(C)
(PHI)
(PHI-INDUCT)
(C-LEMMA
 (8 4 (:REWRITE DEFAULT-+-2))
 (8 4 (:REWRITE DEFAULT-+-1))
 (8 4 (:REWRITE DEFAULT-*-2))
 (4 4 (:REWRITE DEFAULT-*-1))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 )
(PHI-D
 (120 40 (:REWRITE A4))
 (107 95 (:REWRITE DEFAULT-+-2))
 (102 95 (:REWRITE DEFAULT-+-1))
 (93 53 (:REWRITE DEFAULT-*-2))
 (53 53 (:REWRITE DEFAULT-*-1))
 (27 27 (:REWRITE DEFAULT-<-2))
 (27 27 (:REWRITE DEFAULT-<-1))
 )
(NAT-INDUCT)
(LOP1-HACK1)
(LOP1-HACK2)
(LOP1-HACK3
 (16 2 (:LINEAR *-WEAKLY-MONOTONIC-NEGATIVE-MULTIPLIER . 2))
 (16 2 (:LINEAR *-STRONGLY-MONOTONIC-NEGATIVE-MULTIPLIER . 2))
 (16 2 (:LINEAR *-STRONGLY-MONOTONIC . 2))
 (7 3 (:REWRITE DEFAULT-<-1))
 (6 2 (:REWRITE DEFAULT-*-2))
 (5 3 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-*-1))
 (2 2 (:LINEAR *-WEAKLY-MONOTONIC-NEGATIVE-MULTIPLIER . 1))
 (2 2 (:LINEAR *-STRONGLY-MONOTONIC-NEGATIVE-MULTIPLIER . 1))
 (2 2 (:LINEAR *-STRONGLY-MONOTONIC . 1))
 )
(REM-C
 (42 2 (:REWRITE C-LEMMA))
 (27 9 (:TYPE-PRESCRIPTION RATIONALP-REM))
 (24 2 (:DEFINITION EXPT))
 (12 8 (:REWRITE DEFAULT-<-2))
 (12 8 (:REWRITE DEFAULT-<-1))
 (11 11 (:TYPE-PRESCRIPTION A14 . 2))
 (11 11 (:TYPE-PRESCRIPTION A14 . 1))
 (10 4 (:REWRITE DEFAULT-*-2))
 (9 9 (:TYPE-PRESCRIPTION INTEGERP-REM))
 (8 6 (:REWRITE DEFAULT-+-2))
 (8 6 (:REWRITE DEFAULT-+-1))
 (6 6 (:TYPE-PRESCRIPTION NATP-BITN))
 (6 2 (:REWRITE COMMUTATIVITY-OF-+))
 (4 4 (:REWRITE DEFAULT-*-1))
 )
(REM-C-2
 (84 4 (:REWRITE C-LEMMA))
 (54 18 (:TYPE-PRESCRIPTION RATIONALP-REM))
 (50 18 (:REWRITE DEFAULT-*-2))
 (42 28 (:REWRITE DEFAULT-+-2))
 (40 28 (:REWRITE DEFAULT-+-1))
 (28 28 (:TYPE-PRESCRIPTION A14 . 2))
 (28 28 (:TYPE-PRESCRIPTION A14 . 1))
 (26 18 (:REWRITE DEFAULT-<-2))
 (26 18 (:REWRITE DEFAULT-<-1))
 (18 18 (:TYPE-PRESCRIPTION INTEGERP-REM))
 (18 18 (:REWRITE DEFAULT-*-1))
 (14 6 (:REWRITE A4))
 (4 4 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (4 4 (:REWRITE ZIP-OPEN))
 (2 2 (:REWRITE FOLD-CONSTS-IN-+))
 )
(PHI-REM
 (334 42 (:REWRITE C-LEMMA))
 (162 54 (:TYPE-PRESCRIPTION RATIONALP-REM))
