(COMMUTATIVITY-OF-LOGAND
 (54 36 (:REWRITE DEFAULT-+-2))
 (54 36 (:REWRITE DEFAULT-+-1))
 (48 12 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (36 30 (:REWRITE DEFAULT-*-2))
 (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 RATIONALP-OF-MOD))
 (12 12 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (12 12 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-TYPE))
 (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
 (5162 212 (:DEFINITION NONNEGATIVE-INTEGER-QUOTIENT))
 (3952 16 (:REWRITE FLOOR-MINUS-ARG1-HACK))
 (2800 32 (:REWRITE FLOOR-PEEL-OFF-CONSTANT))
 (1886 1373 (:REWRITE DEFAULT-+-2))
 (1862 1862 (:META CANCEL_PLUS-LESSP-CORRECT))
 (1656 1373 (:REWRITE DEFAULT-+-1))
 (1588 136 (:REWRITE <-OF-NUMERATOR-AND-DENOMINATOR-SAME))
 (1360 334 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (1331 1252 (:REWRITE DEFAULT-*-2))
 (1252 1252 (:REWRITE DEFAULT-*-1))
 (1186 1049 (:REWRITE DEFAULT-<-1))
 (1053 1049 (:REWRITE DEFAULT-<-2))
 (869 253 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (852 158 (:REWRITE FLOOR-WHEN-<))
 (848 212 (:DEFINITION NFIX))
 (606 404 (:REWRITE DEFAULT-UNARY-MINUS))
 (528 132 (:REWRITE <-OF-*-OF-/-ARG2-ARG1))
 (446 446 (:TYPE-PRESCRIPTION RATIONALP-OF-MOD))
 (446 446 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (446 446 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-TYPE))
 (334 334 (:REWRITE INTEGERP-OF-*))
 (320 32 (:REWRITE INTEGERP-OF-+-OF-1/2-AND-*-OF-1/2))
 (316 136 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (274 270 (:REWRITE DEFAULT-DENOMINATOR))
 (262 262 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (232 136 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (216 72 (:REWRITE *-OF-*-COMBINE-CONSTANTS))
 (208 204 (:REWRITE DEFAULT-NUMERATOR))
 (208 16 (:REWRITE INTEGERP-OF-+-OF---AND--))
 (192 32 (:REWRITE MOD-WHEN-INTEGERP-OF-QUOTIENT))
 (192 32 (:REWRITE DISTRIBUTIVITY))
 (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))
 (159 95 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (141 71 (:REWRITE ZIP-OPEN))
 (126 126 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (100 20 (:REWRITE EQUAL-OF-*-OF-/))
 (96 16 (:REWRITE MOD-WHEN-MULTIPLE))
 (95 95 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (80 16 (:REWRITE MOD-WHEN-<))
 (68 68 (:LINEAR <=-OF-*-AND-*-SAME-ALT-LINEAR))
 (68 68 (:LINEAR <-OF-*-AND-*))
 (64 16 (:REWRITE *-OF---ARG2))
 (37 37 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (34 34 (:LINEAR <-OF-*-SAME-LINEAR-SPECIAL))
 (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))
 (16 16 (: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))
 (2 2 (:TYPE-PRESCRIPTION FLOOR-TYPE-WHEN-NONPOSITIVE-AND-NONNEGATIVE))
 (2 2 (:TYPE-PRESCRIPTION FLOOR-TYPE-NON-NEGATIVE))
 (2 2 (:TYPE-PRESCRIPTION FLOOR-TYPE-1-PART-1-BETTER))
 )
(<-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
 (136 6 (:REWRITE COMMUTATIVITY-OF-+))
 (118 118 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (78 12 (:REWRITE DEFAULT-+-2))
 (78 12 (:REWRITE DEFAULT-+-1))
 (52 4 (:REWRITE UNICITY-OF-0))
 (48 48 (:TYPE-PRESCRIPTION FLOOR-TYPE-WHEN-NONPOSITIVE-AND-NONNEGATIVE))
 (48 48 (:TYPE-PRESCRIPTION FLOOR-TYPE-NON-NEGATIVE))
 (48 48 (:TYPE-PRESCRIPTION FLOOR-TYPE-1-PART-1-BETTER))
 (48 4 (:DEFINITION FIX))
 (48 4 (:DEFINITION EVENP))
 (32 10 (:REWRITE DEFAULT-*-2))
 (23 10 (:REWRITE DEFAULT-<-2))
 (16 4 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (14 6 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (14 6 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (12 4 (:REWRITE COMMUTATIVITY-OF-*))
 (10 10 (:REWRITE DEFAULT-<-1))
 (10 10 (:REWRITE DEFAULT-*-1))
 (10 10 (:META CANCEL_PLUS-LESSP-CORRECT))
 (7 7 (:REWRITE ZIP-OPEN))
 (7 7 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (4 4 (:TYPE-PRESCRIPTION RATIONALP-OF-MOD))
 (4 4 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (4 4 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-TYPE))
 (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
 (1118 96 (:REWRITE FLOOR-WHEN-<))
 (801 801 (:TYPE-PRESCRIPTION FLOOR-TYPE-WHEN-NONPOSITIVE-AND-NONNEGATIVE))
 (801 801 (:TYPE-PRESCRIPTION FLOOR-TYPE-NON-NEGATIVE))
 (801 801 (:TYPE-PRESCRIPTION FLOOR-TYPE-1-PART-1-BETTER))
 (465 209 (:REWRITE DEFAULT-*-2))
 (452 452 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (450 14 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (373 33 (:REWRITE ZIP-OPEN))
 (289 209 (:REWRITE DEFAULT-*-1))
 (288 66 (:REWRITE DEFAULT-+-2))
 (264 66 (:REWRITE DEFAULT-+-1))
 (258 10 (:LINEAR MY-FLOOR-LOWER-BOUND-LINEAR))
 (256 14 (:REWRITE <-OF-*-OF-/-ARG1-ARG1))
 (238 10 (:LINEAR FLOOR-BOUND-BETTER-LINEAR))
 (198 10 (:LINEAR FLOOR-UPPER-BOUND-LINEAR))
 (193 161 (:REWRITE DEFAULT-<-2))
 (185 185 (:META CANCEL_PLUS-LESSP-CORRECT))
 (176 96 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (176 96 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (176 96 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (170 20 (:REWRITE FLOOR-OF-FLOOR))
 (161 161 (:REWRITE DEFAULT-<-1))
 (160 20 (:REWRITE EQUAL-OF-0-AND-FLOOR-GEN))
 (108 24 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (108 24 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (96 96 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (78 4 (:LINEAR MOD-BOUND-LINEAR-ARG2))
 (76 76 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (57 57 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (54 8 (:REWRITE MOD-WHEN-MULTIPLE))
 (52 13 (:REWRITE MOD-WHEN-<-OF-0))
 (40 10 (:REWRITE <-OF-FLOOR-OF-CONSTANT-AND-CONSTANT-GEN))
 (40 10 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (40 10 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (32 8 (:REWRITE MOD-WHEN-<))
 (24 24 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (24 24 (:REWRITE INTEGERP-OF-*))
 (22 22 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (22 22 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (16 4 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 (10 10 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE))
 (10 10 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (10 10 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (8 8 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (8 8 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (8 8 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (8 8 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (8 8 (:REWRITE MOD-OF-2-WHEN-EVEN-CHEAP))
 (4 4 (:LINEAR <=-OF-*-AND-*-SAME-LINEAR))
 (4 4 (:LINEAR <=-OF-*-AND-*-SAME-ALT-LINEAR))
 (4 4 (:LINEAR <-OF-*-AND-*))
 (3 3 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (3 3 (:REWRITE EQUAL-OF-+-COMBINE-CONSTANTS))
 (3 3 (:REWRITE EQUAL-OF-*-AND-CONSTANT))
 (2 2 (:LINEAR <-OF-*-SAME-LINEAR-SPECIAL))
 (2 2 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-4))
 (2 2 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-3))
 (2 2 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-2))
 (2 2 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-1))
 )
(<=-OF-LOGAND-SAME-ARG1
 (864 864 (:TYPE-PRESCRIPTION FLOOR-TYPE-WHEN-NONPOSITIVE-AND-NONNEGATIVE))
 (864 864 (:TYPE-PRESCRIPTION FLOOR-TYPE-1-PART-1-BETTER))
 (495 495 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (148 37 (:REWRITE FLOOR-WHEN-<))
 (130 22 (:REWRITE DEFAULT-+-2))
 (130 22 (:REWRITE DEFAULT-+-1))
 (130 1 (:REWRITE *-OF-FLOOR-OF-SAME-WHEN-MULTIPLE))
 (110 54 (:REWRITE DEFAULT-<-2))
 (102 62 (:REWRITE DEFAULT-*-2))
 (64 54 (:REWRITE DEFAULT-<-1))
 (62 62 (:REWRITE DEFAULT-*-1))
 (54 54 (:META CANCEL_PLUS-LESSP-CORRECT))
