(|a^0 = 1|
 (3 1 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (2 2 (:TYPE-PRESCRIPTION O-FINP))
 )
(|a^1 = a|
 (9 9 (:TYPE-PRESCRIPTION O-FINP))
 (6 1 (:REWRITE O-INFP->NEQ-0))
 (5 2 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (4 1 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (3 3 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (3 3 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (3 1 (:REWRITE O-P-DEF-O-FINP-1))
 (3 1 (:REWRITE O-FIRST-EXPT-O-INFP))
 (3 1 (:REWRITE O*-O-FINP))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (1 1 (:REWRITE NATP-RW))
 )
(|~(0 = a)  <=>  0^a = 0|
 (22 5 (:REWRITE O-FIRST-EXPT-O-INFP))
 (16 16 (:TYPE-PRESCRIPTION O-FINP))
 (11 3 (:REWRITE O-INFP->NEQ-0))
 (9 4 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (4 1 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (4 1 (:REWRITE NATP-POSP))
 (4 1 (:LINEAR O-FIRST-EXPT-<=))
 (3 3 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (3 3 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (3 1 (:REWRITE O-P-DEF-O-FINP-1))
 (3 1 (:REWRITE O-FIRST-EXPT-0-NATP))
 (3 1 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (1 1 (:REWRITE POSP-RW))
 (1 1 (:REWRITE NATP-RW))
 )
(|0 < a  =>  0^a = 0 :a|
 (4 1 (:REWRITE NATP-POSP))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (1 1 (:REWRITE POSP-RW))
 (1 1 (:REWRITE NATP-RW))
 )
(|0 < a  =>  0^a = 0 :b|
 (26 3 (:REWRITE O-FIRST-EXPT-O-INFP))
 (21 19 (:TYPE-PRESCRIPTION |0 < a  =>  0^a = 0 :a|))
 (6 2 (:REWRITE O-P-DEF-O-FINP-1))
 (6 1 (:REWRITE O-FIRST-EXPT-0-NATP))
 (6 1 (:LINEAR O-FIRST-EXPT-<=))
 (4 4 (:TYPE-PRESCRIPTION O-P))
 (4 2 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (4 1 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (4 1 (:REWRITE O-INFP->NEQ-0))
 (2 2 (:TYPE-PRESCRIPTION POSP))
 (1 1 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (1 1 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (1 1 (:META CANCEL_PLUS-EQUAL-CORRECT))
 )
(|1^a = 1|
 (24 3 (:REWRITE O-FIRST-EXPT-O-INFP))
 (12 12 (:TYPE-PRESCRIPTION O-FINP))
 (6 2 (:REWRITE O-P-DEF-O-FINP-1))
 (6 1 (:REWRITE O-FIRST-EXPT-0-NATP))
 (6 1 (:LINEAR O-FIRST-EXPT-<=))
 (4 4 (:TYPE-PRESCRIPTION O-P))
 (4 2 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (4 1 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (4 1 (:REWRITE O-INFP->NEQ-0))
 (4 1 (:REWRITE NATP-POSP))
 (3 1 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (1 1 (:REWRITE POSP-RW))
 (1 1 (:REWRITE NATP-RW))
 (1 1 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (1 1 (:META CANCEL_PLUS-EQUAL-CORRECT))
 )
(|(a-1 = 0)  <=>  a <= 1|
 (31 7 (:REWRITE O-FIRST-EXPT-O-INFP))
 (20 3 (:REWRITE O-INFP->NEQ-0))
 (14 6 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (13 1 (:REWRITE O--0))
 (8 8 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (6 1 (:REWRITE O-INFP-O-FINP-O<=))