 (146 126 (:REWRITE DEFAULT-+-2))
 (140 126 (:REWRITE DEFAULT-+-1))
 (120 40 (:REWRITE A4))
 (102 51 (:REWRITE DEFAULT-*-2))
 (101 77 (:REWRITE DEFAULT-<-2))
 (101 77 (:REWRITE DEFAULT-<-1))
 (98 8 (:DEFINITION EXPT))
 (62 62 (:TYPE-PRESCRIPTION A14 . 2))
 (62 62 (:TYPE-PRESCRIPTION A14 . 1))
 (54 54 (:TYPE-PRESCRIPTION INTEGERP-REM))
 (51 51 (:REWRITE DEFAULT-*-1))
 (24 8 (:REWRITE UNICITY-OF-0))
 (2 2 (:REWRITE ZIP-OPEN))
 )
(LOP1-INDUCT
 (14 12 (:REWRITE DEFAULT-<-2))
 (14 12 (:REWRITE DEFAULT-<-1))
 (14 10 (:REWRITE DEFAULT-+-2))
 (14 10 (:REWRITE DEFAULT-+-1))
 (10 2 (:REWRITE C-LEMMA))
 (8 4 (:REWRITE DEFAULT-*-2))
 (6 6 (:TYPE-PRESCRIPTION INTEGERP-REM))
 (4 4 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (4 4 (:REWRITE DEFAULT-*-1))
 )
(LOP1-1)
(LOP1-2)
(LOP1-3)
(LOP1-4
 (26 2 (:DEFINITION PHI))
 (26 2 (:DEFINITION EXPT))
 (22 2 (:DEFINITION C))
 (17 17 (:REWRITE DEFAULT-<-2))
 (17 17 (:REWRITE DEFAULT-<-1))
 (16 13 (:REWRITE DEFAULT-+-2))
 (15 13 (:REWRITE DEFAULT-+-1))
 (6 6 (:TYPE-PRESCRIPTION NATP-BITN))
 (6 2 (:REWRITE DEFAULT-*-2))
 (2 2 (:REWRITE ZIP-OPEN))
 (2 2 (:REWRITE DEFAULT-*-1))
 (2 2 (:REWRITE C-LEMMA))
 )
(LOP1-5
 (122 35 (:REWRITE DEFAULT-*-2))
 (118 84 (:REWRITE DEFAULT-<-2))
 (106 106 (:REWRITE DEFAULT-+-2))
 (106 106 (:REWRITE DEFAULT-+-1))
 (84 84 (:REWRITE DEFAULT-<-1))
 (35 35 (:REWRITE DEFAULT-*-1))
 (21 7 (:REWRITE C-LEMMA))
 (17 17 (:REWRITE ZIP-OPEN))
 )
(LOP1-6
 (240 75 (:REWRITE DEFAULT-*-2))
 (176 168 (:REWRITE DEFAULT-+-2))
 (175 168 (:REWRITE DEFAULT-+-1))
 (122 107 (:REWRITE DEFAULT-<-2))
 (107 107 (:REWRITE DEFAULT-<-1))
 (75 75 (:REWRITE DEFAULT-*-1))
 (72 32 (:REWRITE C-LEMMA))
 (6 2 (:REWRITE UNICITY-OF-0))
 )
(LOP1-7
 (266 84 (:REWRITE DEFAULT-*-2))
 (226 166 (:REWRITE DEFAULT-<-2))
 (224 211 (:REWRITE DEFAULT-+-2))
 (221 211 (:REWRITE DEFAULT-+-1))
 (166 166 (:REWRITE DEFAULT-<-1))
 (84 84 (:REWRITE DEFAULT-*-1))
 (40 14 (:REWRITE C-LEMMA))
 (31 31 (:REWRITE ZIP-OPEN))
 )
(LOP1-8
 (338 165 (:REWRITE DEFAULT-*-2))
 (279 267 (:REWRITE DEFAULT-+-2))
 (279 267 (:REWRITE DEFAULT-+-1))
