(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 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
 (5886 212 (:DEFINITION NONNEGATIVE-INTEGER-QUOTIENT))
 (3952 16 (:REWRITE FLOOR-MINUS-ARG1-HACK))
 (2800 32 (:REWRITE FLOOR-PEEL-OFF-CONSTANT))
 (2186 2186 (:META CANCEL_PLUS-LESSP-CORRECT))
 (1886 1373 (:REWRITE DEFAULT-+-2))
 (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))
 (1262 1125 (:REWRITE DEFAULT-<-1))
 (1252 1252 (:REWRITE DEFAULT-*-1))
 (1129 1125 (:REWRITE DEFAULT-<-2))
 (1029 269 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (876 76 (:REWRITE <-OF---OF-NUMERATOR-AND-DENOMINATOR-SAME))
 (852 158 (:REWRITE FLOOR-WHEN-<))
 (848 212 (:DEFINITION NFIX))
 (832 208 (:REWRITE <-OF-*-OF-/-ARG2-ARG1))
 (606 404 (:REWRITE DEFAULT-UNARY-MINUS))
 (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))
 (191 95 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (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))
 (141 71 (:REWRITE ZIP-OPEN))
 (126 126 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (120 20 (:REWRITE EQUAL-OF-*-OF-/))
 (96 16 (:REWRITE MOD-WHEN-MULTIPLE))
 (80 16 (:REWRITE MOD-WHEN-<))
 (79 79 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (79 79 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (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))
 (5 5 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (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))
 (48 4 (:DEFINITION EVENP))
 (44 10 (:REWRITE DEFAULT-*-2))
 (23 10 (:REWRITE DEFAULT-<-2))
 (20 6 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (20 6 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (16 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))
 (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 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
 (1142 86 (:REWRITE FLOOR-WHEN-<))
 (789 789 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (789 789 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (789 789 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (789 789 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (789 789 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (789 789 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (582 14 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (571 189 (:REWRITE DEFAULT-*-2))
 (493 33 (:REWRITE ZIP-OPEN))
 (452 452 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (369 66 (:REWRITE DEFAULT-+-2))
 (342 14 (:REWRITE <-OF-*-OF-/-ARG1-ARG1))
 (336 66 (:REWRITE DEFAULT-+-1))
 (329 189 (:REWRITE DEFAULT-*-1))
 (324 10 (:LINEAR MY-FLOOR-LOWER-BOUND-LINEAR))
 (304 10 (:LINEAR FLOOR-UPPER-BOUND-LINEAR))
 (226 86 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (226 86 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (226 86 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (195 151 (:REWRITE DEFAULT-<-2))
 (175 175 (:META CANCEL_PLUS-LESSP-CORRECT))
 (171 24 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (171 24 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (170 20 (:REWRITE FLOOR-OF-FLOOR))
 (160 20 (:REWRITE EQUAL-OF-0-AND-FLOOR-GEN))
 (151 151 (:REWRITE DEFAULT-<-1))
 (86 86 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (78 4 (:LINEAR MOD-BOUND-LINEAR-ARG2))
 (66 66 (: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 MOVE-MINUS-TO-CONSTANT))
 (22 22 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (22 22 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (20 20 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (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 (:REWRITE <-OF-CONSTANT-AND-*-OF-CONSTANT))
 (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
 (860 860 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (860 860 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (860 860 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (860 860 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (860 860 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (495 495 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (184 22 (:REWRITE DEFAULT-+-2))
 (184 22 (:REWRITE DEFAULT-+-1))
 (132 33 (:REWRITE FLOOR-WHEN-<))
 (130 50 (:REWRITE DEFAULT-<-2))
 (130 1 (:REWRITE *-OF-FLOOR-OF-SAME-WHEN-MULTIPLE))
 (115 54 (:REWRITE DEFAULT-*-2))
 (63 50 (:REWRITE DEFAULT-<-1))
 (54 54 (:REWRITE DEFAULT-*-1))
 (50 50 (:META CANCEL_PLUS-LESSP-CORRECT))
 (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 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))
 (23 9 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (23 9 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (17 17 (:TYPE-PRESCRIPTION RATIONALP-OF-MOD))
 (17 17 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (17 17 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-TYPE))
 (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 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
 (398 398 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (398 398 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (398 398 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (398 398 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (398 398 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (398 398 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (372 60 (:REWRITE DEFAULT-+-2))
 (372 60 (:REWRITE DEFAULT-+-1))
 (366 366 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (366 366 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (292 152 (: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 MOVE-MINUS-TO-CONSTANT))