 (5 5 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (5 5 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (4 1 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (4 1 (:LINEAR O-FIRST-EXPT-<=))
 (3 1 (:REWRITE O-P-DEF-O-FINP-1))
 (3 1 (:REWRITE O-FIRST-EXPT-0-NATP))
 (3 1 (:REWRITE O-FINP-<))
 (3 1 (:REWRITE AC-<))
 (2 2 (:REWRITE |a < b & b < c  =>  a < c|))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 1 (:REWRITE O-FIRST-EXPT-<))
 (2 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1 1 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (1 1 (:REWRITE O-FIRST-COEFF-<))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:META CANCEL_PLUS-LESSP-CORRECT))
 )
(O-P-O^
 (297 22 (:REWRITE MAKE-ORD-EQUAL-4))
 (176 30 (:REWRITE O-FIRST-EXPT-<))
 (167 30 (:REWRITE O-FIRST-COEFF-<))
 (126 126 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (126 126 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (118 3 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (115 20 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (102 51 (:TYPE-PRESCRIPTION O+-O-FINP))
 (89 5 (:REWRITE O--0))
 (88 30 (:REWRITE O-FINP-<))
 (80 9 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (76 1 (:REWRITE O*-O-FIRST-EXPT))
 (64 4 (:REWRITE O-INFP-O+-2))
 (64 1 (:REWRITE |(o-first-expt a) < a|))
 (60 4 (:REWRITE O-INFP-O+))
 (59 20 (:REWRITE O*-O-FINP))
 (54 32 (:REWRITE |a < b & b < c  =>  a < c|))
 (54 15 (:REWRITE NATP-POSP))
 (51 51 (:TYPE-PRESCRIPTION OB+))
 (42 6 (:REWRITE O+-O-FIRST-EXPT-2))
 (40 4 (:REWRITE LIMITP-DEF))
 (34 6 (:REWRITE O+-O-FIRST-EXPT-1))
 (31 31 (:REWRITE NATP-RW))
 (26 16 (:REWRITE O-FINP-O-RST))
 (16 8 (:REWRITE O*-O-FIRST-COEFF))
 (16 4 (:REWRITE O-INFP-O+-3))
 (15 15 (:REWRITE POSP-RW))
 (8 8 (:TYPE-PRESCRIPTION LIMITP))
 (5 5 (:REWRITE DEFAULT-+-2))
 (5 5 (:REWRITE DEFAULT-+-1))
 (4 2 (:REWRITE O<=-O-FINP-DEF))
 (4 2 (:REWRITE O-INFP-O-FINP-O<=))
 (3 3 (:REWRITE O+-ATOM-DEF))
 (2 2 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 )
(|(a = 0) & ~(b = 0)  <=>  (a^b = 0)|
 (1101 16 (:REWRITE MAKE-ORD-EQUAL-4))
 (485 11 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (463 14 (:REWRITE O*-O-FIRST-EXPT))
 (352 8 (:REWRITE |(o-first-expt a) < a|))
 (324 10 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (263 2 (:REWRITE O-FIRST-EXPT-<-O+))
 (181 32 (:REWRITE O-FIRST-EXPT-<))
 (173 173 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (173 173 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (160 32 (:REWRITE O-FIRST-COEFF-<))
 (151 21 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (126 5 (:REWRITE O-INFP-O*))
 (118 59 (:TYPE-PRESCRIPTION O+-O-FINP))
 (80 8 (:REWRITE LIMITP-DEF))
 (79 32 (:REWRITE O-FINP-<))
 (76 21 (:REWRITE O*-O-FINP))
 (74 5 (:REWRITE O+-O-FIRST-EXPT-2))
 (61 61 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (61 16 (:REWRITE NATP-POSP))
 (59 59 (:TYPE-PRESCRIPTION OB+))