 (183 165 (:REWRITE DEFAULT-*-1))
 (119 104 (:REWRITE DEFAULT-<-2))
 (104 104 (:REWRITE DEFAULT-<-1))
 (21 7 (:REWRITE C-LEMMA))
 (6 6 (:LINEAR *-WEAKLY-MONOTONIC-NEGATIVE-MULTIPLIER . 2))
 (6 6 (:LINEAR *-WEAKLY-MONOTONIC-NEGATIVE-MULTIPLIER . 1))
 (6 6 (:LINEAR *-WEAKLY-MONOTONIC . 2))
 (6 6 (:LINEAR *-WEAKLY-MONOTONIC . 1))
 )
(LOP1-9
 (62 37 (:REWRITE DEFAULT-<-2))
 (51 45 (:REWRITE DEFAULT-+-2))
 (51 45 (:REWRITE DEFAULT-+-1))
 (37 37 (:REWRITE DEFAULT-<-1))
 (18 9 (:REWRITE DEFAULT-*-2))
 (9 9 (:REWRITE DEFAULT-*-1))
 )
(LOP1-10
 (216 154 (:REWRITE DEFAULT-+-2))
 (193 154 (:REWRITE DEFAULT-+-1))
 (106 45 (:REWRITE DEFAULT-*-2))
 (86 60 (:REWRITE DEFAULT-<-2))
 (60 60 (:REWRITE DEFAULT-<-1))
 (45 45 (:REWRITE DEFAULT-*-1))
 )
(LOP1-11
 (213 141 (:REWRITE DEFAULT-+-2))
 (189 141 (:REWRITE DEFAULT-+-1))
 (131 74 (:REWRITE DEFAULT-<-2))
 (107 49 (:REWRITE DEFAULT-*-2))
 (74 74 (:REWRITE DEFAULT-<-1))
 (49 49 (:REWRITE DEFAULT-*-1))
 )
(LOP1-12
 (134 83 (:REWRITE DEFAULT-+-2))
 (113 83 (:REWRITE DEFAULT-+-1))
 (105 69 (:REWRITE DEFAULT-<-2))
 (78 69 (:REWRITE DEFAULT-<-1))
 (70 35 (:REWRITE DEFAULT-*-2))
 (35 35 (:REWRITE DEFAULT-*-1))
 )
(LOP1-13
 (57 37 (:REWRITE DEFAULT-+-2))
 (45 37 (:REWRITE DEFAULT-+-1))
 (28 16 (:REWRITE DEFAULT-<-2))
 (24 15 (:REWRITE DEFAULT-*-2))
 (19 16 (:REWRITE DEFAULT-<-1))
 (15 15 (:REWRITE DEFAULT-*-1))
 )
(LOP1-14
 (166 59 (:REWRITE DEFAULT-*-2))
 (116 104 (:REWRITE DEFAULT-+-2))
 (116 104 (:REWRITE DEFAULT-+-1))
 (71 52 (:REWRITE DEFAULT-<-2))
 (59 59 (:REWRITE DEFAULT-*-1))
 (53 52 (:REWRITE DEFAULT-<-1))
 )
(LOP1-15
 (1782 621 (:REWRITE DEFAULT-*-2))
 (1411 1153 (:REWRITE DEFAULT-+-2))
 (1404 1153 (:REWRITE DEFAULT-+-1))
 (621 621 (:REWRITE DEFAULT-*-1))
 (621 521 (:REWRITE DEFAULT-<-2))
 (524 521 (:REWRITE DEFAULT-<-1))
 )
(LOP1-16
 (9 9 (:REWRITE DEFAULT-+-2))
 (9 9 (:REWRITE DEFAULT-+-1))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 )
(LOP1-17
 (23 18 (:REWRITE DEFAULT-<-2))
 (18 18 (:REWRITE DEFAULT-<-1))
 (13 11 (:REWRITE DEFAULT-+-2))
 (13 11 (:REWRITE DEFAULT-+-1))
 (4 2 (:REWRITE DEFAULT-*-2))