 (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
 (20709 1145 (:REWRITE MOD-WHEN-<-OF-0))
 (16820 405 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (13203 9507 (:REWRITE DEFAULT-*-2))
 (12595 64 (:REWRITE <-OF-*-AND-0))
 (9783 9507 (:REWRITE DEFAULT-*-1))
 (8979 116 (:REWRITE <-OF-LOGAND-AND-0))
 (8686 2386 (:REWRITE DEFAULT-+-2))
 (8499 856 (:REWRITE MOD-WHEN-MULTIPLE))
 (7780 2386 (:REWRITE DEFAULT-+-1))
 (6073 69 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (5253 5253 (:META CANCEL_PLUS-LESSP-CORRECT))
 (4994 4994 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (4994 4994 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (4994 4994 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (4994 4994 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (4994 4994 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (4994 4994 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (4195 1047 (:REWRITE <-OF-*-OF-/-ARG1-ARG1))
 (4138 3580 (:REWRITE DEFAULT-<-1))
 (4128 801 (:REWRITE MOD-WHEN-<))
 (3586 3580 (:REWRITE DEFAULT-<-2))
 (1437 1437 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (1356 226 (:REWRITE <-OF-+-OF---AND-0-ARG1))
 (1304 1304 (:REWRITE INTEGERP-OF-*))
 (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))
 (801 801 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (801 801 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (801 801 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (801 801 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (801 801 (:REWRITE MOD-OF-2-WHEN-EVEN-CHEAP))
 (678 678 (: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 MOVE-MINUS-TO-CONSTANT))
 (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-/))
 (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))
 (55 55 (:REWRITE MOD-OF-+-SUBST-CONSTANT))
 (46 46 (:REWRITE MOD-OF-+-OF---WHEN-EQUAL-OF-MOD-ARG1))
 (37 37 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (30 6 (:REWRITE <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE))
 )
(LOGAND-IS-ZERO-HELPER-2
 (20709 1145 (:REWRITE MOD-WHEN-<-OF-0))
 (17554 405 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (13205 9513 (:REWRITE DEFAULT-*-2))
 (12499 64 (:REWRITE <-OF-*-AND-0))
 (9789 9513 (:REWRITE DEFAULT-*-1))
 (8979 116 (:REWRITE <-OF-LOGAND-AND-0))
 (8686 2386 (:REWRITE DEFAULT-+-2))
 (8499 856 (:REWRITE MOD-WHEN-MULTIPLE))
 (7780 2386 (:REWRITE DEFAULT-+-1))
 (6073 69 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (5253 5253 (:META CANCEL_PLUS-LESSP-CORRECT))
 (4994 4994 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (4994 4994 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (4994 4994 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (4994 4994 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (4994 4994 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (4994 4994 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (4195 1047 (:REWRITE <-OF-*-OF-/-ARG1-ARG1))
 (4138 3580 (:REWRITE DEFAULT-<-1))
 (4128 801 (:REWRITE MOD-WHEN-<))
 (3586 3580 (:REWRITE DEFAULT-<-2))
 (1435 1435 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (1356 226 (:REWRITE <-OF-+-OF---AND-0-ARG1))
 (1304 1304 (:REWRITE INTEGERP-OF-*))
 (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))
 (801 801 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (801 801 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (801 801 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (801 801 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (801 801 (:REWRITE MOD-OF-2-WHEN-EVEN-CHEAP))
 (678 678 (: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 MOVE-MINUS-TO-CONSTANT))
 (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-/))
 (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))
 (55 55 (:REWRITE MOD-OF-+-SUBST-CONSTANT))
 (46 46 (:REWRITE MOD-OF-+-OF---WHEN-EQUAL-OF-MOD-ARG1))
 (37 37 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (30 6 (:REWRITE <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE))
 )
(LOGAND-ASSOCIATIVE
 (576196 14303 (:LINEAR MY-FLOOR-LOWER-BOUND-LINEAR))
 (547598 14303 (:LINEAR FLOOR-UPPER-BOUND-LINEAR))
 (447098 1014 (:REWRITE <-OF-*-AND-0))
 (322682 266612 (:REWRITE DEFAULT-*-2))
 (283460 266612 (:REWRITE DEFAULT-*-1))
 (268443 921 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 (203837 20927 (:REWRITE MOD-WHEN-MULTIPLE))
 (145071 145071 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (145071 145071 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (145071 145071 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (145071 145071 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (145071 145071 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (145071 145071 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (135471 135471 (:META CANCEL_PLUS-LESSP-CORRECT))
 (133320 51158 (:REWRITE DEFAULT-+-2))
 (120187 19847 (:REWRITE MOD-WHEN-<))
 (119518 51158 (:REWRITE DEFAULT-+-1))
 (117397 105409 (:REWRITE DEFAULT-<-1))
 (105413 105409 (:REWRITE DEFAULT-<-2))
 (57216 14303 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (57216 14303 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (57184 14299 (:REWRITE <-OF-FLOOR-OF-CONSTANT-AND-CONSTANT-GEN))
 (45748 11292 (:REWRITE <-OF-*-OF-/-ARG1-ARG1))
 (22580 22580 (:REWRITE INTEGERP-OF-*))