 (58 29 (:REWRITE O*-O-FIRST-COEFF))
 (51 3 (:REWRITE O--0))
 (46 5 (:REWRITE O-INFP-O*-2))
 (45 5 (:REWRITE O+-O-FIRST-EXPT-1))
 (44 33 (:REWRITE |a < b & b < c  =>  a < c|))
 (43 43 (:REWRITE NATP-RW))
 (32 2 (:REWRITE O-INFP-O+-2))
 (31 15 (:REWRITE O-FINP-O-RST))
 (30 2 (:REWRITE O-INFP-O+))
 (25 2 (:REWRITE O-INFP-O-FINP-O<=))
 (19 16 (:REWRITE POSP-RW))
 (16 16 (:TYPE-PRESCRIPTION LIMITP))
 (10 10 (:REWRITE O+-ATOM-DEF))
 (9 9 (:REWRITE DEFAULT-+-2))
 (9 9 (:REWRITE DEFAULT-+-1))
 (8 2 (:REWRITE O-INFP-O+-3))
 (5 2 (:REWRITE O<=-O-FINP-DEF))
 (2 2 (:REWRITE |0+a = a|))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:META CANCEL_PLUS-LESSP-CORRECT))
 )
(O^-^
 (63 63 (:TYPE-PRESCRIPTION |x < y  =>  0 < y-x|))
 (39 3 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (30 3 (:REWRITE LIMITP-DEF))
 (20 4 (:REWRITE DEFAULT-*-2))
 (18 18 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (18 18 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (18 3 (:REWRITE NATP-POSP))
 (17 3 (:REWRITE POSP-RW))
 (16 4 (:LINEAR EXPT-IS-INCREASING-FOR-BASE>1))
 (15 15 (:TYPE-PRESCRIPTION O-FINP))
 (15 15 (:META CANCEL_PLUS-LESSP-CORRECT))
 (14 14 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (14 14 (:REWRITE DEFAULT-<-2))
 (14 14 (:REWRITE DEFAULT-<-1))
 (12 3 (:REWRITE O-FIRST-EXPT-O-INFP))
 (11 11 (:REWRITE DEFAULT-+-2))
 (11 11 (:REWRITE DEFAULT-+-1))
 (11 8 (:REWRITE NATP-RW))
 (8 8 (:REWRITE O-INFP->NEQ-0))
 (8 2 (:LINEAR EXPT->-1))
 (6 6 (:TYPE-PRESCRIPTION LIMITP))
 (4 4 (:REWRITE DEFAULT-*-1))
 (4 1 (:REWRITE <-0-+-NEGATIVE-1))
 (3 3 (:TYPE-PRESCRIPTION |0 < a  =>  0^a = 0 :b|))
 (3 3 (:REWRITE ZIP-OPEN))
 (3 1 (:REWRITE FOLD-CONSTS-IN-+))
 (3 1 (:REWRITE EQUAL-CONSTANT-+))
 (2 2 (:TYPE-PRESCRIPTION POSP))
 )
(O-INFP-O^-1
 (929 111 (:REWRITE O-FIRST-EXPT-O-INFP))
 (568 19 (:REWRITE MAKE-ORD-EQUAL-4))
 (352 158 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (350 2 (:REWRITE O-P-O*))
 (313 30 (:LINEAR O-FIRST-EXPT-<=))
 (239 9 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (232 18 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (227 56 (:REWRITE O-INFP->NEQ-0))
 (124 124 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (124 124 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (90 3 (:REWRITE O*-O-FIRST-EXPT))
 (89 3 (:REWRITE |(o-first-expt a) < a|))
 (86 43 (:TYPE-PRESCRIPTION O+-O-FINP))
 (85 1 (:REWRITE O-FIRST-EXPT-<-O+))
 (77 19 (:REWRITE O-FIRST-EXPT-<))
 (74 19 (:REWRITE O-FIRST-COEFF-<))
 (71 21 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (69 57 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (44 8 (:REWRITE NATP-POSP))
 (43 43 (:TYPE-PRESCRIPTION OB+))
 (41 19 (:REWRITE O-FINP-<))
 (41 19 (:REWRITE AC-<))
 (40 21 (:REWRITE O*-O-FINP))
 (33 4 (:REWRITE O-INFP-O*-2))
 (28 28 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (24 8 (:REWRITE POSP-RW))