 (37 37 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (37 37 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (37 37 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (37 37 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (37 37 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (30 1 (:LINEAR MOD-BOUND-LINEAR-ARG2-STRONG))
 (30 1 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 (27 1 (:LINEAR MOD-BOUND-LINEAR-ARG2))
 (24 6 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (24 4 (:REWRITE MOD-WHEN-MULTIPLE))
 (24 4 (:REWRITE MOD-WHEN-INTEGERP-OF-QUOTIENT))
 (17 17 (:TYPE-PRESCRIPTION RATIONALP-OF-MOD))
 (17 17 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (17 17 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-TYPE))
 (17 9 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (17 9 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (16 4 (:REWRITE MOD-WHEN-<))
 (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 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (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-<-OF-0))
 (4 4 (:REWRITE MOD-OF-2-WHEN-EVEN-CHEAP))
 (4 4 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (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
 (398 398 (:TYPE-PRESCRIPTION FLOOR-TYPE-WHEN-NONPOSITIVE-AND-NONNEGATIVE))
 (398 398 (:TYPE-PRESCRIPTION FLOOR-TYPE-NON-NEGATIVE))
 (398 398 (:TYPE-PRESCRIPTION FLOOR-TYPE-1-PART-1-BETTER))
 (366 366 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (366 366 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (318 60 (:REWRITE DEFAULT-+-2))
 (318 60 (:REWRITE DEFAULT-+-1))
 (262 152 (:REWRITE DEFAULT-*-2))
 (152 152 (:REWRITE DEFAULT-*-1))
 (144 12 (:REWRITE MOD-WHEN-MULTIPLE))
 (144 12 (:REWRITE MOD-WHEN-INTEGERP-OF-QUOTIENT))
 (48 12 (:REWRITE MOD-WHEN-<-OF-0))
 (48 12 (:REWRITE MOD-WHEN-<))
 (42 42 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (41 41 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (41 41 (:REWRITE INTEGERP-OF-*))
 (40 32 (:REWRITE DEFAULT-<-1))
 (38 23 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (38 23 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (32 32 (:REWRITE DEFAULT-<-2))
 (32 32 (:META CANCEL_PLUS-LESSP-CORRECT))
 (30 30 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (30 30 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (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
 (24536 1414 (:REWRITE MOD-WHEN-<-OF-0))
 (20898 405 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (14941 11893 (:REWRITE DEFAULT-*-2))
 (14869 64 (:REWRITE <-OF-*-AND-0))
 (12097 11893 (:REWRITE DEFAULT-*-1))
 (10871 116 (:REWRITE <-OF-LOGAND-AND-0))
 (9717 1049 (:REWRITE MOD-WHEN-MULTIPLE))
 (8339 2579 (:REWRITE DEFAULT-+-2))
 (7601 2579 (:REWRITE DEFAULT-+-1))
 (7002 69 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (5715 5715 (:META CANCEL_PLUS-LESSP-CORRECT))
 (4994 4994 (:TYPE-PRESCRIPTION FLOOR-TYPE-WHEN-NONPOSITIVE-AND-NONNEGATIVE))
 (4994 4994 (:TYPE-PRESCRIPTION FLOOR-TYPE-NON-NEGATIVE))
 (4994 4994 (:TYPE-PRESCRIPTION FLOOR-TYPE-1-PART-1-BETTER))
 (4900 994 (:REWRITE MOD-WHEN-<))
 (4516 4042 (:REWRITE DEFAULT-<-1))
 (4188 1047 (:REWRITE <-OF-*-OF-/-ARG1-ARG1))
 (4048 4042 (:REWRITE DEFAULT-<-2))
 (1630 1630 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (1372 1372 (:REWRITE INTEGERP-OF-*))
 (1356 226 (:REWRITE <-OF-+-OF---AND-0-ARG1))
 (1106 275 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (1106 275 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (1063 134 (:REWRITE INTEGERP-OF-+-OF--1/2))
 (1050 267 (:REWRITE <-OF-FLOOR-OF-CONSTANT-AND-CONSTANT-GEN))
 (994 994 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (994 994 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (994 994 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (994 994 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (994 994 (:REWRITE MOD-OF-2-WHEN-EVEN-CHEAP))
 (746 746 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (661 134 (:REWRITE INTEGERP-OF-+-OF-1/2-AND-*-OF-1/2))
 (523 138 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-2))
 (494 494 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (494 494 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (276 46 (:REWRITE EQUAL-OF-0-AND-+-OF---ALT))
 (275 275 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (275 275 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (229 229 (:REWRITE MOD-OF-*-SUBST-CONSTANT-ARG2))
 (229 229 (:REWRITE MOD-OF-*-SUBST-CONSTANT-ARG1))
 (138 138 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-1-CHEAP))
 (138 138 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-1))
 (112 112 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE))
 (102 102 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (91 91 (:REWRITE EQUAL-OF-/))
 (84 21 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 (78 6 (:REWRITE <-OF-FLOOR-AND-0))
 (77 7 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (69 69 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (55 55 (:REWRITE MOD-OF-+-SUBST-CONSTANT))
 (46 46 (:REWRITE MOD-OF-+-OF---WHEN-EQUAL-OF-MOD-ARG1))
 (30 6 (:REWRITE <-OF-FLOOR-AND-0-2))
 )
(LOGAND-IS-ZERO-HELPER-2
 (24536 1414 (:REWRITE MOD-WHEN-<-OF-0))
 (21984 405 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (14943 11899 (:REWRITE DEFAULT-*-2))
 (14773 64 (:REWRITE <-OF-*-AND-0))
 (12103 11899 (:REWRITE DEFAULT-*-1))
 (10871 116 (:REWRITE <-OF-LOGAND-AND-0))
 (9717 1049 (:REWRITE MOD-WHEN-MULTIPLE))
 (8339 2579 (:REWRITE DEFAULT-+-2))
 (7601 2579 (:REWRITE DEFAULT-+-1))
 (7002 69 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (5715 5715 (:META CANCEL_PLUS-LESSP-CORRECT))
 (4994 4994 (:TYPE-PRESCRIPTION FLOOR-TYPE-WHEN-NONPOSITIVE-AND-NONNEGATIVE))
 (4994 4994 (:TYPE-PRESCRIPTION FLOOR-TYPE-NON-NEGATIVE))
 (4994 4994 (:TYPE-PRESCRIPTION FLOOR-TYPE-1-PART-1-BETTER))
 (4900 994 (:REWRITE MOD-WHEN-<))
 (4516 4042 (:REWRITE DEFAULT-<-1))
 (4188 1047 (:REWRITE <-OF-*-OF-/-ARG1-ARG1))
 (4048 4042 (:REWRITE DEFAULT-<-2))
 (1628 1628 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (1372 1372 (:REWRITE INTEGERP-OF-*))
 (1356 226 (:REWRITE <-OF-+-OF---AND-0-ARG1))
 (1106 275 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (1106 275 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (1063 134 (:REWRITE INTEGERP-OF-+-OF--1/2))
 (1050 267 (:REWRITE <-OF-FLOOR-OF-CONSTANT-AND-CONSTANT-GEN))
 (994 994 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (994 994 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (994 994 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (994 994 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (994 994 (:REWRITE MOD-OF-2-WHEN-EVEN-CHEAP))
 (746 746 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (661 134 (:REWRITE INTEGERP-OF-+-OF-1/2-AND-*-OF-1/2))
 (523 138 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-2))
 (494 494 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (494 494 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (276 46 (:REWRITE EQUAL-OF-0-AND-+-OF---ALT))
 (275 275 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (275 275 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (229 229 (:REWRITE MOD-OF-*-SUBST-CONSTANT-ARG2))
 (229 229 (:REWRITE MOD-OF-*-SUBST-CONSTANT-ARG1))
 (138 138 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-1-CHEAP))
 (138 138 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-1))
 (112 112 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE))
 (102 102 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (91 91 (:REWRITE EQUAL-OF-/))
 (84 21 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 (78 6 (:REWRITE <-OF-FLOOR-AND-0))
