(INTEGERP-OF-CEILING-OF-LG)
(NATP-OF-CEILING-OF-LG)
(<-OF-CEILING-OF-LG-ARG1-WHEN-CONSTANT
 (615 615 (:TYPE-PRESCRIPTION EVENP))
 (410 205 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (410 205 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (410 205 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (205 205 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (119 72 (:REWRITE DEFAULT-<-2))
 (111 72 (:REWRITE DEFAULT-<-1))
 (88 16 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR))
 (60 25 (:REWRITE DEFAULT-+-2))
 (60 25 (:REWRITE DEFAULT-+-1))
 (44 8 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-4))
 (44 8 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-2))
 (40 8 (:REWRITE <-OF-INTEGER-LENGTH-ARG2))
 (33 27 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (32 16 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR-NEGATIVE-EXPONENT))
 (27 27 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (24 8 (:REWRITE <-OF-0-AND-INTEGER-LENGTH))
 (24 8 (:LINEAR <-OF-1-AND-INTEGER-LENGTH-LINEAR))
 (16 8 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-3))
 (16 8 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-1))
 (8 8 (:TYPE-PRESCRIPTION POSP))
 (7 7 (:REWRITE INTEGER-LENGTH-WHEN-NOT-INTEGERP-CHEAP))
 (4 4 (:REWRITE <-OF-CONSTANT-AND-EXPT-2))
 (3 3 (:REWRITE <-OF-EXPT-2-AND-CONSTANT))
 )
(<-OF-CEILING-OF-LG-ARG2-WHEN-CONSTANT
 (390 390 (:TYPE-PRESCRIPTION EVENP))
 (260 130 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (260 130 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (260 130 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (130 130 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NON-POSITIVE-EXPONENT))
 (130 130 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (47 14 (:REWRITE DEFAULT-<-1))
 (27 14 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (4 4 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (4 4 (:REWRITE DEFAULT-+-2))
 (4 4 (:REWRITE DEFAULT-+-1))
 (3 3 (:REWRITE <-OF-EXPT-2-AND-CONSTANT))
 (1 1 (:REWRITE INTEGER-LENGTH-WHEN-NOT-INTEGERP-CHEAP))
 (1 1 (:REWRITE <-OF-CONSTANT-AND-EXPT-2))
 )
(EQUAL-OF-CEILING-OF-LG-AND-CONSTANT
 (843 843 (:TYPE-PRESCRIPTION EVENP))
 (562 281 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (562 281 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (562 281 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (281 281 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (110 42 (:REWRITE DEFAULT-<-1))
 (48 42 (:REWRITE DEFAULT-<-2))
 (38 10 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR))
 (32 9 (:REWRITE DEFAULT-+-2))
 (32 9 (:REWRITE DEFAULT-+-1))
 (26 22 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (22 22 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (19 5 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-4))
 (19 5 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-2))
 (16 10 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR-NEGATIVE-EXPONENT))
 (8 5 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-3))
 (8 5 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-1))
 (6 6 (:REWRITE <-OF-EXPT-2-AND-CONSTANT))
 )
(<-OF-CEILING-OF-LG-AND-CONSTANT)
(EQUAL-OF-0-AND-CEILING-OF-LG
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE INTEGER-LENGTH-WHEN-NOT-INTEGERP-CHEAP))
 )
(UNSIGNED-BYTE-P-OF-CEILING-OF-LG-WHEN-<
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE INTEGER-LENGTH-WHEN-NOT-INTEGERP-CHEAP))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(CEILING-OF-LG-OF-EXPT2
 (178 2 (:LINEAR <-OF-1-AND-INTEGER-LENGTH-LINEAR))
 (39 39 (:TYPE-PRESCRIPTION EVENP))
 (31 9 (:REWRITE DEFAULT-<-2))
