRIPTION INTEGERP-OF-EXPT-TYPE))
 (123 123 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NON-POSITIVE-EXPONENT))
 (123 123 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (38 38 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (38 38 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (15 10 (:REWRITE DEFAULT-<-2))
 (14 10 (:REWRITE DEFAULT-<-1))
 (10 10 (:META CANCEL_PLUS-LESSP-CORRECT))
 (10 2 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR-NEGATIVE-EXPONENT))
 (10 2 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR))
 (9 9 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (5 1 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-4))
 (5 1 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-3))
 (5 1 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-2))
 (5 1 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-1))
 (5 1 (:LINEAR <=-OF-2-AND-EXPT2-LINEAR))
 (4 1 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 (2 2 (:LINEAR EXPT-BOUND-LINEAR-WEAK))
 (2 2 (:LINEAR EXPT-BOUND-LINEAR))
 (2 2 (:LINEAR <=-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (2 2 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (1 1 (:LINEAR EXPT-BOUND-LINEAR-2))
 (1 1 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (1 1 (:LINEAR <-OF-EXPT2-SAME-LINEAR))
 )
(<-OF-LOGAND
 (524 2 (:DEFINITION BINARY-LOGAND))
 (361 73 (:TYPE-PRESCRIPTION LOGAND-NON-POSITIVE-TYPE))
 (226 6 (:REWRITE COMMUTATIVITY-OF-+))
 (132 12 (:REWRITE DEFAULT-+-2))
 (132 12 (:REWRITE DEFAULT-+-1))
 (88 4 (:REWRITE UNICITY-OF-0))
 (84 4 (:DEFINITION FIX))
 (73 73 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (50 10 (:REWRITE DEFAULT-*-2))
 (44 4 (:DEFINITION EVENP))
 (40 40 (:TYPE-PRESCRIPTION FLOOR))
 (40 40 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (20 4 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (20 4 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (16 4 (:REWRITE FLOOR-WHEN-<))
 (12 4 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (12 4 (:REWRITE COMMUTATIVITY-OF-*))
 (10 10 (:REWRITE DEFAULT-*-1))
 (9 7 (:REWRITE DEFAULT-<-2))
 (7 7 (:REWRITE DEFAULT-<-1))
 (7 7 (:META CANCEL_PLUS-LESSP-CORRECT))
 (4 4 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (4 4 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-OF-2))
 (4 4 (:REWRITE ZIP-OPEN))
 (4 4 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (4 4 (:REWRITE INTEGERP-OF-*))
 (4 4 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (4 4 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (4 4 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (4 4 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (4 4 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(LOGAND-OF-X-AND-NOT-X-LEMMA
 (29 29 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (29 29 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (29 3 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 (20 3 (:REWRITE <-OF-+-OF---AND-0-ARG1))
 (12 3 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (11 11 (:META CANCEL_PLUS-LESSP-CORRECT))
 (8 2 (:REWRITE <-OF-MINUS-AND-CONSTANT))
 (7 6 (:REWRITE DEFAULT-<-2))
 (6 6 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (1 1 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (1 1 (:REWRITE DEFAULT-UNARY-MINUS))
 )
(LOGAND-OF-FLOOR-AND-FLOOR-WHEN-0
 (944 52 (:REWRITE FLOOR-WHEN-<))
 (396 12 (:LINEAR MY-FLOOR-LOWER-BOUND-LINEAR))
 (375 375 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (375 375 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (375 375 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (375 375 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (372 12 (:LINEAR FLOOR-UPPER-BOUND-LINEAR))
 (369 369 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (283 43 (:REWRITE DEFAULT-+-2))
 (283 43 (:REWRITE DEFAULT-+-1))
 (238 94 (:REWRITE DEFAULT-*-2))
 (212 12 (:REWRITE ZIP-OPEN))
 (212 3 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 (212 3 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (158 94 (:REWRITE DEFAULT-*-1))
 (126 126 (:META CANCEL_PLUS-LESSP-CORRECT))
 (116 52 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (116 52 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (116 52 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (106 106 (:REWRITE DEFAULT-<-2))
 (106 106 (:REWRITE DEFAULT-<-1))
 (104 8 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (101 13 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (100 12 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (97 97 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (93 13 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (80 8 (:REWRITE FLOOR-OF-FLOOR))
 (76 12 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-OF-2))
 (64 8 (:REWRITE EQUAL-OF-0-AND-FLOOR-GEN))
 (52 52 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (48 12 (:REWRITE <-OF-FLOOR-OF-CONSTANT-AND-CONSTANT-GEN))
 (48 12 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (48 12 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (44 44 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (40 8 (:REWRITE <-OF-*-OF-CONSTANT-AND-CONSTANT-GEN))
 (22 22 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (16 16 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (12 12 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (12 12 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (12 12 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (12 12 (:REWRITE INTEGERP-OF-*))
 (12 12 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (12 12 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (12 12 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (12 12 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 )