 (77 7 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (69 69 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (55 55 (:REWRITE MOD-OF-+-SUBST-CONSTANT))
 (46 46 (:REWRITE MOD-OF-+-OF---WHEN-EQUAL-OF-MOD-ARG1))
 (30 6 (:REWRITE <-OF-FLOOR-AND-0-2))
 )
(LOGAND-ASSOCIATIVE
 (576196 14303 (:LINEAR MY-FLOOR-LOWER-BOUND-LINEAR))
 (547598 14303 (:LINEAR FLOOR-BOUND-BETTER-LINEAR))
 (533468 14303 (:LINEAR FLOOR-UPPER-BOUND-LINEAR))
 (528910 1014 (:REWRITE <-OF-*-AND-0))
 (415166 371360 (:REWRITE DEFAULT-*-2))
 (382016 371360 (:REWRITE DEFAULT-*-1))
 (316826 921 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 (247505 28149 (:REWRITE MOD-WHEN-MULTIPLE))
 (156992 156992 (:META CANCEL_PLUS-LESSP-CORRECT))
 (156088 27069 (:REWRITE MOD-WHEN-<))
 (145071 145071 (:TYPE-PRESCRIPTION FLOOR-TYPE-WHEN-NONPOSITIVE-AND-NONNEGATIVE))
 (145071 145071 (:TYPE-PRESCRIPTION FLOOR-TYPE-NON-NEGATIVE))
 (145071 145071 (:TYPE-PRESCRIPTION FLOOR-TYPE-1-PART-1-BETTER))
 (136200 126930 (:REWRITE DEFAULT-<-1))
 (134644 58380 (:REWRITE DEFAULT-+-2))
 (126934 126930 (:REWRITE DEFAULT-<-2))
 (123578 58380 (:REWRITE DEFAULT-+-1))
 (57216 14303 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (57216 14303 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (57184 14299 (:REWRITE <-OF-FLOOR-OF-CONSTANT-AND-CONSTANT-GEN))
 (45168 11292 (:REWRITE <-OF-*-OF-/-ARG1-ARG1))
 (28221 27069 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (28221 27069 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (28221 27069 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (27069 27069 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (26790 26790 (:REWRITE INTEGERP-OF-*))
 (17408 17408 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (14303 14303 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (14303 14303 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (12840 2140 (:REWRITE <-OF-+-OF---AND-0-ARG1))
 (9107 2502 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-2))
 (6380 580 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (5589 5589 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (5589 5589 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (3521 3521 (:REWRITE MOD-OF-*-SUBST-CONSTANT-ARG2))
 (3521 3521 (:REWRITE MOD-OF-*-SUBST-CONSTANT-ARG1))
 (2502 2502 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-1-CHEAP))
 (2502 2502 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-1))
 (2326 290 (:REWRITE EQUAL-OF-0-AND-FLOOR-GEN))
 (1770 1770 (:REWRITE EQUAL-OF-/))
 (1753 1753 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE))
 (1317 1317 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (1166 1166 (:REWRITE MOD-OF-+-SUBST-CONSTANT))
 (834 834 (:REWRITE MOD-OF-+-OF---WHEN-EQUAL-OF-MOD-ARG1))
 (58 58 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (52 4 (:REWRITE <-OF-FLOOR-AND-0))
 (20 4 (:REWRITE <-OF-FLOOR-AND-0-2))
 )
(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
 (2564 170 (:REWRITE FLOOR-WHEN-<))
 (1969 1969 (:TYPE-PRESCRIPTION FLOOR-TYPE-WHEN-NONPOSITIVE-AND-NONNEGATIVE))
 (1969 1969 (:TYPE-PRESCRIPTION FLOOR-TYPE-NON-NEGATIVE))
 (1969 1969 (:TYPE-PRESCRIPTION FLOOR-TYPE-1-PART-1-BETTER))
 (1060 352 (:REWRITE DEFAULT-*-2))
 (780 780 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (600 24 (:LINEAR MY-FLOOR-LOWER-BOUND-LINEAR))
 (580 73 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (552 96 (:REWRITE DEFAULT-+-2))
 (552 24 (:LINEAR FLOOR-BOUND-BETTER-LINEAR))
 (504 96 (:REWRITE DEFAULT-+-1))
 (463 55 (:REWRITE ZIP-OPEN))
 (456 24 (:LINEAR FLOOR-UPPER-BOUND-LINEAR))
 (424 352 (:REWRITE DEFAULT-*-1))
 (361 73 (:TYPE-PRESCRIPTION RATIONALP-OF-MOD))
 (334 334 (:META CANCEL_PLUS-LESSP-CORRECT))
 (286 286 (:REWRITE DEFAULT-<-2))
 (286 286 (:REWRITE DEFAULT-<-1))
 (266 170 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (266 170 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (266 170 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (264 24 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (240 24 (:REWRITE FLOOR-OF-FLOOR))
 (192 24 (:REWRITE EQUAL-OF-0-AND-FLOOR-GEN))
 (170 170 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (164 44 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (164 44 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (146 146 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (96 24 (:REWRITE <-OF-FLOOR-OF-CONSTANT-AND-CONSTANT-GEN))
 (96 24 (:REWRITE <-OF-*-OF-/-ARG1-ARG1))
 (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 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-TYPE))
 (73 73 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (73 73 (:REWRITE INTEGERP-OF-*))
 (51 51 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (51 51 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (24 24 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (24 24 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 )
(FLOOR-FLOOR-SUB1-INDUCT
 (6 6 (:TYPE-PRESCRIPTION FLOOR-TYPE-WHEN-NONPOSITIVE-AND-NONNEGATIVE))
 (6 6 (:TYPE-PRESCRIPTION FLOOR-TYPE-NON-NEGATIVE))
 (6 6 (:TYPE-PRESCRIPTION FLOOR-TYPE-1-PART-1-BETTER))
 )
(FLOOR-OF-LOGAND-AND-EXPT
 (10060 55 (:REWRITE <-OF-*-OF-/-ARG2-ARG1))
 (4853 211 (:LINEAR FLOOR-BOUND-BETTER-LINEAR))
 (3649 252 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (3584 1576 (:REWRITE DEFAULT-*-2))
 (2253 1603 (:REWRITE DEFAULT-<-1))
 (2204 1603 (:REWRITE DEFAULT-<-2))
 (2182 1576 (:REWRITE DEFAULT-*-1))
 (2178 5 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (2116 12 (:REWRITE <-OF-LOGAND-AND-0))
 (1945 1945 (:META CANCEL_PLUS-LESSP-CORRECT))
 (1890 1890 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (1686 783 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (1676 4 (:REWRITE <-OF-*-AND-0))
 (1371 783 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (1371 783 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (1345 781 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (879 234 (:REWRITE <-OF-FLOOR-OF-CONSTANT-AND-CONSTANT-GEN))
 (843 24 (:LINEAR <-OF-*-SAME-LINEAR-SPECIAL))
 (783 783 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (777 294 (:REWRITE DEFAULT-+-2))
 (658 19 (:REWRITE <-OF-FLOOR-AND-0))
 (553 79 (:REWRITE DEFAULT-UNARY-/))
 (484 2 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (484 2 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (414 294 (:REWRITE DEFAULT-+-1))
 (299 1 (:REWRITE <-OF-*-OF-/-ARG1-ARG1))
 (288 240 (:LINEAR EXPT-BOUND-LINEAR-WEAK))
 (252 252 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (252 252 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (240 240 (:LINEAR EXPT-BOUND-LINEAR))
 (163 32 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (156 32 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (80 80 (:REWRITE *-OF-*-COMBINE-CONSTANTS))
 (76 19 (:REWRITE <-OF-FLOOR-AND-0-2))
 (74 5 (:LINEAR FLOOR-UPPER-BOUND-STRONG-LINEAR-CHEAP))
 (48 48 (:LINEAR <=-OF-*-AND-*-SAME-LINEAR))
 (48 48 (:LINEAR <=-OF-*-AND-*-SAME-ALT-LINEAR))
 (48 48 (:LINEAR <-OF-*-AND-*))
 (40 10 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (25 25 (:REWRITE <-OF-1-AND-EXPT))
 (24 24 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-4))
 (24 24 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-3))
 (24 24 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-2))
 (24 24 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-1))
 (19 19 (:REWRITE <-OF-0-AND-EXPT))
 (18 18 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (15 15 (:TYPE-PRESCRIPTION NATP-OF-EXPT))
 (14 14 (:REWRITE ZIP-OPEN))
 (13 13 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (13 13 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (10 10 (:TYPE-PRESCRIPTION RATIONALP-OF-MOD))