 (20 10 (:REWRITE O*-O-FIRST-COEFF))
 (19 19 (:REWRITE |a < b & b < c  =>  a < c|))
 (17 1 (:REWRITE O+-O-FIRST-EXPT-1))
 (16 16 (:REWRITE O^-^))
 (16 1 (:REWRITE O+-O-FIRST-EXPT-2))
 (13 13 (:REWRITE NATP-RW))
 (11 11 (:REWRITE O-FINP-O-RST))
 (10 10 (:REWRITE DEFAULT-+-2))
 (10 10 (:REWRITE DEFAULT-+-1))
 (9 9 (:REWRITE O+-ATOM-DEF))
 (9 1 (:REWRITE O*-O-RST))
 (8 2 (:REWRITE <-0-+-NEGATIVE-1))
 (6 2 (:REWRITE FOLD-CONSTS-IN-+))
 (6 2 (:REWRITE EQUAL-CONSTANT-+))
 (5 5 (:REWRITE O-FIRST-EXPT-O-P))
 (4 4 (:META CANCEL_PLUS-LESSP-CORRECT))
 (3 1 (:REWRITE O*-0))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 )
(O-INFP-O^-2
 (678 32 (:REWRITE MAKE-ORD-EQUAL-4))
 (260 7 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (211 10 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (153 4 (:REWRITE |(o-first-expt a) < a|))
 (150 2 (:REWRITE O*-O-FIRST-EXPT))
 (125 125 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (125 125 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (101 25 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (90 6 (:REWRITE O--0))
 (85 1 (:REWRITE O-FIRST-EXPT-<-O+))
 (83 22 (:REWRITE O-FIRST-EXPT-<))
 (72 22 (:REWRITE O-FIRST-COEFF-<))
 (66 33 (:TYPE-PRESCRIPTION O+-O-FINP))
 (66 2 (:DEFINITION EXPT))
 (54 22 (:REWRITE O-FINP-<))
 (54 22 (:REWRITE AC-<))
 (46 3 (:REWRITE O-INFP-O*-2))
 (33 33 (:TYPE-PRESCRIPTION OB+))
 (33 22 (:REWRITE |a < b & b < c  =>  a < c|))
 (31 31 (:REWRITE NATP-RW))
 (24 6 (:REWRITE NATP-POSP))
 (23 23 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (23 21 (:REWRITE O-FINP-O-RST))
 (22 4 (:REWRITE DEFAULT-*-2))
 (20 10 (:REWRITE O*-O-FIRST-COEFF))
 (18 2 (:REWRITE O-INFP-O^-1))
 (17 1 (:REWRITE O+-O-FIRST-EXPT-1))
 (16 2 (:REWRITE ZIP-OPEN))
 (16 1 (:REWRITE O+-O-FIRST-EXPT-2))
 (14 12 (:REWRITE DEFAULT-+-2))
 (14 12 (:REWRITE DEFAULT-+-1))
 (14 2 (:REWRITE COMMUTATIVITY-OF-+))
 (8 2 (:REWRITE <-0-+-NEGATIVE-1))
 (7 7 (:REWRITE O-FIRST-EXPT-O-P))
 (7 7 (:REWRITE O+-ATOM-DEF))
 (6 6 (:REWRITE POSP-RW))
 (6 2 (:REWRITE FOLD-CONSTS-IN-+))
 (6 2 (:REWRITE EQUAL-CONSTANT-+))
 (4 4 (:REWRITE DEFAULT-*-1))
 (4 4 (:META CANCEL_PLUS-LESSP-CORRECT))
 (2 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP))
 (2 2 (:REWRITE EXPONENTS-ADD-FOR-NONNEG-EXPONENTS))
 (2 2 (:REWRITE EXPONENTS-ADD))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:DEFINITION FIX))
 )
(O^-O-FINP
 (355 33 (:REWRITE O-FIRST-EXPT-O-INFP))
 (102 28 (:REWRITE O-P-DEF-O-FINP-1))
 (90 11 (:REWRITE O-FIRST-EXPT-0-NATP))
 (90 11 (:LINEAR O-FIRST-EXPT-<=))
 (56 11 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (49 16 (:REWRITE O-INFP->NEQ-0))
 (30 6 (:REWRITE O-P-O^))
 (28 7 (:REWRITE O^-^))
 (22 22 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (22 22 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (20 6 (:REWRITE O-INFP-O^-1))
 (19 19 (:REWRITE NATP-RW))
 (16 4 (:REWRITE NATP-POSP))