 (30 4 (:LINEAR <=-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (26 13 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (26 13 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (26 13 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (13 13 (:TYPE-PRESCRIPTION INTEGERP-OF-EXPT-TYPE))
 (13 13 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NON-POSITIVE-EXPONENT))
 (13 13 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (13 13 (:TYPE-PRESCRIPTION <=-OF-0-AND-EXPT-TYPE))
 (13 13 (:TYPE-PRESCRIPTION <-OF-0-AND-EXPT-TYPE))
 (12 1 (:REWRITE DEFAULT-+-2))
 (9 9 (:REWRITE DEFAULT-<-1))
 (8 4 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR))
 (6 2 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-4))
 (6 2 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-2))
 (4 4 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR-NEGATIVE-EXPONENT))
 (4 4 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (3 3 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (3 3 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (2 2 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-3))
 (2 2 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-1))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(CEILING-OF-LG-OF-*-OF-2
 (516 516 (:TYPE-PRESCRIPTION EVENP))
 (344 172 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (344 172 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (344 172 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (290 32 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR))
 (231 77 (:LINEAR <-OF-1-AND-INTEGER-LENGTH-LINEAR))
 (217 63 (:REWRITE DEFAULT-+-2))
 (192 156 (:REWRITE DEFAULT-<-2))
 (180 156 (:REWRITE DEFAULT-<-1))
 (172 172 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (172 32 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR-NEGATIVE-EXPONENT))
 (151 63 (:REWRITE DEFAULT-+-1))
 (149 16 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-4))
 (149 16 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-2))
 (86 16 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-3))
 (86 16 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-1))
 (82 41 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (56 16 (:REWRITE <-OF-INTEGER-LENGTH-ARG2))
 (41 41 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (32 32 (:LINEAR <=-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (32 32 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (22 22 (:REWRITE INTEGER-LENGTH-WHEN-NOT-INTEGERP-CHEAP))
 (3 3 (:REWRITE EQUAL-OF-*-AND-CONSTANT))
 (3 3 (:REWRITE DEFAULT-*-2))
 (3 3 (:REWRITE DEFAULT-*-1))
 )
(CEILING-OF-LG-OF-*-OF-EXPT-ARG2
 (1593 1593 (:TYPE-PRESCRIPTION EVENP))
 (1062 531 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (1062 531 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (1062 531 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (531 531 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (510 48 (:REWRITE DEFAULT-*-2))
 (270 26 (:LINEAR <=-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (70 70 (:REWRITE DEFAULT-<-2))
 (70 70 (:REWRITE DEFAULT-<-1))
 (66 26 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR))
 (48 48 (:REWRITE DEFAULT-*-1))
 (44 13 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-4))
 (37 28 (:REWRITE DEFAULT-+-2))
 (33 13 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-2))
 (28 28 (:REWRITE DEFAULT-+-1))
 (27 9 (:REWRITE COMMUTATIVITY-OF-+))
 (26 26 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR-NEGATIVE-EXPONENT))
 (24 24 (:LINEAR <=-OF-*-AND-*-SAME-ALT-LINEAR))
 (24 24 (:LINEAR <-OF-*-AND-*-LINEAR))
 (21 21 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (21 21 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (13 13 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-3))