 (10 10 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (10 10 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-TYPE))
 (10 10 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (10 10 (:REWRITE INTEGERP-OF-*))
 (6 6 (:REWRITE ZP-OPEN))
 (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 FLOOR-TYPE-NON-NEGATIVE))
 (40 40 (:TYPE-PRESCRIPTION FLOOR-TYPE-1-PART-1-BETTER))
 (28 28 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (28 28 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 )
(FLOOR-OF-LOGAND-AND-2-BACK
 (190 2 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 (190 2 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (111 111 (:TYPE-PRESCRIPTION FLOOR-TYPE-NON-NEGATIVE))
 (111 111 (:TYPE-PRESCRIPTION FLOOR-TYPE-1-PART-1-BETTER))
 (100 4 (:LINEAR MY-FLOOR-LOWER-BOUND-LINEAR))
 (92 4 (:LINEAR FLOOR-BOUND-BETTER-LINEAR))
 (76 4 (:LINEAR FLOOR-UPPER-BOUND-LINEAR))
 (58 16 (:REWRITE FLOOR-WHEN-<))
 (50 50 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (50 50 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (36 12 (:REWRITE COMMUTATIVITY-OF-*))
 (30 30 (:META CANCEL_PLUS-LESSP-CORRECT))
 (26 26 (:REWRITE DEFAULT-<-2))
 (26 26 (:REWRITE DEFAULT-<-1))
 (24 24 (:REWRITE DEFAULT-*-2))
 (24 24 (:REWRITE DEFAULT-*-1))
 (16 16 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (16 16 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (16 16 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (16 16 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (16 16 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (16 4 (:REWRITE <-OF-FLOOR-OF-CONSTANT-AND-CONSTANT-GEN))
 (16 4 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (16 4 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (11 3 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (11 3 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (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
 (156 2 (:LINEAR FLOOR-UPPER-BOUND-LINEAR))
 (102 102 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (102 102 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (82 2 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (74 2 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (65 41 (:REWRITE DEFAULT-*-2))
 (65 41 (:REWRITE DEFAULT-*-1))
 (63 63 (:TYPE-PRESCRIPTION FLOOR-TYPE-NON-NEGATIVE))
 (63 63 (:TYPE-PRESCRIPTION FLOOR-TYPE-1-PART-1-BETTER))
 (57 15 (:REWRITE FLOOR-WHEN-<))
 (56 8 (:REWRITE <-OF-*-AND-0))
 (54 6 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (50 50 (:META CANCEL_PLUS-LESSP-CORRECT))
 (50 42 (:REWRITE DEFAULT-<-2))
 (43 11 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (42 42 (:REWRITE DEFAULT-<-1))
 (30 2 (:REWRITE <-OF-LOGAND-AND-0))
 (28 7 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (24 6 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 (22 22 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (22 22 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (15 15 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (15 15 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (15 15 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (15 11 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (10 2 (:REWRITE DEFAULT-+-2))
 (7 7 (:TYPE-PRESCRIPTION RATIONALP-OF-MOD))
 (7 7 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (7 7 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-TYPE))
 (7 7 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (7 7 (: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
 (954 954 (:TYPE-PRESCRIPTION FLOOR-TYPE-NON-NEGATIVE))
 (101 1 (:REWRITE *-OF-FLOOR-OF-SAME-WHEN-MULTIPLE))
 (59 11 (:REWRITE DEFAULT-<-2))
 (58 42 (:REWRITE DEFAULT-*-2))
 (45 9 (:REWRITE DEFAULT-+-2))
 (45 9 (:REWRITE DEFAULT-+-1))
 (42 42 (:REWRITE DEFAULT-*-1))
 (30 1 (:LINEAR MOD-BOUND-LINEAR-ARG2-STRONG))
 (27 1 (:LINEAR MOD-BOUND-LINEAR-ARG2))
 (21 21 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (21 21 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (21 21 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (21 21 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (21 21 (:REWRITE FLOOR-WHEN-<))
 (21 21 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (18 3 (:REWRITE MOD-WHEN-MULTIPLE))
 (18 3 (:REWRITE MOD-WHEN-INTEGERP-OF-QUOTIENT))
 (17 5 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 (17 5 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (15 11 (:REWRITE DEFAULT-<-1))
 (13 13 (:META CANCEL_PLUS-LESSP-CORRECT))
 (12 3 (:REWRITE MOD-WHEN-<-OF-0))
 (11 11 (:TYPE-PRESCRIPTION RATIONALP-OF-MOD))
 (11 11 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (11 11 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-TYPE))
 (8 2 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (6 6 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (5 5 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (5 5 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (5 1 (:REWRITE <=-OF-LOGAND-SAME-ARG1))
 (3 3 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (3 3 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (3 3 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (3 3 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (3 3 (:REWRITE MOD-WHEN-EQUAL-OF-MOD-AND-0-FREE-CHEAP))
 (3 3 (:REWRITE MOD-WHEN-<))
 (3 3 (:REWRITE MOD-OF-2-WHEN-EVEN-CHEAP))
 (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
 (1390 160 (:REWRITE FLOOR-WHEN-<))
 (950 38 (:LINEAR MY-FLOOR-LOWER-BOUND-LINEAR))
 (874 38 (:LINEAR FLOOR-BOUND-BETTER-LINEAR))
 (818 21 (:REWRITE <-OF-MINUS-AND-CONSTANT))
 (789 789 (:TYPE-PRESCRIPTION FLOOR-TYPE-WHEN-NONPOSITIVE-AND-NONNEGATIVE))
 (789 789 (:TYPE-PRESCRIPTION FLOOR-TYPE-NON-NEGATIVE))
 (789 789 (:TYPE-PRESCRIPTION FLOOR-TYPE-1-PART-1-BETTER))
 (723 357 (:REWRITE DEFAULT-*-2))
 (722 38 (:LINEAR FLOOR-UPPER-BOUND-LINEAR))
 (711 18 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (616 13 (:REWRITE <-OF-+-OF---AND-0-ARG1))
 (488 146 (:REWRITE DEFAULT-+-2))
 (432 146 (:REWRITE DEFAULT-+-1))
 (394 394 (:META CANCEL_PLUS-LESSP-CORRECT))
 (385 357 (:REWRITE DEFAULT-*-1))
 (348 324 (:REWRITE DEFAULT-<-1))
 (338 324 (:REWRITE DEFAULT-<-2))
 (250 17 (:REWRITE MOD-WHEN-<-OF-0))
 (239 6 (:REWRITE FLOOR-OF-ONE-LESS-GEN))
 (237 237 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (222 12 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (219 6 (:DEFINITION NATP))
 (198 166 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (198 166 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (198 166 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (166 166 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (159 35 (:REWRITE DEFAULT-UNARY-MINUS))
 (152 38 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (152 38 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (143 143 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (142 14 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (127 9 (:REWRITE MOD-WHEN-<))
 (68 17 (:REWRITE <-OF-FLOOR-OF-CONSTANT-AND-CONSTANT-GEN))
 (66 9 (:REWRITE MOD-WHEN-MULTIPLE))
 (57 14 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (50 5 (:REWRITE FLOOR-OF-FLOOR))
 (46 14 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (40 5 (:REWRITE <-OF-0-AND-FLOOR))
 (38 38 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (38 38 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (36 2 (:LINEAR MOD-BOUND-LINEAR-ARG2))
 (24 3 (:REWRITE EQUAL-OF-0-AND-FLOOR-GEN))
 (22 2 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (16 16 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (16 16 (:REWRITE INTEGERP-OF-*))