 (21863 19847 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (21863 19847 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (21863 19847 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (19847 19847 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (14303 14303 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (14303 14303 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (13198 13198 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (12840 2140 (:REWRITE <-OF-+-OF---AND-0-ARG1))
 (9107 2502 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-2))
 (7540 580 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (5589 5589 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (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))
 (1643 1643 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (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-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE))
 )
(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
 (2612 146 (:REWRITE FLOOR-WHEN-<))
 (1945 1945 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (1945 1945 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (1945 1945 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (1945 1945 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (1945 1945 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (1945 1945 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (1384 304 (:REWRITE DEFAULT-*-2))
 (780 780 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (780 96 (:REWRITE DEFAULT-+-2))
 (744 24 (:LINEAR MY-FLOOR-LOWER-BOUND-LINEAR))
 (727 73 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (708 96 (:REWRITE DEFAULT-+-1))
 (696 24 (:LINEAR FLOOR-UPPER-BOUND-LINEAR))
 (607 55 (:REWRITE ZIP-OPEN))
 (508 73 (:TYPE-PRESCRIPTION RATIONALP-OF-MOD))
 (430 304 (:REWRITE DEFAULT-*-1))
 (314 146 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (314 146 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (314 146 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (312 24 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (310 310 (:META CANCEL_PLUS-LESSP-CORRECT))
 (262 262 (:REWRITE DEFAULT-<-2))
 (262 262 (:REWRITE DEFAULT-<-1))
 (254 44 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (254 44 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (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-/-ARG1-ARG1))
 (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 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-TYPE))
 (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-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
 (11536 55 (:REWRITE <-OF-*-OF-/-ARG2-ARG1))
 (6040 6040 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (6040 6040 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (5548 264 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (3927 1202 (:REWRITE DEFAULT-*-2))
 (2868 5 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (2414 1452 (:REWRITE DEFAULT-<-1))
 (2160 12 (:REWRITE <-OF-LOGAND-AND-0))
 (2146 1452 (:REWRITE DEFAULT-<-2))
 (2030 1202 (:REWRITE DEFAULT-*-1))
 (1918 1918 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (1843 7 (:REWRITE <-OF-CONSTANT-AND-*-OF-CONSTANT))
 (1812 1812 (:META CANCEL_PLUS-LESSP-CORRECT))
 (1787 596 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (1780 4 (:REWRITE <-OF-*-AND-0))
 (1472 596 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (1472 596 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (1434 594 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (1078 2 (:REWRITE <-OF-+-COMBINE-CONSTANTS-1))
 (967 24 (:LINEAR <-OF-*-SAME-LINEAR-SPECIAL))
 (963 306 (:REWRITE DEFAULT-+-2))
 (927 246 (:REWRITE <-OF-FLOOR-OF-CONSTANT-AND-CONSTANT-GEN))
 (677 19 (:REWRITE <-OF-FLOOR-AND-0))
 (596 596 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (553 79 (:REWRITE DEFAULT-UNARY-/))
 (542 2 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (480 306 (:REWRITE DEFAULT-+-1))
 (435 1 (:REWRITE <-OF-*-OF-/-ARG1-ARG1))
 (288 240 (:LINEAR EXPT-BOUND-LINEAR-WEAK))
 (264 264 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (264 264 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (241 32 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (240 240 (:LINEAR EXPT-BOUND-LINEAR))
 (231 32 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (120 120 (:LINEAR EXPT-BOUND-LINEAR-2))
 (98 5 (:LINEAR FLOOR-UPPER-BOUND-STRONG-LINEAR-CHEAP))
 (80 80 (:REWRITE *-OF-*-COMBINE-CONSTANTS))
 (76 19 (:REWRITE <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE))
 (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-GEN))
 (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 MOVE-MINUS-TO-CONSTANT))
 (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-CONSTANT-AND-MINUS))
 (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-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))
 (28 28 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (28 28 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 )
(FLOOR-OF-LOGAND-AND-2-BACK
 (194 2 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 (194 2 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (124 4 (:LINEAR MY-FLOOR-LOWER-BOUND-LINEAR))
 (116 4 (:LINEAR FLOOR-UPPER-BOUND-LINEAR))
 (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))
 (50 50 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (50 50 (: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))
 (17 3 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (17 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