 (13 13 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-1))
 (12 12 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-4))
 (12 12 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-3))
 (12 12 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-1))
 (9 9 (:REWRITE ZIP-OPEN))
 (4 4 (:REWRITE EQUAL-OF-CEILING-OF-LG-AND-CONSTANT))
 (2 2 (:REWRITE *-OF-*-COMBINE-CONSTANTS))
 )
(CEILING-OF-LG-OF-*-OF-1/2
 (54 27 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (54 27 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (54 27 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (37 13 (:REWRITE DEFAULT-*-2))
 (35 12 (:REWRITE DEFAULT-+-2))
 (27 27 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (13 13 (:REWRITE DEFAULT-*-1))
 (12 12 (:REWRITE DEFAULT-+-1))
 (9 3 (:LINEAR <-OF-1-AND-INTEGER-LENGTH-LINEAR))
 (8 4 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (6 6 (:REWRITE INTEGER-LENGTH-WHEN-NOT-INTEGERP-CHEAP))
 (6 1 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-2))
 (4 4 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (4 1 (:REWRITE MULTIPLE-WHEN-MOD-0-CHEAP))
 (2 2 (:REWRITE EQUAL-OF-*-AND-CONSTANT))
 (2 2 (:LINEAR <=-OF-*-AND-*-SAME-LINEAR))
 (2 2 (:LINEAR <=-OF-*-AND-*-SAME-ALT-LINEAR))
 (2 2 (:LINEAR <-OF-*-AND-*-LINEAR))
 (1 1 (:TYPE-PRESCRIPTION RATIONALP-OF-MOD))
 (1 1 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE-2))
 (1 1 (:TYPE-PRESCRIPTION INTEGERP-OF-MOD-TYPE))
 (1 1 (:REWRITE INTEGERP-OF-*))
 (1 1 (:LINEAR <-OF-*-SAME-LINEAR-SPECIAL))
 (1 1 (:LINEAR <-OF-*-SAME-LINEAR-2))
 (1 1 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-4))
 (1 1 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-3))
 (1 1 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-1))
 )
(INTEGERP-OF-*-OF-/-WHEN-EQUAL-OF-0-AND-MOD
 (22 22 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE))
 (18 6 (:REWRITE MOD-WHEN-<-OF-0))
 (18 6 (:REWRITE MOD-WHEN-<))
 (17 17 (:REWRITE DEFAULT-<-2))
 (17 17 (:REWRITE DEFAULT-<-1))
 (13 13 (:REWRITE DEFAULT-*-2))
 (13 13 (:REWRITE DEFAULT-*-1))
 (6 6 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (6 6 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (6 6 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (6 6 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (6 6 (:REWRITE MOD-WHEN-INTEGERP-OF-QUOTIENT))
 (6 6 (:REWRITE MOD-WHEN-EQUAL-OF-MOD-AND-0-FREE-CHEAP))
 (6 2 (:LINEAR MOD-BOUND-LINEAR-ARG1))
 (5 5 (:REWRITE DEFAULT-+-2))
 (5 5 (:REWRITE DEFAULT-+-1))
 (3 3 (:REWRITE DEFAULT-UNARY-/))
 (2 2 (:REWRITE INTEGERP-OF-*))
 (1 1 (:REWRITE *-OF-*-COMBINE-CONSTANTS))
 )
(CEILING-OF-LG-OF-*-OF-EXPT-OF--
 (864 864 (:TYPE-PRESCRIPTION EVENP))
 (576 288 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (576 288 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (576 288 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (288 288 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (147 11 (:REWRITE DEFAULT-*-2))
 (138 6 (:REWRITE DEFAULT-UNARY-/))
 (119 3 (:LINEAR <-OF-1-AND-INTEGER-LENGTH-LINEAR))
 (116 2 (:LINEAR <-OF-*-SAME-LINEAR-SPECIAL))
 (116 2 (:LINEAR <-OF-*-SAME-LINEAR-2))
 (69 14 (:REWRITE DEFAULT-<-2))
 (60 2 (:REWRITE MOD-WHEN-<))
 (58 15 (:REWRITE DEFAULT-+-2))
 (36 14 (:REWRITE DEFAULT-<-1))
 (34 1 (:REWRITE INTEGERP-OF-*))
 (32 15 (:REWRITE DEFAULT-+-1))
 (24 2 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (24 2 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (22 11 (:REWRITE DEFAULT-*-1))
 (15 10 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (12 12 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE))
 (10 10 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (6 6 (:REWRITE INTEGER-LENGTH-WHEN-NOT-INTEGERP-CHEAP))