 (13 9 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (13 9 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (13 9 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (12 12 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (9 9 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (9 9 (:REWRITE MOD-OF-2-WHEN-EVEN-CHEAP))
 (8 2 (:REWRITE <-OF-*-OF-/-ARG1-ARG1))
 (8 2 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 (6 6 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE))
 (6 6 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(MOD-OF-LOGAND-AND-EXPT-ALT
 (27457 1802 (:REWRITE FLOOR-WHEN-<))
 (15136 94 (:REWRITE <-OF-LOGAND-AND-0))
 (14249 325 (:REWRITE MOD-WHEN-MULTIPLE))
 (13972 13972 (:TYPE-PRESCRIPTION FLOOR-TYPE-1-PART-1-BETTER))
 (13491 4705 (:REWRITE DEFAULT-*-2))
 (11432 69 (:REWRITE <-OF-*-OF-/-ARG2-ARG1))
 (8493 122 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 (7579 4705 (:REWRITE DEFAULT-*-1))
 (7482 156 (:REWRITE COMMUTATIVITY-2-OF-*))
 (5600 4363 (:REWRITE DEFAULT-<-1))
 (5243 4363 (:REWRITE DEFAULT-<-2))
 (5066 5066 (:META CANCEL_PLUS-LESSP-CORRECT))
 (4480 4480 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (4414 1073 (:REWRITE DEFAULT-+-2))
 (3986 578 (:REWRITE DEFAULT-UNARY-/))
 (3482 1073 (:REWRITE DEFAULT-+-1))
 (2592 8 (:REWRITE <-OF-*-AND-0))
 (2324 1818 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (2260 1802 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (2260 1802 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (2021 293 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (1916 18 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (1860 1722 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (1802 1802 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (1704 138 (:REWRITE /-OF-*))
 (1509 62 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (1260 26 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-2))
 (1205 293 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (1205 293 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (1109 293 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (736 113 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (609 489 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (564 564 (:TYPE-PRESCRIPTION NATP-OF-EXPT))
 (538 113 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (489 489 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (453 453 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE))
 (270 270 (:LINEAR EXPT-BOUND-LINEAR))
 (180 36 (:REWRITE UNICITY-OF-1))
 (125 26 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-1))
 (112 28 (:REWRITE DEFAULT-UNARY-MINUS))
 (86 86 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (86 86 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (40 16 (:REWRITE MOD-OF-2-WHEN-EVEN-CHEAP))
 (11 11 (:REWRITE ZP-OPEN))
 (9 9 (:REWRITE MOD-OF-+-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-+-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
 (39790 2822 (:REWRITE FLOOR-WHEN-<))
 (23962 133 (:REWRITE <-OF-LOGAND-AND-0))
 (21266 474 (:REWRITE MOD-WHEN-MULTIPLE))
 (21184 7269 (:REWRITE DEFAULT-*-2))
 (20947 20947 (:TYPE-PRESCRIPTION FLOOR-TYPE-1-PART-1-BETTER))
 (12186 248 (:REWRITE COMMUTATIVITY-2-OF-*))
 (11757 7269 (:REWRITE DEFAULT-*-1))
 (11722 181 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 (9344 78 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (8604 6467 (:REWRITE DEFAULT-<-1))
 (7745 1736 (:REWRITE DEFAULT-+-2))
 (7727 6467 (:REWRITE DEFAULT-<-2))
 (7505 7505 (:META CANCEL_PLUS-LESSP-CORRECT))
 (6838 758 (:REWRITE <-OF-FLOOR-OF-CONSTANT-AND-CONSTANT-GEN))
 (6664 6664 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (6123 1736 (:REWRITE DEFAULT-+-1))
 (5356 784 (:REWRITE DEFAULT-UNARY-/))
 (3888 12 (:REWRITE <-OF-*-AND-0))
 (3696 2844 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (3608 2822 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (3608 2822 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (3008 2702 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (2974 424 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (2822 2822 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (2804 30 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (2688 222 (:REWRITE /-OF-*))
 (1936 44 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-2))
 (1864 424 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (1864 424 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (1534 424 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (1438 202 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (1160 1160 (:TYPE-PRESCRIPTION NATP-OF-EXPT))
 (1068 758 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (980 202 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (758 758 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (614 614 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE))
 (324 81 (:REWRITE DEFAULT-UNARY-MINUS))
 (260 52 (:REWRITE UNICITY-OF-1))
 (187 44 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-1))
 (132 132 (:LINEAR EXPT-BOUND-LINEAR))
 (106 106 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (106 106 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (97 43 (:REWRITE MOD-OF-2-WHEN-EVEN-CHEAP))
 (18 18 (:REWRITE ZP-OPEN))
 (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))
 (11 11 (:REWRITE FOLD-CONSTS-IN-+))
 (11 11 (:REWRITE +-COMBINE-CONSTANTS))
 (11 11 (:REWRITE *-OF---ARG1))
 (3 3 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (3 3 (:REWRITE EQUAL-OF-+-COMBINE-CONSTANTS))
 )
(MOD-OF-LOGAND-AND-2
 (29 29 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 )
(LOGAND-OF-NEGATIVE-AND-POSITIVE
 (83 83 (:TYPE-PRESCRIPTION NATP-OF-EXPT))
 (83 83 (:TYPE-PRESCRIPTION INTEGERP-OF-EXPT-TYPE))
 (25 25 (:TYPE-PRESCRIPTION LOGAND-NON-POSITIVE-TYPE))
 (25 25 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (2 2 (:LINEAR EXPT-BOUND-LINEAR-WEAK))
 (2 2 (:LINEAR EXPT-BOUND-LINEAR))
 (1 1 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (1 1 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (1 1 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 )
(LOGAND-OF-NEGATIVE-AND-NEGATIVE
 (9 9 (:TYPE-PRESCRIPTION NATP-OF-EXPT))
 (9 9 (:TYPE-PRESCRIPTION INTEGERP-OF-EXPT-TYPE))
 (3 3 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 )
(<-OF-LOGAND
 (368 2 (:DEFINITION BINARY-LOGAND))
 (217 73 (:TYPE-PRESCRIPTION LOGAND-NON-POSITIVE-TYPE))
 (146 6 (:REWRITE COMMUTATIVITY-OF-+))
 (84 12 (:REWRITE DEFAULT-+-2))
 (84 12 (:REWRITE DEFAULT-+-1))
 (73 73 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (56 4 (:REWRITE UNICITY-OF-0))
 (52 4 (:DEFINITION FIX))
 (48 4 (:DEFINITION EVENP))
 (40 40 (:TYPE-PRESCRIPTION FLOOR-TYPE-WHEN-NONPOSITIVE-AND-NONNEGATIVE))
 (40 40 (:TYPE-PRESCRIPTION FLOOR-TYPE-NON-NEGATIVE))
 (40 40 (:TYPE-PRESCRIPTION FLOOR-TYPE-1-PART-1-BETTER))
 (40 40 (:TYPE-PRESCRIPTION FLOOR))
 (34 10 (:REWRITE DEFAULT-*-2))
 (16 4 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (16 4 (:REWRITE FLOOR-WHEN-<))
 (12 4 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (12 4 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (12 4 (:REWRITE COMMUTATIVITY-OF-*))
 (10 10 (:REWRITE DEFAULT-*-1))
 (7 7 (:REWRITE DEFAULT-<-2))
 (7 7 (:REWRITE DEFAULT-<-1))
 (7 7 (:META CANCEL_PLUS-LESSP-CORRECT))
 (4 4 (:TYPE-PRESCRIPTION RATIONALP-OF-MOD))
 (4 4 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (4 4 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-TYPE))
 (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))
 )
(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
 (888 64 (:REWRITE FLOOR-WHEN-<))
 (387 387 (:TYPE-PRESCRIPTION FLOOR-TYPE-1-PART-1-BETTER))