(LOGAND-OF-+-1-OF-*-2-AND-+-1-OF-*-2
 (154 22 (:REWRITE DEFAULT-+-2))
 (146 22 (:REWRITE DEFAULT-+-1))
 (88 4 (:REWRITE UNICITY-OF-0))
 (83 31 (:REWRITE DEFAULT-*-2))
 (77 77 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (77 77 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (44 6 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (42 8 (:REWRITE FLOOR-WHEN-<))
 (40 40 (:TYPE-PRESCRIPTION FLOOR))
 (40 40 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (36 8 (:REWRITE <-OF-*-OF-CONSTANT-AND-CONSTANT-GEN))
 (31 31 (:REWRITE DEFAULT-*-1))
 (28 28 (:META CANCEL_PLUS-LESSP-CORRECT))
 (24 8 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (24 8 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (22 2 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 (22 2 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (16 16 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (14 14 (:REWRITE DEFAULT-<-2))
 (14 14 (:REWRITE DEFAULT-<-1))
 (13 13 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (13 13 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (13 13 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (12 4 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (12 2 (:REWRITE MOD-WHEN-<-OF-0))
 (10 10 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (10 10 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (8 8 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (8 8 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (8 8 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (6 6 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (6 6 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (5 5 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (4 4 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (4 4 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-OF-2))
 (4 4 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (4 4 (:REWRITE INTEGERP-OF-*))
 (2 2 (:REWRITE MOD-WHEN-EQUAL-OF-MOD-AND-0-FREE-CHEAP))
 (2 2 (:REWRITE MOD-OF-*-SUBST-CONSTANT-ARG2))
 (2 2 (:REWRITE MOD-OF-*-SUBST-CONSTANT-ARG1))
 )
(LOGAND-OF-*-2-AND-*-2
 (138 14 (:REWRITE DEFAULT-+-2))
 (138 14 (:REWRITE DEFAULT-+-1))
 (84 84 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (69 17 (:REWRITE DEFAULT-*-2))
 (40 40 (:TYPE-PRESCRIPTION FLOOR))
 (40 40 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (24 8 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (24 8 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (24 6 (:REWRITE FLOOR-WHEN-<))
 (17 17 (:REWRITE DEFAULT-*-1))
 (16 4 (:REWRITE <-OF-*-OF-CONSTANT-AND-CONSTANT-GEN))
 (14 14 (:META CANCEL_PLUS-LESSP-CORRECT))
 (13 13 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (12 4 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (12 2 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (10 10 (:REWRITE DEFAULT-<-2))
 (10 10 (:REWRITE DEFAULT-<-1))
 (8 8 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (8 8 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (6 6 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (6 6 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (6 6 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (6 6 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (6 6 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (6 6 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (4 4 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (4 4 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-OF-2))
 (4 4 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (4 4 (:REWRITE INTEGERP-OF-*))
 )
(LOGAND-OF-+-1-OF-*-2-AND-*-2
 (139 15 (:REWRITE DEFAULT-+-2))
 (139 15 (:REWRITE DEFAULT-+-1))
 (84 84 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (74 22 (:REWRITE DEFAULT-*-2))
 (40 40 (:TYPE-PRESCRIPTION FLOOR))
 (40 40 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (33 7 (:REWRITE FLOOR-WHEN-<))
 (26 10 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (26 10 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (26 6 (:REWRITE <-OF-*-OF-CONSTANT-AND-CONSTANT-GEN))
 (22 22 (:REWRITE DEFAULT-*-1))
 (22 3 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (22 2 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (21 21 (:META CANCEL_PLUS-LESSP-CORRECT))
 (15 15 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (12 12 (:REWRITE DEFAULT-<-2))
 (12 12 (:REWRITE DEFAULT-<-1))
 (12 4 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (9 9 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (9 9 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (9 9 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (9 9 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (9 9 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (7 7 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (7 7 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (6 6 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (6 1 (:REWRITE MOD-WHEN-<-OF-0))
 (4 4 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (4 4 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-OF-2))
 (4 4 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (4 4 (:REWRITE INTEGERP-OF-*))
 (4 4 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (3 3 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (2 2 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (1 1 (:REWRITE MOD-WHEN-EQUAL-OF-MOD-AND-0-FREE-CHEAP))
 (1 1 (:REWRITE MOD-OF-*-SUBST-CONSTANT-ARG2))
 (1 1 (:REWRITE MOD-OF-*-SUBST-CONSTANT-ARG1))
 )
(LOGAND-OF-*-2-AND-+-1-OF-*-2
 (139 15 (:REWRITE DEFAULT-+-2))
 (139 15 (:REWRITE DEFAULT-+-1))
 (90 90 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (90 90 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (74 22 (:REWRITE DEFAULT-*-2))