 (6 2 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR))
 (5 5 (:REWRITE MOD-WHEN-EQUAL-OF-MOD-AND-0-FREE-CHEAP))
 (5 5 (:REWRITE MOD-WHEN-<-OF-0))
 (4 4 (:REWRITE DEFAULT-UNARY-MINUS))
 (4 4 (:LINEAR <=-OF-*-AND-*-SAME-ALT-LINEAR))
 (4 4 (:LINEAR <-OF-*-AND-*-LINEAR))
 (3 3 (:REWRITE EQUAL-OF-*-AND-CONSTANT))
 (3 1 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-4))
 (3 1 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-2))
 (2 2 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (2 2 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (2 2 (:REWRITE FOLD-CONSTS-IN-+))
 (2 2 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR-NEGATIVE-EXPONENT))
 (2 2 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (2 2 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-4))
 (2 2 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-3))
 (2 2 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-1))
 (1 1 (:REWRITE <-OF-CONSTANT-AND-EXPT-2))
 (1 1 (:REWRITE *-OF-*-COMBINE-CONSTANTS))
 (1 1 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-3))
 (1 1 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-1))
 )
(CEILING-OF-LG-OF-*-OF-EXPT-WHEN-NEGATIVE
 (5022 5022 (:TYPE-PRESCRIPTION EVENP))
 (3348 1674 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (3348 1674 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (3348 1674 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (2673 15 (:REWRITE MOD-WHEN-INTEGERP-OF-QUOTIENT))
 (2482 13 (:REWRITE INTEGERP-OF-*-OF-/-WHEN-EQUAL-OF-0-AND-MOD))
 (1674 1674 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (1377 20 (:LINEAR <-OF-*-SAME-LINEAR-SPECIAL))
 (882 15 (:REWRITE MOD-WHEN-<))
 (750 30 (:REWRITE DEFAULT-UNARY-/))
 (670 70 (:REWRITE DEFAULT-*-2))
 (445 13 (:REWRITE INTEGERP-OF-*))
 (421 145 (:REWRITE DEFAULT-<-2))
 (366 6 (:DEFINITION POSP))
 (352 38 (:LINEAR <=-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (321 19 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-4))
 (298 70 (:REWRITE DEFAULT-*-1))
 (277 145 (:REWRITE DEFAULT-<-1))
 (195 15 (:REWRITE MOD-WHEN-RATIONALP-ARG1-AND-NOT-RATIONALP-ARG2))
 (195 15 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG2))
 (160 8 (:REWRITE <-OF-EXPT-2-AND-CONSTANT))
 (142 4 (:LINEAR MOD-BOUND-LINEAR-ARG2-STRONG))
 (114 38 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR-NEGATIVE-EXPONENT))
 (99 19 (:REWRITE DEFAULT-+-2))
 (64 64 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (64 64 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (57 19 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-3))
 (57 19 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-1))
 (40 40 (:LINEAR <=-OF-*-AND-*-SAME-ALT-LINEAR))
 (40 40 (:LINEAR <-OF-*-AND-*-LINEAR))
 (38 38 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR))
 (38 38 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (34 34 (:TYPE-PRESCRIPTION NONNEG-OF-MOD-TYPE))
 (24 8 (:REWRITE <-OF-1-AND-EXPT-GEN))
 (21 19 (:REWRITE DEFAULT-+-1))
 (20 20 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-4))
 (20 20 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-3))
 (20 20 (:LINEAR <-OF-*-AND-*-SAME-LINEAR-1))
 (19 19 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-2))
 (15 15 (:REWRITE MOD-WHEN-NOT-RATIONALP-ARG1-AND-RATIONALP-ARG2))
 (15 15 (:REWRITE MOD-WHEN-NOT-ACL2-NUMBERP-ARG1))
 (15 15 (:REWRITE MOD-WHEN-EQUAL-OF-MOD-AND-0-FREE-CHEAP))
 (15 15 (:REWRITE MOD-WHEN-<-OF-0))
 (15 3 (:REWRITE CEILING-OF-LG-OF-*-OF-EXPT-ARG2))
 (10 10 (:REWRITE DEFAULT-UNARY-MINUS))
 (9 3 (:DEFINITION NATP))
 (8 8 (:REWRITE EQUAL-OF-EXPT-AND-1))
 (8 8 (:REWRITE EQUAL-OF-CEILING-OF-LG-AND-CONSTANT))