 (92 92 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (92 92 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (82 2 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (74 2 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (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))
 (56 8 (:REWRITE <-OF-*-AND-0))
 (54 6 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (51 9 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (46 46 (:META CANCEL_PLUS-LESSP-CORRECT))
 (46 38 (:REWRITE DEFAULT-<-2))
 (45 29 (:REWRITE DEFAULT-*-2))
 (45 29 (:REWRITE DEFAULT-*-1))
 (41 11 (:REWRITE FLOOR-WHEN-<))
 (38 38 (:REWRITE DEFAULT-<-1))
 (30 2 (:REWRITE <-OF-LOGAND-AND-0))
 (24 6 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 (20 5 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (16 16 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (16 16 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (16 9 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-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 RATIONALP-OF-MOD))
 (5 5 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (5 5 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-TYPE))
 (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
 (951 951 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (951 951 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (951 951 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (951 951 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (101 1 (:REWRITE *-OF-FLOOR-OF-SAME-WHEN-MULTIPLE))
 (83 11 (:REWRITE DEFAULT-<-2))
 (63 9 (:REWRITE DEFAULT-+-2))
 (63 9 (:REWRITE DEFAULT-+-1))
 (61 36 (:REWRITE DEFAULT-*-2))
 (36 36 (:REWRITE DEFAULT-*-1))
 (30 1 (:LINEAR MOD-BOUND-LINEAR-ARG2-STRONG))
 (27 1 (:LINEAR MOD-BOUND-LINEAR-ARG2))
 (26 5 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 (26 5 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (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))
 (18 11 (:REWRITE DEFAULT-<-1))
 (18 3 (:REWRITE MOD-WHEN-MULTIPLE))
 (18 3 (:REWRITE MOD-WHEN-INTEGERP-OF-QUOTIENT))
 (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))
 (8 1 (:REWRITE <=-OF-LOGAND-SAME-ARG1))
 (6 6 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (5 5 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (5 5 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (3 3 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (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
 (1295 122 (:REWRITE FLOOR-WHEN-<))
 (1178 38 (:LINEAR MY-FLOOR-LOWER-BOUND-LINEAR))
 (1102 38 (:LINEAR FLOOR-UPPER-BOUND-LINEAR))
 (836 281 (:REWRITE DEFAULT-*-2))
 (828 21 (:REWRITE <-OF-MINUS-AND-CONSTANT))
 (753 753 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (753 753 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONNEGATIVE-AND-NONPOSITIVE-TYPE))
 (753 753 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (753 753 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONNEGATIVE-TYPE))
 (753 753 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (753 753 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (725 18 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (665 146 (:REWRITE DEFAULT-+-2))
 (628 13 (:REWRITE <-OF-+-OF---AND-0-ARG1))
 (567 146 (:REWRITE DEFAULT-+-1))
 (356 356 (:META CANCEL_PLUS-LESSP-CORRECT))
 (330 281 (:REWRITE DEFAULT-*-1))
 (313 286 (:REWRITE DEFAULT-<-1))
 (309 286 (:REWRITE DEFAULT-<-2))
 (254 17 (:REWRITE MOD-WHEN-<-OF-0))
 (246 6 (:REWRITE FLOOR-OF-ONE-LESS-GEN))
 (237 237 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (225 35 (:REWRITE DEFAULT-UNARY-MINUS))
 (220 12 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (220 6 (:DEFINITION NATP))
 (211 14 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (184 128 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (184 128 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (184 128 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (152 38 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (152 38 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (129 9 (:REWRITE MOD-WHEN-<))
 (128 128 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (105 105 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (75 9 (:REWRITE MOD-WHEN-MULTIPLE))
 (70 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))
 (36 2 (:LINEAR MOD-BOUND-LINEAR-ARG2))
 (27 3 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (24 3 (:REWRITE EQUAL-OF-0-AND-FLOOR-GEN))
 (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))
 (16 9 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (16 9 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (16 9 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (12 12 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (10 2 (:REWRITE <-OF-*-OF-/-ARG1-ARG1))
 (9 9 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (9 9 (:REWRITE MOD-OF-2-WHEN-EVEN-CHEAP))
 (8 2 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 (6 6 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE))
 (6 6 (:TYPE-PRESCRIPTION NATP))
 (4 4 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(MOD-OF-LOGAND-AND-EXPT-ALT
 (26181 1313 (:REWRITE FLOOR-WHEN-<))
 (16985 325 (:REWRITE MOD-WHEN-MULTIPLE))
 (15448 94 (:REWRITE <-OF-LOGAND-AND-0))
 (15357 3727 (:REWRITE DEFAULT-*-2))
 (13750 69 (:REWRITE <-OF-*-OF-/-ARG2-ARG1))
 (13483 13483 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (13483 13483 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (13483 13483 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (13483 13483 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (9894 156 (:REWRITE COMMUTATIVITY-2-OF-*))