 (2 2 (:REWRITE DEFAULT-*-1))
 )
(LOP1-18
 (37 29 (:REWRITE DEFAULT-<-1))
 (36 24 (:REWRITE DEFAULT-+-2))
 (36 24 (:REWRITE DEFAULT-+-1))
 (33 29 (:REWRITE DEFAULT-<-2))
 (8 4 (:REWRITE DEFAULT-*-2))
 (4 4 (:REWRITE DEFAULT-*-1))
 )
(LOP1-19
 (51 39 (:REWRITE DEFAULT-+-2))
 (50 39 (:REWRITE DEFAULT-+-1))
 (32 15 (:REWRITE DEFAULT-*-2))
 (25 15 (:REWRITE DEFAULT-*-1))
 (22 17 (:REWRITE DEFAULT-<-2))
 (20 17 (:REWRITE DEFAULT-<-1))
 )
(LOP1-HACK4
 (37 2 (:DEFINITION EXPT))
 (13 11 (:REWRITE DEFAULT-+-2))
 (12 4 (:REWRITE DEFAULT-*-2))
 (12 3 (:REWRITE COMMUTATIVITY-OF-+))
 (11 11 (:REWRITE DEFAULT-+-1))
 (9 3 (:REWRITE A4))
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (4 4 (:REWRITE DEFAULT-*-1))
 (2 2 (:TYPE-PRESCRIPTION A14 . 1))
 (1 1 (:REWRITE ZIP-OPEN))
 )
(LOP1-20
 (273 169 (:REWRITE DEFAULT-+-2))
 (215 169 (:REWRITE DEFAULT-+-1))
 (166 64 (:REWRITE DEFAULT-*-2))
 (108 6 (:DEFINITION PHI))
 (92 61 (:REWRITE DEFAULT-<-2))
 (84 64 (:REWRITE DEFAULT-*-1))
 (64 61 (:REWRITE DEFAULT-<-1))
 )
(LOP1-21
 (55 39 (:REWRITE DEFAULT-+-1))
 (53 39 (:REWRITE DEFAULT-+-2))
 (34 19 (:REWRITE DEFAULT-*-2))
 (24 4 (:REWRITE A5))
 (20 18 (:REWRITE DEFAULT-<-2))
 (19 19 (:REWRITE DEFAULT-*-1))
 (18 18 (:REWRITE DEFAULT-<-1))
 (18 6 (:REWRITE A4))
 )
(LOP1-22
 (529 367 (:REWRITE DEFAULT-+-2))
 (519 367 (:REWRITE DEFAULT-+-1))
 (320 178 (:REWRITE DEFAULT-*-2))
 (178 178 (:REWRITE DEFAULT-*-1))
 (105 91 (:REWRITE DEFAULT-<-2))
 (91 91 (:REWRITE DEFAULT-<-1))
 (66 6 (:REWRITE A1))
 (6 6 (:REWRITE FOLD-CONSTS-IN-+))
 )
(LOP1-23
 (72 4 (:REWRITE A9))
 (59 43 (:REWRITE DEFAULT-+-1))
 (57 43 (:REWRITE DEFAULT-+-2))
 (32 18 (:REWRITE DEFAULT-*-2))
 (24 4 (:REWRITE A5))
 (21 19 (:REWRITE DEFAULT-<-2))
 (19 19 (:REWRITE DEFAULT-<-1))
 (18 18 (:REWRITE DEFAULT-*-1))
 (18 6 (:REWRITE A4))
 (8 4 (:REWRITE BITN-REM))
 (6 2 (:REWRITE REM-C))
 )
(LOP1-24
 (500 12 (:REWRITE BITN-REM))
 (348 202 (:REWRITE DEFAULT-+-2))
 (294 202 (:REWRITE DEFAULT-+-1))
 (229 92 (:REWRITE DEFAULT-*-2))
 (206 6 (:REWRITE REM-C))
 (115 62 (:REWRITE DEFAULT-<-2))