 (8 8 (:DEFINITION IFIX))
 (6 6 (:TYPE-PRESCRIPTION POSP))
 (6 6 (:REWRITE *-OF-*-COMBINE-CONSTANTS))
 (6 1 (:REWRITE INTEGERP-OF-EXPT-WHEN-NATP))
 (3 3 (:TYPE-PRESCRIPTION NATP))
 (3 3 (:REWRITE <-OF-CONSTANT-AND-EXPT-2))
 (2 2 (:REWRITE <-OF-CONSTANT-AND-*-OF-CONSTANT))
 )
(<-OF-EXPT-2-OF-CEILING-OF-LG-SAME
 (2124 2124 (:TYPE-PRESCRIPTION EVENP))
 (2102 245 (:LINEAR <-OF-1-AND-INTEGER-LENGTH-LINEAR))
 (1692 80 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR))
 (1416 708 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (1416 708 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (1416 708 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (950 106 (:REWRITE <-OF-INTEGER-LENGTH-ARG2))
 (864 40 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-4))
 (864 40 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-2))
 (763 580 (:REWRITE DEFAULT-<-2))
 (708 708 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (690 80 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR-NEGATIVE-EXPONENT))
 (655 580 (:REWRITE DEFAULT-<-1))
 (504 24 (:REWRITE <-OF-1-AND-EXPT-GEN))
 (351 101 (:REWRITE DEFAULT-+-2))
 (345 40 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-3))
 (345 40 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-1))
 (344 60 (:REWRITE <-OF-0-AND-INTEGER-LENGTH))
 (288 8 (:REWRITE <-OF-EXPT-2-AND-CONSTANT))
 (270 101 (:REWRITE DEFAULT-+-1))
 (236 120 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (135 41 (:DEFINITION NATP))
 (120 120 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (80 80 (:LINEAR <=-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (80 80 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (78 78 (:TYPE-PRESCRIPTION POSP))
 (67 67 (:REWRITE INTEGER-LENGTH-WHEN-NOT-INTEGERP-CHEAP))
 (65 13 (:REWRITE <-OF-INTEGER-LENGTH-ARG1))
 (64 8 (:REWRITE EQUAL-OF-EXPT-AND-1))
 (41 41 (:TYPE-PRESCRIPTION NATP))
 (40 8 (:REWRITE EQUAL-OF-0-AND-INTEGER-LENGTH))
 (24 8 (:REWRITE <-OF-INTEGER-LENGTH-AND-1))
 (15 15 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (8 8 (:DEFINITION IFIX))
 (6 6 (:REWRITE <-OF-CONSTANT-AND-EXPT-2))
 )
(<=-OF-EXPT-OF-CELING-OF-LG-SAME
 (102 102 (:TYPE-PRESCRIPTION EVENP))
 (68 34 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (68 34 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (68 34 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (35 1 (:DEFINITION EXPT))
 (34 34 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (26 5 (:REWRITE <-OF-INTEGER-LENGTH-ARG2))
 (24 2 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR))
 (14 1 (:REWRITE DEFAULT-*-2))
 (13 1 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-4))
 (13 1 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-2))
 (12 4 (:LINEAR <-OF-1-AND-INTEGER-LENGTH-LINEAR))
 (9 9 (:REWRITE DEFAULT-<-2))
 (9 9 (:REWRITE DEFAULT-<-1))
 (4 4 (:TYPE-PRESCRIPTION POSP))
 (4 4 (:DEFINITION POSP))
 (4 2 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (4 2 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR-NEGATIVE-EXPONENT))
 (4 1 (:REWRITE ZIP-OPEN))
 (4 1 (:REWRITE COMMUTATIVITY-OF-+))
 (3 2 (:REWRITE DEFAULT-+-2))
 (3 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (2 2 (:LINEAR <=-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (2 2 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (2 1 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-3))
 (2 1 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-1))
 (1 1 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (1 1 (:REWRITE INTEGER-LENGTH-WHEN-NOT-INTEGERP-CHEAP))
 (1 1 (:REWRITE EQUAL-OF-0-AND-INTEGER-LENGTH))
 (1 1 (:REWRITE DEFAULT-*-1))
 )
(<-OF-EXPT-OF-CEILING-OF-LG-WHEN-<