 (9375 122 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 (7705 3727 (:REWRITE DEFAULT-*-1))
 (5603 3886 (:REWRITE DEFAULT-<-1))
 (5539 1073 (:REWRITE DEFAULT-+-2))
 (4787 3886 (:REWRITE DEFAULT-<-2))
 (4589 4589 (:META CANCEL_PLUS-LESSP-CORRECT))
 (4480 4480 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (4436 1073 (:REWRITE DEFAULT-+-1))
 (3986 578 (:REWRITE DEFAULT-UNARY-/))
 (2784 8 (:REWRITE <-OF-*-AND-0))
 (2453 293 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (2267 18 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (2063 1329 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (1999 1313 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (1999 1313 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (1719 62 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (1704 138 (:REWRITE /-OF-*))
 (1638 26 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-2))
 (1637 293 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (1637 293 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (1359 1233 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (1313 1313 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (1109 293 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (1030 113 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (832 113 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (645 489 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (564 564 (:TYPE-PRESCRIPTION NATP-OF-EXPT))
 (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))
 (135 135 (:LINEAR EXPT-BOUND-LINEAR-2))
 (131 131 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (125 26 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-1))
 (112 28 (:REWRITE DEFAULT-UNARY-MINUS))
 (86 86 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (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-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
 (37760 2064 (:REWRITE FLOOR-WHEN-<))
 (25670 474 (:REWRITE MOD-WHEN-MULTIPLE))
 (24460 133 (:REWRITE <-OF-LOGAND-AND-0))
 (24240 5753 (:REWRITE DEFAULT-*-2))
 (20189 20189 (:TYPE-PRESCRIPTION <=-OF-FLOOR-AND-0-WHEN-NONPOSITIVE-AND-NONNEGATIVE-TYPE))
 (20189 20189 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (20189 20189 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (20189 20189 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (16170 248 (:REWRITE COMMUTATIVITY-2-OF-*))
 (12958 181 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 (11975 5753 (:REWRITE DEFAULT-*-1))
 (10864 78 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (9665 1736 (:REWRITE DEFAULT-+-2))
 (8603 5740 (:REWRITE DEFAULT-<-1))
 (7767 1736 (:REWRITE DEFAULT-+-1))
 (7042 5740 (:REWRITE DEFAULT-<-2))
 (6844 758 (:REWRITE <-OF-FLOOR-OF-CONSTANT-AND-CONSTANT-GEN))
 (6778 6778 (:META CANCEL_PLUS-LESSP-CORRECT))
 (6664 6664 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (5356 784 (:REWRITE DEFAULT-UNARY-/))
 (4176 12 (:REWRITE <-OF-*-AND-0))
 (3658 424 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (3317 30 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (3256 2086 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (3168 2064 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (3168 2064 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (2688 222 (:REWRITE /-OF-*))
 (2548 424 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (2548 424 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (2482 44 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-2))
 (2208 1944 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (2064 2064 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (1942 202 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (1534 424 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (1478 202 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (1161 758 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (1160 1160 (:TYPE-PRESCRIPTION NATP-OF-EXPT))
 (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))
 (163 163 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (132 132 (:LINEAR EXPT-BOUND-LINEAR))
 (106 106 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (106 106 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (106 106 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (97 43 (:REWRITE MOD-OF-2-WHEN-EVEN-CHEAP))
 (66 66 (:LINEAR EXPT-BOUND-LINEAR-2))
 (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))
 (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
 (29 29 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 )
(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
 (123 123 (:TYPE-PRESCRIPTION NATP-OF-EXPT))
 (123 123 (:TYPE-PRESCRIPTION INTEGERP-OF-EXPT-TYPE))
 (38 38 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (38 38 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (4 1 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 (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))
 (1 1 (:LINEAR EXPT-BOUND-LINEAR-2))
 (1 1 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 )
(<-OF-LOGAND
 (488 2 (:DEFINITION BINARY-LOGAND))
 (325 73 (:TYPE-PRESCRIPTION LOGAND-NON-POSITIVE-TYPE))
 (206 6 (:REWRITE COMMUTATIVITY-OF-+))
 (120 12 (:REWRITE DEFAULT-+-2))
 (120 12 (:REWRITE DEFAULT-+-1))
 (80 4 (:REWRITE UNICITY-OF-0))
 (76 4 (:DEFINITION FIX))
 (73 73 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (48 4 (:DEFINITION EVENP))
 (46 10 (:REWRITE DEFAULT-*-2))
 (40 40 (:TYPE-PRESCRIPTION FLOOR))