 (40 40 (:TYPE-PRESCRIPTION FLOOR))
 (40 40 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (33 7 (:REWRITE FLOOR-WHEN-<))
 (26 6 (:REWRITE <-OF-*-OF-CONSTANT-AND-CONSTANT-GEN))
 (24 8 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (24 8 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (24 4 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 (23 23 (:META CANCEL_PLUS-LESSP-CORRECT))
 (22 22 (:REWRITE DEFAULT-*-1))
 (22 3 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (20 4 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (15 15 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (14 14 (:REWRITE DEFAULT-<-2))
 (14 14 (:REWRITE DEFAULT-<-1))
 (12 4 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (9 9 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (9 9 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (9 9 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (9 9 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (9 9 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (7 7 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (7 7 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (6 6 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (6 1 (:REWRITE MOD-WHEN-<-OF-0))
 (4 4 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (4 4 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-OF-2))
 (4 4 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (4 4 (:REWRITE INTEGERP-OF-*))
 (4 4 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (3 3 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (2 2 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (1 1 (:REWRITE MOD-WHEN-EQUAL-OF-MOD-AND-0-FREE-CHEAP))
 (1 1 (:REWRITE MOD-OF-*-SUBST-CONSTANT-ARG2))
 (1 1 (:REWRITE MOD-OF-*-SUBST-CONSTANT-ARG1))
 )
(LOGAND-LOWER-BOUND-NEGATIVE-2
 (7331 174 (:REWRITE FLOOR-WHEN-<))
 (4251 4251 (:TYPE-PRESCRIPTION EVENP))
 (3450 490 (:REWRITE DEFAULT-*-2))
 (2952 12 (:LINEAR EXPT-HALF-LINEAR))
 (2834 1417 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (2834 1417 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (2834 1417 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (2615 23 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (2352 1 (:REWRITE <-OF-LOGAND))
 (1764 12 (:LINEAR EXPT-OF-ONE-LESS-LINEAR))
 (1698 6 (:REWRITE FLOOR-MINUS-ARG1-BETTER))
 (1657 1657 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (1657 1657 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (1657 1657 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (1452 508 (:REWRITE DEFAULT-+-2))
 (1432 508 (:REWRITE DEFAULT-+-1))
 (1417 1417 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (1217 1217 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (1020 12 (:REWRITE FLOOR-OF-*-SAME))
 (912 12 (:REWRITE +-OF-EXPT2-OF-ONE-LESS-AND-EXPT2-OF-ONE-LESS))
 (862 186 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (818 490 (:REWRITE DEFAULT-*-1))
 (760 119 (:REWRITE ZIP-OPEN))
 (712 186 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (676 656 (:META CANCEL_PLUS-LESSP-CORRECT))
 (628 157 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (605 440 (:REWRITE DEFAULT-<-2))
 (580 440 (:REWRITE DEFAULT-<-1))
 (568 174 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (370 26 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (322 42 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (300 25 (:REWRITE DEFAULT-UNARY-MINUS))
 (291 97 (:REWRITE +-COMBINE-CONSTANTS))
 (282 282 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (282 282 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (274 142 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (269 36 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (269 36 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (252 252 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (238 42 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-OF-2))
 (224 26 (:REWRITE FLOOR-OF-FLOOR))
 (194 97 (:REWRITE EQUAL-OF-0-AND-+-OF---ALT))
 (174 174 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (162 6 (:REWRITE *-OF-*-COMBINE-CONSTANTS))
 (144 24 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR))
 (144 12 (:REWRITE FLOOR-OF-1-WHEN-INTEGERP))
 (126 26 (:REWRITE <-OF-*-OF-CONSTANT-AND-CONSTANT-GEN))
 (112 14 (:REWRITE EQUAL-OF-0-AND-FLOOR-GEN))
 (104 1 (:REWRITE LOGAND-OF-NEGATIVE-AND-POSITIVE))
 (88 25 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (88 25 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (78 6 (:REWRITE UNICITY-OF-1))
 (72 12 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-4))
 (72 12 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-2))
 (72 12 (:LINEAR <=-OF-2-AND-EXPT2-LINEAR))
 (68 68 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (42 42 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (42 42 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (42 42 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (42 42 (:REWRITE INTEGERP-OF-*))
 (42 42 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (42 42 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (24 24 (:LINEAR EXPT-BOUND-LINEAR-WEAK))
 (24 24 (:LINEAR EXPT-BOUND-LINEAR-2))
 (24 24 (:LINEAR EXPT-BOUND-LINEAR))
 (24 24 (:LINEAR <=-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (24 24 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR-NEGATIVE-EXPONENT))
 (24 24 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (23 23 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (12 12 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-3))
 (12 12 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-1))
 (3 3 (:REWRITE ZP-OPEN))
 )
(LOGAND-LOWER-BOUND-NEGATIVE-2-ALT
 (600 600 (:TYPE-PRESCRIPTION EVENP))