 (300 12 (:LINEAR MY-FLOOR-LOWER-BOUND-LINEAR))
 (276 12 (:LINEAR FLOOR-BOUND-BETTER-LINEAR))
 (228 12 (:LINEAR FLOOR-UPPER-BOUND-LINEAR))
 (198 118 (:REWRITE DEFAULT-*-2))
 (194 3 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 (194 3 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (187 43 (:REWRITE DEFAULT-+-2))
 (187 43 (:REWRITE DEFAULT-+-1))
 (150 118 (:REWRITE DEFAULT-*-1))
 (148 12 (:REWRITE ZIP-OPEN))
 (138 138 (:META CANCEL_PLUS-LESSP-CORRECT))
 (118 118 (:REWRITE DEFAULT-<-2))
 (118 118 (:REWRITE DEFAULT-<-1))
 (97 97 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (96 64 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (96 64 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (96 64 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (88 8 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (80 12 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (80 8 (:REWRITE FLOOR-OF-FLOOR))
 (64 64 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (64 8 (:REWRITE EQUAL-OF-0-AND-FLOOR-GEN))
 (57 13 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (56 56 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (53 13 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (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 12 (:TYPE-PRESCRIPTION RATIONALP-OF-MOD))
 (32 8 (:REWRITE <-OF-*-OF-/-ARG1-ARG1))
 (22 22 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (12 12 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (12 12 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-TYPE))
 (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
 (106 22 (:REWRITE DEFAULT-+-2))
 (98 22 (:REWRITE DEFAULT-+-1))
 (75 75 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (75 75 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (67 31 (:REWRITE DEFAULT-*-2))
 (56 4 (:REWRITE UNICITY-OF-0))
 (40 40 (:TYPE-PRESCRIPTION FLOOR-TYPE-WHEN-NONPOSITIVE-AND-NONNEGATIVE))
 (40 40 (:TYPE-PRESCRIPTION FLOOR-TYPE-NON-NEGATIVE))
 (40 40 (:TYPE-PRESCRIPTION FLOOR-TYPE-1-PART-1-BETTER))
 (40 40 (:TYPE-PRESCRIPTION FLOOR))
 (38 8 (:REWRITE FLOOR-WHEN-<))
 (31 31 (:REWRITE DEFAULT-*-1))
 (24 24 (:META CANCEL_PLUS-LESSP-CORRECT))
 (24 6 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (18 2 (:REWRITE MOD-WHEN-<-OF-0))
 (16 16 (:REWRITE DEFAULT-<-2))
 (16 16 (:REWRITE DEFAULT-<-1))
 (16 16 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (16 8 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (16 8 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (16 4 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (14 2 (:REWRITE <-OF-*-AND-0))
 (14 2 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 (14 2 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (13 13 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (13 13 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (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))
 (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 RATIONALP-OF-MOD))
 (4 4 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (4 4 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-TYPE))
 (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))
 )
(LOGAND-OF-*-2-AND-*-2
 (90 14 (:REWRITE DEFAULT-+-2))
 (90 14 (:REWRITE DEFAULT-+-1))
 (84 84 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (53 17 (:REWRITE DEFAULT-*-2))
 (40 40 (:TYPE-PRESCRIPTION FLOOR-TYPE-WHEN-NONPOSITIVE-AND-NONNEGATIVE))
 (40 40 (:TYPE-PRESCRIPTION FLOOR-TYPE-NON-NEGATIVE))
 (40 40 (:TYPE-PRESCRIPTION FLOOR-TYPE-1-PART-1-BETTER))
 (40 40 (:TYPE-PRESCRIPTION FLOOR))
 (28 4 (:REWRITE <-OF-*-AND-0))
 (24 6 (:REWRITE FLOOR-WHEN-<))
 (18 18 (:META CANCEL_PLUS-LESSP-CORRECT))
 (18 2 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (17 17 (:REWRITE DEFAULT-*-1))
 (16 8 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (16 8 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (16 4 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (14 14 (:REWRITE DEFAULT-<-2))
 (14 14 (:REWRITE DEFAULT-<-1))
 (13 13 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (8 8 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (8 8 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (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 RATIONALP-OF-MOD))
 (4 4 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (4 4 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-TYPE))
 (4 4 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (4 4 (:REWRITE INTEGERP-OF-*))
 )
(LOGAND-OF-+-1-OF-*-2-AND-*-2
 (91 15 (:REWRITE DEFAULT-+-2))
 (91 15 (:REWRITE DEFAULT-+-1))
 (84 84 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (58 22 (:REWRITE DEFAULT-*-2))
 (40 40 (:TYPE-PRESCRIPTION FLOOR-TYPE-WHEN-NONPOSITIVE-AND-NONNEGATIVE))
 (40 40 (:TYPE-PRESCRIPTION FLOOR-TYPE-NON-NEGATIVE))
 (40 40 (:TYPE-PRESCRIPTION FLOOR-TYPE-1-PART-1-BETTER))
 (40 40 (:TYPE-PRESCRIPTION FLOOR))
 (31 7 (:REWRITE FLOOR-WHEN-<))
 (22 22 (:REWRITE DEFAULT-*-1))
 (21 21 (:META CANCEL_PLUS-LESSP-CORRECT))
 (21 3 (:REWRITE <-OF-*-AND-0))
 (18 10 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (18 10 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (16 4 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (15 15 (:REWRITE DEFAULT-<-2))
 (15 15 (:REWRITE DEFAULT-<-1))
 (15 15 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (14 2 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (12 3 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (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))
 (9 1 (:REWRITE MOD-WHEN-<-OF-0))
 (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))
 (4 4 (:TYPE-PRESCRIPTION RATIONALP-OF-MOD))
 (4 4 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (4 4 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-TYPE))
 (4 4 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (4 4 (:REWRITE INTEGERP-OF-*))
 (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))
 )
(LOGAND-OF-*-2-AND-+-1-OF-*-2
 (91 15 (:REWRITE DEFAULT-+-2))
 (91 15 (:REWRITE DEFAULT-+-1))
 (90 90 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (90 90 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (58 22 (:REWRITE DEFAULT-*-2))
 (40 40 (:TYPE-PRESCRIPTION FLOOR-TYPE-WHEN-NONPOSITIVE-AND-NONNEGATIVE))
 (40 40 (:TYPE-PRESCRIPTION FLOOR-TYPE-NON-NEGATIVE))
 (40 40 (:TYPE-PRESCRIPTION FLOOR-TYPE-1-PART-1-BETTER))
 (40 40 (:TYPE-PRESCRIPTION FLOOR))
 (31 7 (:REWRITE FLOOR-WHEN-<))
 (26 4 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (23 23 (:META CANCEL_PLUS-LESSP-CORRECT))
 (22 22 (:REWRITE DEFAULT-*-1))
 (21 3 (:REWRITE <-OF-*-AND-0))
 (17 17 (:REWRITE DEFAULT-<-2))
 (17 17 (:REWRITE DEFAULT-<-1))
 (16 8 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (16 8 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (16 4 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (16 4 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 (15 15 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (12 3 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (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))
 (9 1 (:REWRITE MOD-WHEN-<-OF-0))
 (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))
 (4 4 (:TYPE-PRESCRIPTION RATIONALP-OF-MOD))
 (4 4 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (4 4 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-TYPE))
 (4 4 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (4 4 (:REWRITE INTEGERP-OF-*))
 (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))
 )
(LOGAND-LOWER-BOUND-NEGATIVE
 (920 1 (:REWRITE <-OF-LOGAND))
 (500 119 (:REWRITE DEFAULT-*-2))
 (472 472 (:TYPE-PRESCRIPTION FLOOR-TYPE-NON-NEGATIVE))