 (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))
 (18 4 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (18 4 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (16 4 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (16 4 (:REWRITE FLOOR-WHEN-<))
 (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 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))
 (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
 (888 52 (:REWRITE FLOOR-WHEN-<))
 (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 MY-FLOOR-LOWER-BOUND-LINEAR))
 (348 12 (:LINEAR FLOOR-UPPER-BOUND-LINEAR))
 (259 43 (:REWRITE DEFAULT-+-2))
 (259 43 (:REWRITE DEFAULT-+-1))
 (222 94 (:REWRITE DEFAULT-*-2))
 (198 3 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 (198 3 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (196 12 (:REWRITE ZIP-OPEN))
 (150 94 (:REWRITE DEFAULT-*-1))
 (126 126 (:META CANCEL_PLUS-LESSP-CORRECT))
 (108 52 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (108 52 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (108 52 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (106 106 (:REWRITE DEFAULT-<-2))
 (106 106 (:REWRITE DEFAULT-<-1))
 (104 12 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (104 8 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (97 97 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (90 13 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (83 13 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (80 8 (:REWRITE FLOOR-OF-FLOOR))
 (68 12 (:TYPE-PRESCRIPTION RATIONALP-OF-MOD))
 (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-/-ARG1-ARG1))
 (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 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-TYPE))
 (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
 (142 22 (:REWRITE DEFAULT-+-2))
 (134 22 (:REWRITE DEFAULT-+-1))
 (80 4 (:REWRITE UNICITY-OF-0))
 (79 31 (:REWRITE DEFAULT-*-2))
 (75 75 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (75 75 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (40 40 (:TYPE-PRESCRIPTION FLOOR))
 (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))
 (38 8 (:REWRITE FLOOR-WHEN-<))
 (31 31 (:REWRITE DEFAULT-*-1))
 (28 6 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (24 24 (:META CANCEL_PLUS-LESSP-CORRECT))
 (22 8 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (22 8 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (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 4 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (16 2 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 (16 2 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (14 2 (:REWRITE <-OF-*-AND-0))
 (13 13 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (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-*))
 (4 4 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (2 2 (:REWRITE MOD-WHEN-EQUAL-OF-MOD-AND-0-FREE-CHEAP))
 )
(LOGAND-OF-*-2-AND-*-2
 (126 14 (:REWRITE DEFAULT-+-2))
 (126 14 (:REWRITE DEFAULT-+-1))
 (84 84 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (65 17 (:REWRITE DEFAULT-*-2))
 (40 40 (:TYPE-PRESCRIPTION FLOOR))
 (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))
 (28 4 (:REWRITE <-OF-*-AND-0))
 (24 6 (:REWRITE FLOOR-WHEN-<))
 (22 8 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (22 8 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (18 18 (:META CANCEL_PLUS-LESSP-CORRECT))
 (18 2 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (17 17 (:REWRITE DEFAULT-*-1))
 (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 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 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
 (127 15 (:REWRITE DEFAULT-+-2))
 (127 15 (:REWRITE DEFAULT-+-1))
 (84 84 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (70 22 (:REWRITE DEFAULT-*-2))
 (40 40 (:TYPE-PRESCRIPTION FLOOR))
 (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))
 (31 7 (:REWRITE FLOOR-WHEN-<))
 (24 10 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (24 10 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (22 22 (:REWRITE DEFAULT-*-1))
 (21 21 (:META CANCEL_PLUS-LESSP-CORRECT))
 (21 3 (:REWRITE <-OF-*-AND-0))
 (16 4 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (16 2 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (15 15 (:REWRITE DEFAULT-<-2))
 (15 15 (:REWRITE DEFAULT-<-1))
 (15 15 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (14 3 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (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))
 (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))
 (2 2 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (1 1 (:REWRITE MOD-WHEN-EQUAL-OF-MOD-AND-0-FREE-CHEAP))
 )
(LOGAND-OF-*-2-AND-+-1-OF-*-2
 (127 15 (:REWRITE DEFAULT-+-2))
 (127 15 (:REWRITE DEFAULT-+-1))
 (90 90 (:TYPE-PRESCRIPTION LOGAND-NON-NEGATIVE-TYPE))
 (90 90 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (70 22 (:REWRITE DEFAULT-*-2))
 (40 40 (:TYPE-PRESCRIPTION FLOOR))
 (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))
 (31 7 (:REWRITE FLOOR-WHEN-<))
 (26 4 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (23 23 (:META CANCEL_PLUS-LESSP-CORRECT))
 (22 22 (:REWRITE DEFAULT-*-1))
 (22 8 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (22 8 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (21 3 (:REWRITE <-OF-*-AND-0))
 (18 4 (:LINEAR <=-OF-LOGAND-SAME-ARG2))
 (17 17 (:REWRITE DEFAULT-<-2))
 (17 17 (:REWRITE DEFAULT-<-1))