 (92 92 (:REWRITE DEFAULT-*-1))
 (72 12 (:REWRITE A5))
 (62 62 (:REWRITE DEFAULT-<-1))
 (54 18 (:REWRITE A4))
 )
(LOP1-25
 (452 4 (:DEFINITION PHI))
 (228 195 (:REWRITE DEFAULT-+-1))
 (226 195 (:REWRITE DEFAULT-+-2))
 (101 67 (:REWRITE DEFAULT-*-2))
 (74 61 (:REWRITE DEFAULT-<-2))
 (67 67 (:REWRITE DEFAULT-*-1))
 (64 16 (:REWRITE BITN-REM))
 (61 61 (:REWRITE DEFAULT-<-1))
 (48 8 (:REWRITE A5))
 (36 12 (:REWRITE A4))
 (36 8 (:REWRITE REM-C))
 )
(LOP1-26
 (192 6 (:REWRITE REARRANGE-NEGATIVE-COEFS-<))
 (172 8 (:REWRITE BITN-REM))
 (164 108 (:REWRITE DEFAULT-+-2))
 (157 108 (:REWRITE DEFAULT-+-1))
 (126 61 (:REWRITE DEFAULT-*-2))
 (88 4 (:REWRITE REM-C))
 (61 61 (:REWRITE DEFAULT-*-1))
 (58 46 (:REWRITE DEFAULT-<-2))
 (46 46 (:REWRITE DEFAULT-<-1))
 (8 8 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 )
(LOP1-27
 (117 79 (:REWRITE DEFAULT-+-2))
 (96 79 (:REWRITE DEFAULT-+-1))
 (80 30 (:REWRITE DEFAULT-*-2))
 (63 39 (:REWRITE DEFAULT-<-2))
 (39 39 (:REWRITE DEFAULT-<-1))
 (39 30 (:REWRITE DEFAULT-*-1))
 )
(LOP1-28
 (169 109 (:REWRITE DEFAULT-+-2))
 (144 109 (:REWRITE DEFAULT-+-1))
 (96 37 (:REWRITE DEFAULT-*-2))
 (91 51 (:REWRITE DEFAULT-<-2))
 (51 51 (:REWRITE DEFAULT-<-1))
 (46 37 (:REWRITE DEFAULT-*-1))
 )
(LOP1-29
 (107 65 (:REWRITE DEFAULT-+-2))
 (85 65 (:REWRITE DEFAULT-+-1))
 (78 33 (:REWRITE DEFAULT-*-2))
 (33 33 (:REWRITE DEFAULT-*-1))
 (29 27 (:REWRITE DEFAULT-<-2))
 (27 27 (:REWRITE DEFAULT-<-1))
 (24 4 (:REWRITE A5))
 (16 16 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 )
(LOP1-30
 (104 2 (:DEFINITION PHI))
 (39 25 (:REWRITE DEFAULT-+-2))
 (34 25 (:REWRITE DEFAULT-+-1))
 (30 14 (:REWRITE DEFAULT-*-2))
 (14 14 (:REWRITE DEFAULT-*-1))
 (12 2 (:REWRITE A5))
 (11 11 (:REWRITE DEFAULT-<-2))
 (11 11 (:REWRITE DEFAULT-<-1))
 (9 3 (:REWRITE A4))
 (4 4 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 )
(LOP1-31
 (320 167 (:REWRITE DEFAULT-+-2))
 (239 167 (:REWRITE DEFAULT-+-1))
 (164 55 (:REWRITE DEFAULT-*-2))
 (75 42 (:REWRITE DEFAULT-<-2))
 (55 55 (:REWRITE DEFAULT-*-1))
 (48 42 (:REWRITE DEFAULT-<-1))
 )