 (448 4 (:LINEAR EXPT-HALF-LINEAR))
 (355 151 (:REWRITE DEFAULT-+-2))
 (343 151 (:REWRITE DEFAULT-+-1))
 (324 4 (:LINEAR EXPT-OF-ONE-LESS-LINEAR))
 (281 281 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (163 119 (:REWRITE DEFAULT-*-1))
 (158 37 (:REWRITE ZIP-OPEN))
 (134 86 (:REWRITE DEFAULT-<-1))
 (129 129 (:META CANCEL_PLUS-LESSP-CORRECT))
 (119 86 (:REWRITE DEFAULT-<-2))
 (116 29 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (108 32 (:REWRITE FLOOR-WHEN-<))
 (88 14 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (88 8 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (87 29 (:REWRITE +-COMBINE-CONSTANTS))
 (74 74 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (71 71 (:TYPE-PRESCRIPTION NATP-OF-EXPT))
 (66 34 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (64 32 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (58 29 (:REWRITE EQUAL-OF-0-AND-+-OF---ALT))
 (56 8 (:REWRITE FLOOR-OF-FLOOR))
 (52 13 (:REWRITE DEFAULT-UNARY-MINUS))
 (47 11 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (47 11 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (46 14 (:TYPE-PRESCRIPTION RATIONALP-OF-MOD))
 (32 32 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (32 8 (:REWRITE <-OF-*-OF-/-ARG1-ARG1))
 (24 24 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (16 2 (:REWRITE EQUAL-OF-0-AND-FLOOR-GEN))
 (14 14 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (14 14 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-TYPE))
 (14 14 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (14 14 (:REWRITE INTEGERP-OF-*))
 (14 14 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (14 14 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (12 12 (:LINEAR EXPT-BOUND-LINEAR))
 (12 3 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 (12 3 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (4 4 (:REWRITE <-OF-FLOOR-OF-CONSTANT-AND-CONSTANT-GEN))
 (1 1 (:REWRITE ZP-OPEN))
 )
(LOGAND-LOWER-BOUND-NEGATIVE-2
 (4941 217 (:REWRITE FLOOR-WHEN-<))
 (1624 539 (:REWRITE DEFAULT-*-2))
 (1568 14 (:LINEAR EXPT-HALF-LINEAR))
 (1134 14 (:LINEAR EXPT-OF-ONE-LESS-LINEAR))
 (1132 484 (:REWRITE DEFAULT-+-2))
 (1102 484 (:REWRITE DEFAULT-+-1))
 (920 1 (:REWRITE <-OF-LOGAND))
 (718 539 (:REWRITE DEFAULT-*-1))
 (596 106 (:REWRITE ZIP-OPEN))
 (557 1 (:REWRITE LOGAND-LOWER-BOUND-NEGATIVE))
 (549 529 (:META CANCEL_PLUS-LESSP-CORRECT))
 (549 217 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (491 29 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (470 386 (:REWRITE DEFAULT-<-1))
 (434 386 (:REWRITE DEFAULT-<-2))
 (411 217 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (411 217 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (359 29 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (336 84 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (326 26 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (281 191 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (272 42 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (252 84 (:REWRITE +-COMBINE-CONSTANTS))
 (226 226 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (224 26 (:REWRITE FLOOR-OF-FLOOR))
 (217 217 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (198 18 (:REWRITE *-OF-*-COMBINE-CONSTANTS))
 (168 84 (:REWRITE EQUAL-OF-0-AND-+-OF---ALT))
 (160 36 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (160 36 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (156 39 (:REWRITE DEFAULT-UNARY-MINUS))
 (146 42 (:TYPE-PRESCRIPTION RATIONALP-OF-MOD))
 (112 31 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (112 31 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (112 14 (:REWRITE EQUAL-OF-0-AND-FLOOR-GEN))
 (104 26 (:REWRITE <-OF-*-OF-/-ARG1-ARG1))
 (100 100 (:TYPE-PRESCRIPTION NATP-OF-EXPT))
 (90 18 (:REWRITE UNICITY-OF-1))
 (42 42 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (42 42 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-TYPE))
 (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))
 (28 28 (:LINEAR EXPT-BOUND-LINEAR-WEAK))
 (28 28 (:LINEAR EXPT-BOUND-LINEAR))
 (3 3 (:REWRITE ZP-OPEN))
 )
(LOGAND-LOWER-BOUND-NEGATIVE-2-ALT
 (66 1 (:REWRITE <-OF-LOGAND))
 (46 46 (:TYPE-PRESCRIPTION LOGAND-NON-POSITIVE-TYPE))
 (46 46 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (46 46 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (30 1 (:REWRITE LOGAND-LOWER-BOUND-NEGATIVE))
 (28 10 (:REWRITE DEFAULT-<-2))
 (27 27 (:TYPE-PRESCRIPTION NATP-OF-EXPT))
 (16 4 (:REWRITE DEFAULT-UNARY-MINUS))
 (15 6 (:LINEAR EXPT-BOUND-LINEAR-WEAK))
 (14 10 (:REWRITE DEFAULT-<-1))
 (10 10 (:META CANCEL_PLUS-LESSP-CORRECT))
 (6 6 (:LINEAR EXPT-BOUND-LINEAR))
 (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
 (40 4 (:REWRITE <-OF-LOGAND))
 (33 21 (:REWRITE DEFAULT-<-2))
 (32 21 (:REWRITE DEFAULT-<-1))
 (22 22 (:TYPE-PRESCRIPTION LOGAND-NON-POSITIVE-TYPE))
 (22 22 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (21 21 (:META CANCEL_PLUS-LESSP-CORRECT))
 (8 2 (:DEFINITION NATP))
 (5 2 (:REWRITE LOGAND-OF-NEGATIVE-AND-NEGATIVE))
 (4 4 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (4 4 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (4 4 (:LINEAR EXPT-BOUND-LINEAR))
 (3 3 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:REWRITE LOGAND-OF-NEGATIVE-AND-POSITIVE))
 )
(FLOOR-BY-2-AND-SUB-1-INDUCT
 (3 3 (:TYPE-PRESCRIPTION FLOOR-TYPE-WHEN-NONPOSITIVE-AND-NONNEGATIVE))
 (3 3 (:TYPE-PRESCRIPTION FLOOR-TYPE-NON-NEGATIVE))
 (3 3 (:TYPE-PRESCRIPTION FLOOR-TYPE-1-PART-1-BETTER))
 )
(LOGAND-OF-PLUS--1-OF-EXPT
 (3297 82 (:REWRITE FLOOR-WHEN-<))
 (2344 14 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (1750 21 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (1482 76 (:REWRITE MOD-WHEN-MULTIPLE))
 (1228 14 (:REWRITE <-OF-*-OF-/-ARG1-ARG1))
 (1166 383 (:REWRITE DEFAULT-*-2))
 (1024 68 (:REWRITE MOD-WHEN-<))
 (784 112 (:REWRITE DEFAULT-UNARY-/))
 (744 181 (:REWRITE DEFAULT-+-2))
 (662 662 (:TYPE-PRESCRIPTION FLOOR-TYPE-1-PART-1-BETTER))
 (638 399 (:REWRITE DEFAULT-<-2))
 (633 96 (:REWRITE MOD-WHEN-<-OF-0))
 (588 383 (:REWRITE DEFAULT-*-1))
 (549 399 (:REWRITE DEFAULT-<-1))
 (523 181 (:REWRITE DEFAULT-+-1))
 (457 457 (:META CANCEL_PLUS-LESSP-CORRECT))
 (436 10 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (311 311 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (304 96 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (248 82 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (248 82 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (239 68 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (239 68 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (208 16 (:REWRITE INTEGERP-OF--))
 (198 72 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (192 8 (:REWRITE <-OF---AND--))
 (134 30 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (124 124 (:LINEAR EXPT-BOUND-LINEAR))
 (122 30 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (102 102 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (96 24 (:REWRITE DEFAULT-UNARY-MINUS))
 (93 93 (:TYPE-PRESCRIPTION NATP-OF-EXPT))
 (87 24 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 (82 82 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (80 16 (:REWRITE UNICITY-OF-1))
 (80 16 (:REWRITE *-OF--1))
 (68 68 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (68 68 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (64 16 (:REWRITE <-OF-FLOOR-OF-CONSTANT-AND-CONSTANT-GEN))
 (49 49 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE))
 (22 22 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (21 21 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (21 21 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (16 16 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (16 16 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (16 16 (:REWRITE *-OF---ARG1))