 (16 4 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (15 15 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (14 3 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (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))
 (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))
 (2 2 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (1 1 (:REWRITE MOD-WHEN-EQUAL-OF-MOD-AND-0-FREE-CHEAP))
 )
(LOGAND-LOWER-BOUND-NEGATIVE-2
 (3917 174 (:REWRITE FLOOR-WHEN-<))
 (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))
 (1595 442 (:REWRITE DEFAULT-*-2))
 (1354 436 (:REWRITE DEFAULT-+-2))
 (1344 12 (:LINEAR EXPT-HALF-LINEAR))
 (1336 436 (:REWRITE DEFAULT-+-1))
 (1061 23 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (972 12 (:LINEAR EXPT-OF-ONE-LESS-LINEAR))
 (950 1 (:REWRITE <-OF-LOGAND))
 (660 442 (:REWRITE DEFAULT-*-1))
 (636 95 (:REWRITE ZIP-OPEN))
 (594 6 (:REWRITE FLOOR-MINUS-ARG1-BETTER))
 (560 186 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (496 476 (:META CANCEL_PLUS-LESSP-CORRECT))
 (470 344 (:REWRITE DEFAULT-<-1))
 (458 186 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (410 174 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (389 344 (:REWRITE DEFAULT-<-2))
 (370 26 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (350 42 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (348 12 (:REWRITE FLOOR-OF-*-SAME))
 (292 73 (:REWRITE <-OF-+-ARG2-WHEN-NEGATIVE-CONSTANT))
 (253 36 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (253 36 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (224 42 (:TYPE-PRESCRIPTION RATIONALP-OF-MOD))
 (224 26 (:REWRITE FLOOR-OF-FLOOR))
 (219 73 (:REWRITE +-COMBINE-CONSTANTS))
 (204 204 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (178 142 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (174 174 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (146 73 (:REWRITE EQUAL-OF-0-AND-+-OF---ALT))
 (126 26 (:REWRITE <-OF-*-OF-/-ARG1-ARG1))
 (112 14 (:REWRITE EQUAL-OF-0-AND-FLOOR-GEN))
 (100 25 (:REWRITE DEFAULT-UNARY-MINUS))
 (97 1 (:REWRITE LOGAND-OF-NEGATIVE-AND-POSITIVE))
 (89 89 (:TYPE-PRESCRIPTION NATP-OF-EXPT))
 (88 25 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (88 25 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (68 68 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (66 6 (:REWRITE *-OF-*-COMBINE-CONSTANTS))
 (48 12 (:REWRITE FLOOR-OF-1-WHEN-INTEGERP))
 (42 42 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (42 42 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-TYPE))
 (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))
 (30 6 (:REWRITE UNICITY-OF-1))
 (24 24 (:LINEAR EXPT-BOUND-LINEAR-WEAK))
 (24 24 (:LINEAR EXPT-BOUND-LINEAR-2))
 (24 24 (:LINEAR EXPT-BOUND-LINEAR))
 (23 23 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (3 3 (:REWRITE ZP-OPEN))
 )
(LOGAND-LOWER-BOUND-NEGATIVE-2-ALT
 (70 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))
 (27 27 (:TYPE-PRESCRIPTION NATP-OF-EXPT))
 (25 10 (:REWRITE DEFAULT-<-2))
 (14 10 (:REWRITE DEFAULT-<-1))
 (12 3 (:REWRITE DEFAULT-UNARY-MINUS))
 (10 10 (:META CANCEL_PLUS-LESSP-CORRECT))
 (10 4 (:LINEAR EXPT-BOUND-LINEAR-WEAK))
 (5 5 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (4 4 (:LINEAR EXPT-BOUND-LINEAR))
 (4 1 (:REWRITE LOGAND-OF-NEGATIVE-AND-POSITIVE))
 (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
 (40 4 (:REWRITE <-OF-LOGAND))
 (37 2 (:REWRITE LOGAND-OF-NEGATIVE-AND-NEGATIVE))
 (31 21 (:REWRITE DEFAULT-<-2))
 (30 21 (:REWRITE DEFAULT-<-1))
 (21 21 (:META CANCEL_PLUS-LESSP-CORRECT))
 (12 12 (:TYPE-PRESCRIPTION LOGAND-NON-POSITIVE-TYPE))
 (12 12 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (8 2 (:DEFINITION NATP))
 (4 4 (:LINEAR EXPT-BOUND-LINEAR))
 (4 1 (:REWRITE DEFAULT-UNARY-MINUS))
 (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-BOUND-LINEAR-2))
 (1 1 (:REWRITE <-OF-MINUS-AND-CONSTANT))
 )
(FLOOR-BY-2-AND-SUB-1-INDUCT
 (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
 (2641 61 (:REWRITE FLOOR-WHEN-<))
 (2608 14 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (1381 14 (:REWRITE <-OF-*-OF-/-ARG1-ARG1))
 (1326 21 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (1108 325 (:REWRITE DEFAULT-*-2))
 (978 52 (:REWRITE MOD-WHEN-MULTIPLE))
 (844 52 (:REWRITE MOD-WHEN-<))
 (808 173 (:REWRITE DEFAULT-+-2))
 (645 645 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (645 645 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (645 645 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-NEGATIVE-AND-POSITIVE-TYPE))
 (563 173 (:REWRITE DEFAULT-+-1))
 (560 80 (:REWRITE DEFAULT-UNARY-/))
 (533 330 (:REWRITE DEFAULT-<-2))
 (530 325 (:REWRITE DEFAULT-*-1))
 (450 330 (:REWRITE DEFAULT-<-1))
 (412 10 (:LINEAR <=-OF-LOGAND-SAME-ARG1))
 (396 396 (:META CANCEL_PLUS-LESSP-CORRECT))
 (311 311 (:TYPE-PRESCRIPTION LOGAND-NEGATIVE-TYPE))
 (283 75 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (227 61 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (227 61 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (191 30 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (175 52 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (175 52 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (147 51 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (134 30 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (108 108 (:LINEAR EXPT-BOUND-LINEAR))
 (93 93 (:TYPE-PRESCRIPTION NATP-OF-EXPT))
 (87 24 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 (86 86 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (64 16 (:REWRITE <-OF-FLOOR-OF-CONSTANT-AND-CONSTANT-GEN))