 (102 102 (:TYPE-PRESCRIPTION EVENP))
 (68 34 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (68 34 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (68 34 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (63 1 (:DEFINITION EXPT))
 (34 34 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (28 5 (:REWRITE <-OF-INTEGER-LENGTH-ARG2))
 (27 2 (:REWRITE DEFAULT-*-2))
 (24 2 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR))
 (13 1 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-4))
 (13 1 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-2))
 (12 4 (:LINEAR <-OF-1-AND-INTEGER-LENGTH-LINEAR))
 (9 9 (:REWRITE DEFAULT-<-2))
 (9 9 (:REWRITE DEFAULT-<-1))
 (8 2 (:REWRITE COMMUTATIVITY-OF-+))
 (6 4 (:REWRITE DEFAULT-+-2))
 (6 4 (:REWRITE DEFAULT-+-1))
 (6 3 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (6 1 (:REWRITE ZIP-OPEN))
 (5 5 (:TYPE-PRESCRIPTION POSP))
 (5 5 (:DEFINITION POSP))
 (4 2 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR-NEGATIVE-EXPONENT))
 (3 3 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (3 1 (:REWRITE EQUAL-OF-0-AND-INTEGER-LENGTH))
 (2 2 (:REWRITE DEFAULT-*-1))
 (2 2 (:LINEAR <=-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (2 2 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (2 1 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-3))
 (2 1 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-1))
 (1 1 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (1 1 (:TYPE-PRESCRIPTION NATP))
 (1 1 (:REWRITE INTEGER-LENGTH-WHEN-NOT-INTEGERP-CHEAP))
 (1 1 (:DEFINITION NATP))
 )
(<=-OF-CEILING-OF-LG-AND-CEILING-OF-LG
 (6 6 (:REWRITE DEFAULT-<-2))
 (6 6 (:REWRITE DEFAULT-<-1))
 (6 2 (:LINEAR <-OF-1-AND-INTEGER-LENGTH-LINEAR))
 (6 2 (:DEFINITION POSP))
 (5 1 (:REWRITE <-OF-INTEGER-LENGTH-ARG2))
 (5 1 (:REWRITE <-OF-INTEGER-LENGTH-ARG1))
 (2 2 (:TYPE-PRESCRIPTION POSP))
 (2 2 (:REWRITE INTEGER-LENGTH-WHEN-NOT-INTEGERP-CHEAP))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(<=-OF-CEILING-OF-LG-AND-CEILING-OF-LG-LINEAR
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 )
(EXPT-OF-CEILING-OF-LG-WHEN-POWER-OF-2P
 (586 30 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR))
 (546 546 (:TYPE-PRESCRIPTION EVENP))
 (448 78 (:LINEAR <-OF-1-AND-INTEGER-LENGTH-LINEAR))
 (364 182 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (364 182 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (364 182 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (358 44 (:REWRITE <-OF-INTEGER-LENGTH-ARG2))
 (324 15 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-4))
 (324 15 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-2))
 (218 184 (:REWRITE DEFAULT-<-2))
 (203 184 (:REWRITE DEFAULT-<-1))
 (182 182 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (175 33 (:DEFINITION POSP))
 (168 20 (:REWRITE <-OF-0-AND-INTEGER-LENGTH))
 (134 30 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR-NEGATIVE-EXPONENT))
 (67 15 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-3))
 (67 15 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-1))
 (64 34 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (49 24 (:REWRITE DEFAULT-+-2))
 (34 34 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (33 33 (:TYPE-PRESCRIPTION POSP))
 (30 30 (:LINEAR <=-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (30 30 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (24 24 (:REWRITE DEFAULT-+-1))
 (21 21 (:REWRITE INTEGER-LENGTH-WHEN-NOT-INTEGERP-CHEAP))
 (14 14 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (6 6 (:TYPE-PRESCRIPTION NATP))
 )
(UNSIGNED-BYTE-P-OF-+-OF-1-AND-CEILING-OF-LG-SAME
 (48 48 (:TYPE-PRESCRIPTION EVENP))