 (400 200 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (400 200 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (400 200 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (342 1 (:REWRITE <-OF-LOGAND))
 (200 200 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NON-POSITIVE-EXPONENT))
 (200 200 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (75 20 (:REWRITE DEFAULT-<-2))
 (50 2 (:LINEAR <-OF-EXPT2-SAME-LINEAR))
 (46 46 (:TYPE-PRESCRIPTION LOGAND-NON-POSITIVE-TYPE))
 (46 46 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (46 46 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (36 3 (:REWRITE DEFAULT-UNARY-MINUS))
 (30 4 (:LINEAR EXPT-BOUND-LINEAR-WEAK))
 (30 4 (:LINEAR <=-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (24 20 (:REWRITE DEFAULT-<-1))
 (20 20 (:META CANCEL_PLUS-LESSP-CORRECT))
 (16 4 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR))
 (9 9 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (9 9 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (8 2 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-4))
 (8 2 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-2))
 (8 2 (:LINEAR <=-OF-2-AND-EXPT2-LINEAR))
 (5 5 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (4 4 (:LINEAR EXPT-BOUND-LINEAR))
 (4 4 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR-NEGATIVE-EXPONENT))
 (4 4 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (4 1 (:REWRITE LOGAND-OF-NEGATIVE-AND-POSITIVE))
 (2 2 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-3))
 (2 2 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-1))
 (2 2 (:LINEAR EXPT-BOUND-LINEAR-2))
 (1 1 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (1 1 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (1 1 (:META CANCEL_PLUS-EQUAL-CORRECT))
 )
(UNSIGNED-BYTE-P-OF-LOGAND
 (171 2 (:REWRITE LOGAND-OF-NEGATIVE-AND-NEGATIVE))
 (168 168 (:TYPE-PRESCRIPTION EVENP))
 (112 56 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (112 56 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (112 56 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (65 31 (:REWRITE DEFAULT-<-2))
 (64 4 (:REWRITE <-OF-LOGAND))
 (56 56 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NON-POSITIVE-EXPONENT))
 (56 56 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (48 31 (:REWRITE DEFAULT-<-1))
 (31 31 (:META CANCEL_PLUS-LESSP-CORRECT))
 (16 4 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR))
 (12 12 (:TYPE-PRESCRIPTION LOGAND-NON-POSITIVE-TYPE))
 (12 12 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (12 1 (:REWRITE DEFAULT-UNARY-MINUS))
 (11 11 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (11 11 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (8 2 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-4))
 (8 2 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-2))
 (8 2 (:LINEAR <=-OF-2-AND-EXPT2-LINEAR))
 (8 2 (:DEFINITION NATP))
 (4 4 (:LINEAR EXPT-BOUND-LINEAR))
 (4 4 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR-NEGATIVE-EXPONENT))
 (4 4 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (3 3 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (3 3 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (3 3 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-3))
 (2 2 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-1))
 (2 2 (:LINEAR EXPT-BOUND-LINEAR-2))
 (1 1 (:REWRITE <-OF-MINUS-AND-CONSTANT))
 )
(FLOOR-BY-2-AND-SUB-1-INDUCT
 (3 3 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (3 3 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (3 3 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (3 3 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (3 3 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (3 3 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (3 3 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 )
(LOGAND-OF-PLUS--1-OF-EXPT
 (7206 7206 (:TYPE-PRESCRIPTION EVENP))
 (4804 2402 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (4804 2402 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (4804 2402 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (4766 14 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (3160 55 (:REWRITE MOD-WHEN-<))
 (2467 4 (:REWRITE <-OF-*-OF-/-ARG1-ARG1))
 (2402 2402 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (1968 275 (:REWRITE DEFAULT-*-2))
 (1597 172 (:REWRITE DEFAULT-+-2))
 (955 364 (:REWRITE DEFAULT-<-2))
 (943 41 (:REWRITE DEFAULT-UNARY-/))
 (778 275 (:REWRITE DEFAULT-*-1))
 (740 172 (:REWRITE DEFAULT-+-1))
 (663 663 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (663 663 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (663 663 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (644 364 (:REWRITE DEFAULT-<-1))
 (643 643 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (536 78 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (506 55 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (506 55 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (439 439 (:META CANCEL_PLUS-LESSP-CORRECT))
 (372 32 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (368 64 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (368 64 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (318 318 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (277 53 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (252 7 (:LINEAR EXPT-HALF-LINEAR))
 (230 32 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (150 150 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (150 150 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (148 78 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR))
 (96 8 (:REWRITE DEFAULT-UNARY-MINUS))