 (12 12 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (8 2 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (4 4 (:REWRITE POSP-RW))
 (3 1 (:REWRITE EQUAL-CONSTANT-+))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 1 (:REWRITE DEFAULT-*-1))
 (1 1 (:TYPE-PRESCRIPTION |0 < a  =>  0^a = 0 :b|))
 (1 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1 1 (:REWRITE DEFAULT-*-2))
 )
(O-INFP-O^
 (274 33 (:REWRITE O-FIRST-EXPT-O-INFP))
 (102 27 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (71 11 (:REWRITE O^-^))
 (65 8 (:LINEAR O-FIRST-EXPT-<=))
 (56 8 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (53 8 (:REWRITE O-FIRST-EXPT-0-NATP))
 (45 9 (:DEFINITION OMEGA-TERM))
 (43 14 (:REWRITE O-INFP->NEQ-0))
 (39 3 (:REWRITE O--0))
 (36 9 (:REWRITE MAKE-ORD-EQUAL-4))
 (34 34 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (34 34 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (33 1 (:DEFINITION EXPT))
 (23 7 (:REWRITE O*-O-FINP))
 (18 18 (:TYPE-PRESCRIPTION MAKE-ORD))
 (18 9 (:TYPE-PRESCRIPTION |0 < a  =>  0^a = 0 :b|))
 (18 9 (:TYPE-PRESCRIPTION |0 < a  =>  0^a = 0 :a|))
 (18 6 (:REWRITE O-P-O^))
 (18 6 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (17 9 (:REWRITE O-INFP-O^-1))
 (14 10 (:REWRITE O-P-DEF-O-FINP-1))
 (14 10 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (13 13 (:REWRITE NATP-RW))
 (11 2 (:REWRITE DEFAULT-*-2))
 (9 9 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (9 9 (:TYPE-PRESCRIPTION POSP))
 (9 3 (:REWRITE O-FINP-<))
 (9 3 (:REWRITE AC-<))
 (8 2 (:REWRITE NATP-POSP))
 (8 1 (:REWRITE ZIP-OPEN))
 (7 1 (:REWRITE COMMUTATIVITY-OF-+))
 (6 6 (:REWRITE O-FINP-O-RST))
 (6 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (6 3 (:REWRITE O-FIRST-EXPT-<))
 (5 4 (:REWRITE DEFAULT-+-2))
 (5 4 (:REWRITE DEFAULT-+-1))
 (4 1 (:REWRITE <-0-+-NEGATIVE-1))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONZERO))
 (3 3 (:REWRITE |a < b & b < c  =>  a < c|))
 (3 3 (:REWRITE O-FIRST-COEFF-<))
 (3 1 (:REWRITE FOLD-CONSTS-IN-+))
 (3 1 (:REWRITE EQUAL-CONSTANT-+))
 (2 2 (:REWRITE POSP-RW))
 (2 2 (:REWRITE DEFAULT-*-1))
 (2 2 (:META CANCEL_PLUS-LESSP-CORRECT))
 (1 1 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP))
 (1 1 (:REWRITE EXPONENTS-ADD-FOR-NONNEG-EXPONENTS))
 (1 1 (:REWRITE EXPONENTS-ADD))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:DEFINITION FIX))
 )
(O^-O-FIRST-EXPT-HELPER
 (344 16 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (324 2 (:DEFINITION OB^))
 (274 145 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (267 22 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (235 51 (:REWRITE O-FIRST-EXPT-O-INFP))
 (191 7 (:REWRITE |(o-first-expt a) < a|))
 (170 2 (:REWRITE O-FIRST-EXPT-<-O+))
 (112 17 (:REWRITE O-FIRST-EXPT-<))
 (94 17 (:REWRITE O-FIRST-COEFF-<))
 (90 20 (:REWRITE O-FIRST-EXPT-0-NATP))
 (73 18 (:REWRITE O-INFP->NEQ-0))