 (32 16 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (32 16 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (32 16 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (24 12 (:REWRITE DEFAULT-<-2))
 (24 2 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR))
 (22 4 (:REWRITE <-OF-INTEGER-LENGTH-ARG2))
 (16 16 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (13 12 (:REWRITE DEFAULT-<-1))
 (13 1 (:REWRITE DEFAULT-*-2))
 (13 1 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-4))
 (13 1 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-2))
 (12 4 (:LINEAR <-OF-1-AND-INTEGER-LENGTH-LINEAR))
 (6 3 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (4 4 (:TYPE-PRESCRIPTION POSP))
 (4 4 (:DEFINITION POSP))
 (4 2 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR-NEGATIVE-EXPONENT))
 (3 3 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (3 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE INTEGER-LENGTH-WHEN-NOT-INTEGERP-CHEAP))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:LINEAR <=-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (2 2 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (2 1 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-3))
 (2 1 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-1))
 (1 1 (:REWRITE DEFAULT-*-1))
 (1 1 (:REWRITE <-OF-CONSTANT-AND-*-OF-CONSTANT))
 )
(UNSIGNED-BYTE-P-OF-CEILING-OF-LG-SAME
 (6362 142 (:REWRITE <-OF-INTEGER-LENGTH-ARG2))
 (5912 8 (:REWRITE <-OF-EXPT-2-AND-CONSTANT))
 (5026 168 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR))
 (2670 464 (:LINEAR <-OF-1-AND-INTEGER-LENGTH-LINEAR))
 (2639 84 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-4))
 (2639 84 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-2))
 (2538 2538 (:TYPE-PRESCRIPTION EVENP))
 (1692 846 (:TYPE-PRESCRIPTION EXPT-TYPE-ODD-EXPONENT-NEGATIVE-BASE))
 (1692 846 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-2))
 (1692 846 (:TYPE-PRESCRIPTION EXPT-TYPE-EVEN-EXPONENT-1))
 (1357 1111 (:REWRITE DEFAULT-<-2))
 (1271 1111 (:REWRITE DEFAULT-<-1))
 (1270 168 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-EXPONENTS-LINEAR-NEGATIVE-EXPONENT))
 (846 846 (:TYPE-PRESCRIPTION EXPT-TYPE-SMALL-BASE-NEGATIVE-EXPONENT))
 (837 185 (:REWRITE DEFAULT-+-2))
 (692 185 (:REWRITE DEFAULT-+-1))
 (635 84 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-3))
 (635 84 (:LINEAR EXPT-WHEN-NEGATIVE-EXPONENT-LINEAR-1))
 (470 235 (:REWRITE EXPT-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (360 24 (:REWRITE <-OF-1-AND-EXPT-GEN))
 (264 96 (:LINEAR <=-OF-CEILING-OF-LG-AND-CEILING-OF-LG-LINEAR))
 (235 235 (:REWRITE EXPT-WHEN-NOT-ACL2-NUMBERP-CHEAP))
 (196 48 (:REWRITE <-OF-CEILING-OF-LG-ARG2-WHEN-CONSTANT))
 (168 168 (:LINEAR <=-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (168 168 (:LINEAR <-OF-EXPT-AND-EXPT-SAME-BASE-LINEAR))
 (168 56 (:REWRITE <-OF-0-AND-INTEGER-LENGTH))
 (104 8 (:REWRITE EQUAL-OF-EXPT-AND-1))
 (103 27 (:REWRITE <-OF-EXPT-OF-CEILING-OF-LG-WHEN-<))
 (100 100 (:REWRITE INTEGER-LENGTH-WHEN-NOT-INTEGERP-CHEAP))
 (40 8 (:REWRITE EQUAL-OF-CEILING-OF-LG-AND-CONSTANT))
 (40 8 (:REWRITE EQUAL-OF-0-AND-CEILING-OF-LG))
 (40 8 (:REWRITE <-OF-CEILING-OF-LG-ARG1-WHEN-CONSTANT))
 (24 24 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (11 3 (:REWRITE <-OF-EXPT-2-OF-CEILING-OF-LG-SAME))
 (8 8 (:TYPE-PRESCRIPTION NATP))
 (8 8 (:DEFINITION IFIX))
 (8 4 (:REWRITE CEILING-OF-LG-OF-EXPT2))
 (3 3 (:REWRITE <-OF-CONSTANT-AND-EXPT-2))
 (3 1 (:REWRITE UNSIGNED-BYTE-P-OF-CEILING-OF-LG-WHEN-<))
 )
(CEILING-OF-LG-OF-+-OF--1
 (49 44 (:REWRITE DEFAULT-+-2))
 (44 44 (:REWRITE DEFAULT-+-1))
 (17 17 (:REWRITE INTEGER-LENGTH-WHEN-NOT-INTEGERP-CHEAP))
 (7 7 (:REWRITE DEFAULT-<-2))
 (7 7 (:REWRITE DEFAULT-<-1))
 )