 (86 86 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (78 78 (:LINEAR EXPT-BOUND-LINEAR))
 (78 78 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR-NEGATIVE-EXPONENT))
 (78 78 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (74 39 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-2))
 (64 64 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (64 16 (:REWRITE <-OF-FLOOR-OF-CONSTANT-AND-CONSTANT-GEN))
 (55 55 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (55 55 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (54 14 (:REWRITE <-OF-*-OF-CONSTANT-AND-CONSTANT-GEN))
 (50 50 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE))
 (46 46 (:LINEAR EXPT-BOUND-LINEAR-2))
 (39 39 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-3))
 (39 39 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-1))
 (23 23 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (23 23 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (21 7 (:REWRITE +-OF-EXPT2-OF-ONE-LESS-AND-EXPT2-OF-ONE-LESS))
 (20 20 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (20 20 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (16 16 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (16 16 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (16 16 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (14 14 (:REWRITE MOD-OF-EXPT-WHEN-EQUAL-OF-MOD-SUBST-CONSTANT))
 (14 14 (:REWRITE MOD-OF-2-WHEN-EVEN-CHEAP))
 (5 5 (:REWRITE ZP-OPEN))
 (4 4 (:REWRITE <-OF-CONSTANT-AND-*-OF-CONSTANT))
 (1 1 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (1 1 (:REWRITE EQUAL-OF-+-COMBINE-CONSTANTS))
 )
(HELPER
 (663 663 (:TYPE-PRESCRIPTION EVENP))
 (502 2 (:LINEAR MY-FLOOR-LOWER-BOUND-LINEAR))
 (476 2 (:LINEAR FLOOR-UPPER-BOUND-LINEAR))
 (442 221 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (442 221 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (442 221 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (309 34 (:REWRITE DEFAULT-*-2))
 (221 221 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (160 4 (:REWRITE *-OF---ARG1))
 (144 12 (:REWRITE DEFAULT-UNARY-MINUS))
 (133 34 (:REWRITE DEFAULT-*-1))
 (115 5 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (115 5 (:REWRITE FLOOR-WHEN-<))
 (100 1 (:LINEAR EXPT-HALF-LINEAR))
 (75 20 (:REWRITE DEFAULT-+-2))
 (60 5 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (60 5 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (58 1 (:LINEAR EXPT-OF-ONE-LESS-LINEAR))
 (53 20 (:REWRITE DEFAULT-+-1))
 (41 41 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (41 41 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (33 33 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (33 33 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (33 33 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (24 2 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (24 2 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (20 5 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (14 4 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR))
 (13 1 (:REWRITE *-OF-*-OF-/-SAME))
 (12 1 (:DEFINITION FIX))
 (11 11 (:META CANCEL_PLUS-LESSP-CORRECT))
 (7 2 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-4))
 (7 2 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-2))
 (6 6 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (6 6 (:REWRITE DEFAULT-<-2))
 (6 6 (:REWRITE DEFAULT-<-1))
 (5 5 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (4 4 (:LINEAR EXPT-BOUND-LINEAR-WEAK))
 (4 4 (:LINEAR <=-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (4 4 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR-NEGATIVE-EXPONENT))
 (2 2 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (2 2 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (2 2 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-3))
 (2 2 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-1))
 )
(HELPER2
 (225 225 (:TYPE-PRESCRIPTION EVENP))
 (150 75 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (150 75 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (150 75 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (75 75 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NON-POSITIVE-EXPONENT))
 (75 75 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (36 3 (:REWRITE DEFAULT-UNARY-MINUS))
 (24 2 (:REWRITE DEFAULT-+-2))
 (24 2 (:REWRITE DEFAULT-+-1))
 (12 1 (:REWRITE DEFAULT-*-2))
 (3 3 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (3 3 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:META CANCEL_PLUS-LESSP-CORRECT))
 (1 1 (:REWRITE DEFAULT-*-1))
 )
(LOGAND-OF-+-OF-EXPT-AND-+-OF-EXPT
 (40650 40650 (:TYPE-PRESCRIPTION EVENP))
 (27100 13550 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (27100 13550 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (27100 13550 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (16728 892 (:REWRITE DEFAULT-+-2))
 (14061 892 (:REWRITE DEFAULT-+-1))
 (13550 13550 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (12873 1543 (:REWRITE DEFAULT-*-2))
 (6052 132 (:REWRITE <-OF-*-OF-CONSTANT-AND-CONSTANT-GEN))
 (5272 5272 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (5272 5272 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (4114 1543 (:REWRITE DEFAULT-*-1))
 (3813 144 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (3388 522 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (2974 400 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-TYPE))
 (2960 48 (:REWRITE FLOOR-OF-+-WHEN-MULT-ARG1))
 (2663 548 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (2464 46 (:REWRITE MOD-WHEN-<))
 (2351 522 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (2289 144 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (2260 175 (:REWRITE DEFAULT-UNARY-MINUS))