 (61 61 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (60 60 (:LINEAR EXPT-BOUND-LINEAR-2))
 (52 52 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (52 52 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (49 49 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE))
 (32 8 (:REWRITE DEFAULT-UNARY-MINUS))
 (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))
 (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))
 (11 11 (: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
 (182 2 (:LINEAR MY-FLOOR-LOWER-BOUND-LINEAR))
 (172 2 (:LINEAR FLOOR-UPPER-BOUND-LINEAR))
 (105 33 (:REWRITE DEFAULT-*-2))
 (64 4 (:REWRITE *-OF---ARG1))
 (60 33 (:REWRITE DEFAULT-*-1))
 (48 12 (:REWRITE DEFAULT-UNARY-MINUS))
 (35 20 (:REWRITE DEFAULT-+-2))
 (35 5 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (35 5 (:REWRITE FLOOR-WHEN-<))
 (34 1 (:LINEAR EXPT-HALF-LINEAR))
 (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))
 (29 20 (:REWRITE DEFAULT-+-1))
 (20 20 (:TYPE-PRESCRIPTION NATP-OF-EXPT))
 (20 5 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (20 5 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (20 1 (:LINEAR EXPT-OF-ONE-LESS-LINEAR))
 (8 2 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (8 2 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (5 5 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (5 1 (:REWRITE *-OF-*-OF-/-SAME))
 (4 4 (:LINEAR EXPT-BOUND-LINEAR-WEAK))
 (4 1 (:DEFINITION FIX))
 (2 2 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (2 2 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR-1))
 (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
 (7596 835 (:REWRITE DEFAULT-+-2))
 (6826 835 (:REWRITE DEFAULT-+-1))
 (5728 1494 (:REWRITE DEFAULT-*-2))
 (4995 4995 (:TYPE-PRESCRIPTION <=-OF-0-AND-FLOOR-WHEN-BOTH-NONPOSITIVE-TYPE))
 (4995 4995 (:TYPE-PRESCRIPTION <-OF-FLOOR-AND-0-WHEN-POSITIVE-AND-NEGATIVE-TYPE))
 (2463 1494 (:REWRITE DEFAULT-*-1))
 (2391 49 (:REWRITE FLOOR-OF-+-WHEN-MULT-ARG1))
 (1786 118 (:REWRITE <-OF-*-OF-/-ARG1-ARG1))
 (1451 137 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (1405 475 (:REWRITE FLOOR-WHEN-NEGATIVE-AND-SMALL-CHEAP))
 (1277 137 (:REWRITE LOGAND-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (1271 60 (:REWRITE INTEGERP-OF-+-WHEN-INTEGERP-1))
 (1103 494 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-OF-QUOTIENT))
 (1027 475 (:REWRITE FLOOR-WHEN-I-IS-NOT-AN-ACL2-NUMBERP))
 (804 166 (:REWRITE DEFAULT-UNARY-MINUS))
 (656 35 (:REWRITE MOD-WHEN-MULTIPLE))
 (646 316 (:REWRITE DEFAULT-<-1))
 (586 35 (:REWRITE MOD-WHEN-<))
 (537 363 (:REWRITE FLOOR-WHEN-NOT-RATIONALP-ARG1))
 (475 475 (:REWRITE FLOOR-MINUS-NEGATIVE-CONSTANT))
 (445 445 (:META CANCEL_PLUS-LESSP-CORRECT))
 (382 316 (:REWRITE DEFAULT-<-2))
 (312 24 (:REWRITE FLOOR-UNIQUE-EQUAL-VERSION))
 (280 280 (:REWRITE INTEGERP-OF-*))
 (200 10 (:REWRITE EQUAL-OF---AND--))
 (189 7 (:REWRITE <-OF-+-OF---AND-0-ARG1))
 (168 24 (:REWRITE FLOOR-OF-FLOOR))
 (160 160 (:REWRITE EQUAL-OF-+-WHEN-NEGATIVE-CONSTANT))
 (158 41 (:REWRITE MOD-WHEN-<-OF-0))
 (147 147 (:REWRITE INTEGERP-OF-HALF-WHEN-MULT-OF-EXPT))
 (135 135 (:REWRITE MOVE-MINUS-TO-CONSTANT))
 (125 125 (:REWRITE EQUAL-OF---WHEN-VARIABLE))
 (125 125 (:REWRITE EQUAL-OF---AND-CONSTANT))
 (92 35 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (92 35 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (92 35 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (92 35 (:REWRITE MOD-OF-2-WHEN-EVEN-CHEAP))
 (72 72 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (69 69 (:LINEAR FLOOR-BOUND-STRICT-LINEAR))
 (69 69 (:LINEAR FLOOR-BOUND-ARG1-LINEAR))
 (60 60 (:LINEAR FLOOR-WEAK-MONOTONE-LINEAR=-2))
 (57 57 (:REWRITE <-OF-+-COMBINE-CONSTANTS-2))
 (57 57 (:REWRITE <-OF-+-ARG1-WHEN-NEGATIVE-CONSTANT))
 (51 51 (:REWRITE FLOOR-PEEL-OFF-CONSTANT))
 (51 51 (:REWRITE FLOOR-OF-PLUS-NORMALIZE-NEGATIVE-CONSTANT))
 (40 40 (:LINEAR EXPT-BOUND-LINEAR))
 (36 36 (:TYPE-PRESCRIPTION NATP-OF-EXPT))
 (35 35 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (24 24 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE))
 (20 20 (:LINEAR EXPT-BOUND-LINEAR-2))
 (19 19 (:REWRITE MOD-OF-*-SUBST-CONSTANT-ARG2))
 (19 19 (:REWRITE MOD-OF-*-SUBST-CONSTANT-ARG1))
 (13 13 (:REWRITE ZP-OPEN))
 (10 10 (:REWRITE EQUAL-OF-*-AND-CONSTANT))
 (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))
 (306 16 (:REWRITE MOD-WHEN-<))
 (302 16 (:REWRITE MOD-WHEN-MULTIPLE))
 (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))
 (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
 (395 14 (:REWRITE MOD-WHEN-INTEGERP-OF-QUOTIENT))
 (231 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))
 (89 1 (:REWRITE MOD-OF-+-SUBST-CONSTANT))
 (69 42 (:REWRITE DEFAULT-<-2))
 (69 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 12 (:LINEAR EXPT-BOUND-LINEAR-2))
 (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
 (259 4 (:REWRITE LOGAND-OF-NEGATIVE-AND-NEGATIVE))
 (144 63 (:REWRITE DEFAULT-<-2))
 (94 63 (:REWRITE DEFAULT-<-1))
 (88 22 (:REWRITE DEFAULT-UNARY-MINUS))
 (63 63 (:META CANCEL_PLUS-LESSP-CORRECT))
 (47 35 (:REWRITE DEFAULT-+-2))
 (47 35 (:REWRITE DEFAULT-+-1))
 (40 40 (:TYPE-PRESCRIPTION NATP-OF-EXPT))
 (23 14 (:LINEAR EXPT-BOUND-LINEAR))
 (16 4 (:REWRITE DEFAULT-*-2))
 (14 14 (:REWRITE <-OF-CONSTANT-AND-MINUS))
 (14 14 (:LINEAR EXPT-BOUND-LINEAR-WEAK))
 (10 10 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (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))
 )