 (11 11 (:REWRITE MOD-OF-2-WHEN-EVEN-CHEAP))
 (5 5 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (1 1 (:REWRITE EQUAL-OF-+-COMBINE-CONSTANTS))
 )
(HELPER
 (212 2 (:LINEAR MY-FLOOR-LOWER-BOUND-LINEAR))
 (202 2 (:LINEAR FLOOR-UPPER-BOUND-LINEAR))
 (202 2 (:LINEAR FLOOR-BOUND-BETTER-LINEAR))
 (116 44 (:REWRITE DEFAULT-*-2))
 (104 44 (:REWRITE DEFAULT-*-1))
 (92 23 (:REWRITE DEFAULT-UNARY-MINUS))
 (49 7 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (49 7 (:REWRITE FLOOR-WHEN-<))
 (34 1 (:LINEAR EXPT-HALF-LINEAR))
 (33 33 (:TYPE-PRESCRIPTION FLOOR-TYPE-NON-NEGATIVE))
 (28 7 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (28 7 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (28 7 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (24 9 (:REWRITE DEFAULT-+-2))
 (20 20 (:TYPE-PRESCRIPTION NATP-OF-EXPT))
 (20 1 (:LINEAR EXPT-OF-ONE-LESS-LINEAR))
 (18 9 (:REWRITE DEFAULT-+-1))
 (8 2 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (8 2 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (7 7 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (5 1 (:REWRITE *-OF-*-OF-/-SAME))
 (2 2 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (2 2 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (2 2 (:LINEAR EXPT-BOUND-LINEAR-WEAK))
 (2 2 (:LINEAR EXPT-BOUND-LINEAR))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:META CANCEL_PLUS-LESSP-CORRECT))
 )
(HELPER2
 (16 16 (:TYPE-PRESCRIPTION NATP-OF-EXPT))
 (12 3 (:REWRITE DEFAULT-UNARY-MINUS))
 (8 2 (:REWRITE DEFAULT-+-2))
 (8 2 (:REWRITE DEFAULT-+-1))
 (4 1 (:REWRITE DEFAULT-*-2))
 (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
 (4747 669 (:REWRITE DEFAULT-+-2))
 (4054 669 (:REWRITE DEFAULT-+-1))
 (3942 1374 (:REWRITE DEFAULT-*-2))
 (2200 1374 (:REWRITE DEFAULT-*-1))
 (2115 597 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (1468 613 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (1404 597 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (1342 38 (:REWRITE FLOOR-OF-+-WHEN-MULT-ARG1))
 (1266 555 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (1122 78 (:REWRITE <-OF-*-OF-/-ARG1-ARG1))
 (965 122 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (820 205 (:REWRITE DEFAULT-UNARY-MINUS))
 (631 122 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (608 46 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-1))
 (597 597 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (566 32 (:REWRITE MOD-WHEN-MULTIPLE))
 (521 257 (:REWRITE DEFAULT-<-1))
 (496 32 (:REWRITE MOD-WHEN-<))
 (345 345 (:META CANCEL_PLUS-LESSP-CORRECT))
 (323 257 (:REWRITE DEFAULT-<-2))
 (264 24 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (227 227 (:REWRITE INTEGERP-OF-*))
 (204 90 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (204 90 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (200 10 (:REWRITE EQUAL-OF---AND--))
 (168 24 (:REWRITE FLOOR-OF-FLOOR))
 (162 6 (:REWRITE <-OF-+-OF---AND-0-ARG1))
 (146 38 (:REWRITE MOD-WHEN-<-OF-0))
 (138 138 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (125 125 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (114 114 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (114 114 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (80 32 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (80 32 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (80 32 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (80 32 (:REWRITE MOD-OF-2-WHEN-EVEN-CHEAP))
 (52 52 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (52 52 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (40 40 (:REWRITE FLOOR-PEEL-OFF-CONSTANT))
 (40 40 (:REWRITE FLOOR-OF-PLUS-NORMALIZE-NEGATIVE-CONSTANT))
 (40 40 (:LINEAR EXPT-BOUND-LINEAR))
 (36 36 (:TYPE-PRESCRIPTION NATP-OF-EXPT))
 (32 32 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (24 24 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE))
 (16 16 (:REWRITE MOD-OF-*-SUBST-CONSTANT-ARG2))
 (16 16 (:REWRITE MOD-OF-*-SUBST-CONSTANT-ARG1))
 (13 13 (:REWRITE ZP-OPEN))
 (6 6 (:REWRITE FOLD-CONSTS-IN-+))
 (6 6 (:REWRITE +-COMBINE-CONSTANTS))
 (6 6 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 )
(LOGAND-OF-MOD-AND-MOD
 (456 16 (:REWRITE MOD-WHEN-INTEGERP-OF-QUOTIENT))
 (302 16 (:REWRITE MOD-WHEN-MULTIPLE))
 (299 16 (:REWRITE MOD-WHEN-<))
 (182 26 (:REWRITE DEFAULT-UNARY-/))
 (180 26 (:REWRITE INTEGERP-OF-*))
 (146 146 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (106 22 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (104 26 (:REWRITE DEFAULT-*-2))
 (96 57 (:REWRITE DEFAULT-<-2))
 (94 22 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (88 11 (:REWRITE INTEGERP-OF-/-OF-EXPT-2))
 (64 16 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (64 16 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (57 57 (:REWRITE DEFAULT-<-1))
 (57 57 (:META CANCEL_PLUS-LESSP-CORRECT))
 (55 16 (:REWRITE MOD-WHEN-<-OF-0))
 (27 27 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE))
 (26 26 (:TYPE-PRESCRIPTION NATP-OF-EXPT))
 (26 26 (:REWRITE DEFAULT-*-1))
 (18 18 (:LINEAR EXPT-BOUND-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 (:REWRITE DEFAULT-+-2))
 (16 4 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 (4 4 (:REWRITE DEFAULT-+-1))
 (1 1 (:META CANCEL_PLUS-EQUAL-CORRECT))
 )
(LOGAND-OF-MOD-AND-+-OF-EXPT
 (395 14 (:REWRITE MOD-WHEN-INTEGERP-OF-QUOTIENT))
 (224 13 (:REWRITE MOD-WHEN-<))
 (211 13 (:REWRITE MOD-WHEN-MULTIPLE))
 (175 175 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (133 19 (:REWRITE DEFAULT-UNARY-/))
 (117 19 (:REWRITE INTEGERP-OF-*))
 (103 19 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (91 19 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (89 23 (:REWRITE DEFAULT-*-2))
 (88 1 (:REWRITE MOD-OF-+-SUBST-CONSTANT))
 (69 42 (:REWRITE DEFAULT-<-2))
 (68 14 (:REWRITE MOD-WHEN-<-OF-0))
 (62 62 (:TYPE-PRESCRIPTION NATP-OF-EXPT))
 (57 42 (:REWRITE DEFAULT-<-1))
 (56 7 (:REWRITE INTEGERP-OF-/-OF-EXPT-2))
 (52 13 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (52 13 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (49 3 (:REWRITE COMMUTATIVITY-OF-*))
 (45 45 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE))
 (42 42 (:META CANCEL_PLUS-LESSP-CORRECT))
 (40 1 (:REWRITE DISTRIBUTIVITY))
 (35 23 (:REWRITE DEFAULT-*-1))
 (33 12 (:REWRITE DEFAULT-+-2))
 (27 12 (:REWRITE DEFAULT-+-1))
 (24 24 (:LINEAR EXPT-BOUND-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 1 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-1-CHEAP))
 (8 2 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 (8 2 (:DEFINITION FIX))
 (8 1 (:REWRITE *-OF-/-SAME))
 (5 5 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (5 5 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (2 2 (:META CANCEL_PLUS-EQUAL-CORRECT))
 )
(SIGNED-BYTE-P-OF-LOGAND
 (235 4 (:REWRITE LOGAND-OF-NEGATIVE-AND-NEGATIVE))
 (149 65 (:REWRITE DEFAULT-<-2))
 (103 65 (:REWRITE DEFAULT-<-1))
 (92 23 (:REWRITE DEFAULT-UNARY-MINUS))
 (80 4 (:REWRITE LOGAND-OF-NEGATIVE-AND-POSITIVE))
 (65 65 (:META CANCEL_PLUS-LESSP-CORRECT))
 (57 39 (:REWRITE DEFAULT-+-2))
 (57 39 (:REWRITE DEFAULT-+-1))
 (40 40 (:TYPE-PRESCRIPTION NATP-OF-EXPT))
 (32 20 (:LINEAR EXPT-BOUND-LINEAR))
 (24 6 (:REWRITE DEFAULT-*-2))
 (20 20 (:LINEAR EXPT-BOUND-LINEAR-WEAK))
 (10 10 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (7 7 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (7 7 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (6 6 (:REWRITE DEFAULT-*-1))
 (4 4 (:REWRITE <-OF-MINUS-AND-CONSTANT))
 )