 (1780 1780 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (1597 345 (:REWRITE DEFAULT-<-1))
 (1482 74 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-1))
 (1193 401 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (587 345 (:REWRITE DEFAULT-<-2))
 (558 558 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (558 558 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (522 522 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (520 10 (:REWRITE EQUAL-OF---AND--))
 (481 481 (:META CANCEL_PLUS-LESSP-CORRECT))
 (418 54 (:REWRITE MOD-WHEN-<-OF-0))
 (332 46 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (332 46 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (332 46 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (332 46 (:REWRITE MOD-OF-2-WHEN-EVEN-CHEAP))
 (312 24 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (287 287 (:REWRITE INTEGERP-OF-*))
 (168 24 (:REWRITE FLOOR-OF-FLOOR))
 (158 158 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (158 158 (:REWRITE EQUAL-OF-+-COMBINE-CONSTANTS))
 (145 145 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (118 118 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (108 108 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (108 108 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (78 78 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (78 78 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (72 72 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (69 69 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (56 56 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (56 56 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (50 50 (:REWRITE FLOOR-PEEL-OFF-CONSTANT))
 (50 50 (:REWRITE FLOOR-OF-PLUS-NORMALIZE-NEGATIVE-CONSTANT))
 (46 46 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (40 40 (:LINEAR EXPT-BOUND-LINEAR))
 (40 40 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR-NEGATIVE-EXPONENT))
 (40 40 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR))
 (40 40 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (26 26 (:REWRITE NATP-OF-*-WHEN-NATP-AND-NATP))
 (26 26 (:REWRITE MOD-OF-*-SUBST-CONSTANT-ARG2))
 (26 26 (:REWRITE MOD-OF-*-SUBST-CONSTANT-ARG1))
 (24 24 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE))
 (20 20 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-3))
 (20 20 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-2))
 (20 20 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-1))
 (20 20 (:LINEAR EXPT-BOUND-LINEAR-2))
 (13 13 (:REWRITE ZP-OPEN))
 (10 10 (:REWRITE EQUAL-OF-*-AND-CONSTANT))
 (6 6 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 (4 4 (:REWRITE FOLD-CONSTS-IN-+))
 (4 4 (:REWRITE +-COMBINE-CONSTANTS))
 )
(LOGAND-OF-MOD-AND-MOD
 (1578 1578 (:TYPE-PRESCRIPTION EVENP))
 (1358 16 (:REWRITE MOD-WHEN-<))
 (1256 16 (:REWRITE MOD-WHEN-INTEGERP-OF-QUOTIENT))
 (1052 526 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (1052 526 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (1052 526 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (526 526 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NON-POSITIVE-EXPONENT))
 (526 526 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (343 13 (:REWRITE INTEGERP-OF-*))
 (299 13 (:REWRITE DEFAULT-UNARY-/))
 (245 102 (:REWRITE DEFAULT-<-2))
 (218 22 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (192 16 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (192 16 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (190 22 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (156 13 (:REWRITE DEFAULT-*-2))
 (142 142 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (102 102 (:REWRITE DEFAULT-<-1))
 (102 102 (:META CANCEL_PLUS-LESSP-CORRECT))
 (88 11 (:REWRITE INTEGERP-OF-/-OF-EXPT-2))
 (72 18 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR))
 (55 16 (:REWRITE MOD-WHEN-<-OF-0))
 (48 4 (:REWRITE DEFAULT-+-2))
 (37 37 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (37 37 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (36 9 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-4))
 (36 9 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-2))
 (36 9 (:LINEAR <=-OF-2-AND-EXPT2-LINEAR))
 (27 27 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE))
 (18 18 (:LINEAR EXPT-BOUND-LINEAR))
 (18 18 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR-NEGATIVE-EXPONENT))
 (18 18 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (16 16 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (16 16 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (16 16 (:REWRITE MOD-WHEN-EQUAL-OF-MOD-AND-0-FREE-CHEAP))
 (16 4 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 (13 13 (:REWRITE DEFAULT-*-1))
 (9 9 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-3))
 (9 9 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-1))
 (9 9 (:LINEAR EXPT-BOUND-LINEAR-2))
 (4 4 (:REWRITE DEFAULT-+-1))
 (1 1 (:META CANCEL_PLUS-EQUAL-CORRECT))
 )
(LOGAND-OF-MOD-AND-+-OF-EXPT
 (1749 1749 (:TYPE-PRESCRIPTION EVENP))
 (1166 583 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (1166 583 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (1166 583 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (1123 13 (:REWRITE MOD-WHEN-<))
 (853 13 (:REWRITE MOD-WHEN-INTEGERP-OF-QUOTIENT))
 (583 583 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NON-POSITIVE-EXPONENT))
 (583 583 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (246 1 (:REWRITE MOD-OF-+-SUBST-CONSTANT))
 (231 19 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (219 9 (:REWRITE INTEGERP-OF-*))
 (211 19 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (207 9 (:REWRITE DEFAULT-UNARY-/))