(LOP1-32
 (258 258 (:REWRITE DEFAULT-+-2))
 (258 258 (:REWRITE DEFAULT-+-1))
 (246 96 (:REWRITE DEFAULT-*-2))
 (202 182 (:REWRITE DEFAULT-<-2))
 (182 182 (:REWRITE DEFAULT-<-1))
 (96 96 (:REWRITE DEFAULT-*-1))
 (50 50 (:REWRITE ZIP-OPEN))
 )
(LOP1-33
 (207 71 (:REWRITE DEFAULT-*-2))
 (193 179 (:REWRITE DEFAULT-+-2))
 (183 179 (:REWRITE DEFAULT-+-1))
 (83 71 (:REWRITE DEFAULT-<-2))
 (71 71 (:REWRITE DEFAULT-<-1))
 (71 71 (:REWRITE DEFAULT-*-1))
 (42 42 (:REWRITE ZIP-OPEN))
 )
(LOP1-34
 (151 44 (:REWRITE DEFAULT-*-2))
 (118 88 (:REWRITE DEFAULT-+-2))
 (102 88 (:REWRITE DEFAULT-+-1))
 (85 67 (:REWRITE DEFAULT-<-2))
 (67 67 (:REWRITE DEFAULT-<-1))
 (53 19 (:REWRITE A4))
 (44 44 (:REWRITE DEFAULT-*-1))
 (17 17 (:REWRITE ZIP-OPEN))
 (1 1 (:REWRITE FOLD-CONSTS-IN-+))
 )
(LOP1-35
 (40 28 (:REWRITE DEFAULT-+-2))
 (40 28 (:REWRITE DEFAULT-+-1))
 (28 28 (:REWRITE DEFAULT-<-2))
 (28 28 (:REWRITE DEFAULT-<-1))
 (18 6 (:REWRITE DEFAULT-*-2))
 (6 6 (:REWRITE DEFAULT-*-1))
 )
(LOP1-36
 (357 309 (:REWRITE DEFAULT-+-2))
 (335 309 (:REWRITE DEFAULT-+-1))
 (175 131 (:REWRITE DEFAULT-<-2))
 (159 131 (:REWRITE DEFAULT-<-1))
 (94 70 (:REWRITE DEFAULT-*-2))
 (70 70 (:REWRITE DEFAULT-*-1))
 (11 11 (:REWRITE FOLD-CONSTS-IN-+))
 (2 2 (:REWRITE BITN-REM))
 )
(LOP1-37
 (37 31 (:REWRITE DEFAULT-+-2))
 (37 31 (:REWRITE DEFAULT-+-1))
 (18 16 (:REWRITE DEFAULT-<-2))
 (16 16 (:REWRITE DEFAULT-<-1))
 (14 7 (:REWRITE DEFAULT-*-2))
 (7 7 (:REWRITE DEFAULT-*-1))
 )
(LOP1-38
 (111 6 (:DEFINITION PHI))
 (77 59 (:REWRITE DEFAULT-+-2))
 (75 59 (:REWRITE DEFAULT-+-1))
 (50 5 (:REWRITE REM-C))
 (38 30 (:REWRITE DEFAULT-<-1))
 (32 30 (:REWRITE DEFAULT-<-2))
 (30 10 (:REWRITE A4))
 (28 12 (:REWRITE DEFAULT-*-2))
 (12 12 (:REWRITE DEFAULT-*-1))
 )
(LOP1-39
 (4 4 (:TYPE-PRESCRIPTION INTEGERP-REM))
 )
(LOP1-HACK5)
(LOP-THM-1
 (130 10 (:DEFINITION EXPT))
 (66 46 (:REWRITE DEFAULT-<-2))
 (46 46 (:REWRITE DEFAULT-<-1))
 (45 25 (:REWRITE DEFAULT-*-2))
 (44 40 (:REWRITE DEFAULT-+-2))
 (40 40 (:REWRITE DEFAULT-+-1))
 (25 25 (:REWRITE DEFAULT-*-1))
 (10 10 (:REWRITE ZIP-OPEN))
 )