 (201 102 (:REWRITE DEFAULT-<-2))
 (185 14 (:REWRITE MOD-WHEN-<-OF-0))
 (175 175 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (157 102 (:REWRITE DEFAULT-<-1))
 (156 13 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (156 13 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (108 9 (:REWRITE DEFAULT-*-2))
 (102 102 (:META CANCEL_PLUS-LESSP-CORRECT))
 (96 24 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR))
 (76 10 (:REWRITE DEFAULT-+-2))
 (56 7 (:REWRITE INTEGERP-OF-/-OF-EXPT-2))
 (54 10 (:REWRITE DEFAULT-+-1))
 (48 48 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (48 48 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (48 12 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-4))
 (48 12 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-2))
 (48 12 (:LINEAR <=-OF-2-AND-EXPT2-LINEAR))
 (45 45 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE))
 (24 24 (:LINEAR EXPT-BOUND-LINEAR))
 (24 24 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR-NEGATIVE-EXPONENT))
 (24 24 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (14 14 (:REWRITE MOD-WHEN-EQUAL-OF-MOD-AND-0-FREE-CHEAP))
 (13 13 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (13 13 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (12 12 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-3))
 (12 12 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-1))
 (12 12 (:LINEAR EXPT-BOUND-LINEAR-2))
 (9 9 (:REWRITE DEFAULT-*-1))
 (8 2 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 (5 5 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (5 5 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (2 2 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (1 1 (:REWRITE MOD-OF-+-REDUCE-POSITIVE-CONSTANT))
 (1 1 (:REWRITE MOD-OF-+-OF-CONSTANT))
 )
(SIGNED-BYTE-P-OF-LOGAND
 (1320 1320 (:TYPE-PRESCRIPTION EVENP))
 (1032 4 (:REWRITE LOGAND-OF-NEGATIVE-AND-NEGATIVE))
 (880 440 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (880 440 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (880 440 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (440 440 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (380 83 (:REWRITE DEFAULT-<-2))
 (264 22 (:REWRITE DEFAULT-UNARY-MINUS))
 (144 4 (:LINEAR EXPT-HALF-LINEAR))
 (138 83 (:REWRITE DEFAULT-<-1))
 (103 103 (:META CANCEL_PLUS-LESSP-CORRECT))
 (80 20 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (66 66 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (66 66 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (66 7 (:LINEAR <=-OF-2-AND-EXPT2-LINEAR))
 (54 14 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR))
 (53 14 (:LINEAR EXPT-BOUND-LINEAR))
 (53 14 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (48 4 (:REWRITE DEFAULT-*-2))
 (31 31 (:REWRITE DEFAULT-+-2))
 (31 31 (:REWRITE DEFAULT-+-1))
 (27 7 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-4))
 (27 7 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-2))
 (14 14 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (14 14 (:LINEAR EXPT-BOUND-LINEAR-WEAK))
 (14 14 (:LINEAR <=-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (14 14 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR-NEGATIVE-EXPONENT))
 (12 4 (:REWRITE +-OF-EXPT2-OF-ONE-LESS-AND-EXPT2-OF-ONE-LESS))
 (10 10 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (7 7 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-3))
 (7 7 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-1))
 (6 6 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (6 6 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (4 4 (:REWRITE DEFAULT-*-1))
 (3 3 (:REWRITE <-OF-MINUS-AND-CONSTANT))
 )
(<-OF-LOGAND-AND--1
 (773 773 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (773 773 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (773 773 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (447 4 (:REWRITE <-OF-LOGAND))
 (394 40 (:REWRITE DEFAULT-+-2))
 (389 73 (:REWRITE DEFAULT-<-1))
 (376 40 (:REWRITE DEFAULT-+-1))
 (236 71 (:REWRITE DEFAULT-*-2))
 (174 174 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (156 6 (:LINEAR FLOOR-UPPER-BOUND-LINEAR))
 (130 4 (:REWRITE LOGAND-OF-NEGATIVE-AND-POSITIVE))
 (110 30 (:REWRITE FLOOR-WHEN-<))
 (102 3 (:LINEAR MY-FLOOR-LOWER-BOUND-LINEAR))
 (99 71 (:REWRITE DEFAULT-*-1))
 (90 90 (:META CANCEL_PLUS-LESSP-CORRECT))
 (86 30 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (85 19 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (73 73 (:REWRITE DEFAULT-<-2))
 (58 30 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (58 30 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (52 4 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (51 51 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (41 13 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (41 13 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (30 30 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (28 4 (:REWRITE FLOOR-OF-FLOOR))
 (28 1 (:LINEAR MOD-OF-2-UPPER-BOUND))
 (26 26 (:REWRITE HELPER))
 (26 26 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (26 1 (:LINEAR MOD-BOUND-LINEAR-ARG2-STRONG))
 (26 1 (:LINEAR MOD-BOUND-LINEAR-ARG2))
 (20 5 (:REWRITE MOD-WHEN-<-OF-0))
 (19 19 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (19 19 (:REWRITE INTEGERP-OF-*))
 (19 19 (:REWRITE HELPER2))
 (17 17 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (15 6 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (15 6 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (11 11 (:REWRITE ZIP-OPEN))
 (11 11 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (11 11 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (11 11 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (8 1 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 (8 1 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (5 5 (:REWRITE MOD-WHEN-EQUAL-OF-MOD-AND-0-FREE-CHEAP))
 (4 4 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (4 4 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (4 4 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (4 4 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (4 4 (:REWRITE MOD-WHEN-<))
 (4 4 (:REWRITE MOD-OF-2-WHEN-EVEN-CHEAP))
 (3 3 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (3 3 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (1 1 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (1 1 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 )
(<-OF--1-AND-LOGAND
 (26 14 (:REWRITE DEFAULT-<-2))
 (21 14 (:REWRITE DEFAULT-<-1))
 (14 14 (:META CANCEL_PLUS-LESSP-CORRECT))
 (9 1 (:REWRITE <-OF-LOGAND))
 (5 5 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (4 1 (:REWRITE LOGAND-OF-NEGATIVE-AND-POSITIVE))
 (3 3 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (1 1 (:REWRITE <-OF-LOGAND-AND-0-HELPER))
 )
(INDUCT-FLOOR-AND-SUB1
 (3 3 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (3 3 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (3 3 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (3 3 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (3 3 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (3 3 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (3 3 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 )
(LOGAND-OF-MINUS-OF-EXPT
 (1224 1224 (:TYPE-PRESCRIPTION EVENP))
 (816 408 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (816 408 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (816 408 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (408 408 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (168 14 (:REWRITE DEFAULT-UNARY-MINUS))
 (125 15 (:REWRITE DEFAULT-*-2))
 (117 117 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (117 117 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (117 117 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (82 82 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (68 68 (:TYPE-PRESCRIPTION <=-OF-FLOOR-WHEN-<-TYPE))
 (52 8 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (52 8 (:REWRITE FLOOR-WHEN-<))
 (51 7 (:REWRITE DEFAULT-<-2))
 (48 15 (:REWRITE DEFAULT-*-1))
 (41 5 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (36 3 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (34 12 (:REWRITE DEFAULT-+-2))
 (34 12 (:REWRITE DEFAULT-+-1))
 (34 5 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (30 8 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (30 8 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (22 22 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (22 22 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (21 7 (:REWRITE DEFAULT-<-1))
 (12 12 (:REWRITE HELPER))
 (8 8 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (8 8 (:META CANCEL_PLUS-LESSP-CORRECT))
 (6 6 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (4 4 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (4 4 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (4 4 (:LINEAR EXPT-BOUND-LINEAR))
 (4 4 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR-NEGATIVE-EXPONENT))
 (4 4 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR))
 (4 4 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (3 3 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (3 3 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 (3 1 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (2 2 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (2 2 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (2 2 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-3))
 (2 2 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-2))
 (2 2 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-1))
 (2 2 (:LINEAR EXPT-BOUND-LINEAR-2))
 (1 1 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (1 1 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-OF-2))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (1 1 (:REWRITE INTEGERP-OF-*))
 (1 1 (:REWRITE HELPER2))
 )
(LOGAND-OF-MINUS-OF-EXPT-AND-LOGNOT
 (360 360 (:TYPE-PRESCRIPTION EVENP))
 (240 120 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (240 120 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (240 120 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (120 120 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NON-POSITIVE-EXPONENT))
 (120 120 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (49 5 (:REWRITE DEFAULT-UNARY-MINUS))
 (34 34 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (34 34 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (26 2 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 (24 2 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (23 10 (:REWRITE DEFAULT-<-2))
 (16 2 (:REWRITE <-OF-+-OF---AND-0-ARG1))
 (12 12 (:META CANCEL_PLUS-LESSP-CORRECT))
 (10 10 (:REWRITE DEFAULT-<-1))
 (8 8 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (8 8 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (8 2 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR))
 (4 1 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-4))
 (4 1 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-2))
 (4 1 (:LINEAR <=-OF-2-AND-EXPT2-LINEAR))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:LINEAR EXPT-BOUND-LINEAR))
 (2 2 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR-NEGATIVE-EXPONENT))
 (2 2 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (1 1 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-3))
 (1 1 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-1))
 (1 1 (:LINEAR EXPT-BOUND-LINEAR-2))
 )