 (71 71 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (71 71 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (68 34 (:TYPE-PRESCRIPTION O^-O-FINP))
 (61 57 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (61 18 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (48 11 (:LINEAR O-FIRST-EXPT-<=))
 (42 22 (:REWRITE O-P-DEF-O-FINP-1))
 (37 17 (:REWRITE O-FINP-<))
 (37 17 (:REWRITE AC-<))
 (36 17 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (34 2 (:REWRITE O+-O-FIRST-EXPT-1))
 (32 2 (:REWRITE O+-O-FIRST-EXPT-2))
 (29 17 (:REWRITE O*-O-FINP))
 (22 22 (:REWRITE O+-ATOM-DEF))
 (17 17 (:TYPE-PRESCRIPTION NATP))
 (17 17 (:REWRITE |a < b & b < c  =>  a < c|))
 (17 17 (:REWRITE O-FINP-O-RST))
 (10 10 (:REWRITE NATP-RW))
 (8 2 (:REWRITE NATP-POSP))
 (6 6 (:REWRITE O^-^))
 (2 2 (:REWRITE POSP-RW))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(O^-O-FIRST-EXPT
 (549 16 (:REWRITE MAKE-ORD-EQUAL-4))
 (420 93 (:REWRITE O-FIRST-EXPT-O-INFP))
 (389 389 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (341 13 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (311 13 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (222 111 (:TYPE-PRESCRIPTION O+-O-FINP))
 (205 40 (:REWRITE O-INFP->NEQ-0))
 (181 35 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (161 32 (:REWRITE O-FIRST-EXPT-<))
 (117 117 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (117 117 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (105 25 (:REWRITE O-FIRST-COEFF-<))
 (92 14 (:REWRITE NATP-POSP))
 (89 3 (:REWRITE |(o-first-expt a) < a|))
 (85 1 (:REWRITE O-FIRST-EXPT-<-O+))
 (78 35 (:REWRITE O*-O-FINP))
 (70 32 (:REWRITE O-FINP-<))
 (70 32 (:REWRITE AC-<))
 (62 14 (:REWRITE POSP-RW))
 (53 53 (:TYPE-PRESCRIPTION NATP))
 (42 32 (:REWRITE |a < b & b < c  =>  a < c|))
 (32 16 (:REWRITE O*-O-FIRST-COEFF))
 (28 28 (:REWRITE NATP-RW))
 (26 22 (:REWRITE O^-^))
 (25 25 (:REWRITE DEFAULT-+-2))
 (25 25 (:REWRITE DEFAULT-+-1))
 (24 6 (:REWRITE <-0-+-NEGATIVE-1))
 (18 6 (:REWRITE FOLD-CONSTS-IN-+))
 (18 6 (:REWRITE EQUAL-CONSTANT-+))
 (18 3 (:REWRITE |a+0 = a|))
 (17 1 (:REWRITE O+-O-FIRST-EXPT-1))
 (16 1 (:REWRITE O+-O-FIRST-EXPT-2))
 (14 2 (:REWRITE O-INFP-O^-1))
 (13 13 (:REWRITE O+-ATOM-DEF))
 (12 12 (:REWRITE O-FINP-O-RST))
 (12 12 (:META CANCEL_PLUS-LESSP-CORRECT))
 (9 1 (:REWRITE O*-O-RST))
 (8 8 (:REWRITE O-FIRST-EXPT-O-P))
 (7 7 (:REWRITE |~(a < a)|))
 (6 6 (:REWRITE DEFAULT-<-2))
 (6 6 (:REWRITE DEFAULT-<-1))
 (6 1 (:REWRITE O-INFP-O-FINP-O<=))
 (3 1 (:REWRITE O<=-O-FINP-DEF))
 )
(|~(a=0)  =>  (a < b  <=>  a-1 < b-1)|
 (569 99 (:REWRITE O-FIRST-EXPT-O-INFP))
 (456 20 (:REWRITE O-FIRST-EXPT-<))
 (235 95 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (121 23 (:LINEAR O-FIRST-EXPT-<=))
 (105 20 (:REWRITE O-FIRST-COEFF-<))
 (90 20 (:REWRITE O-FIRST-EXPT-0-NATP))
 (89 20 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (86 21 (:REWRITE O-INFP->NEQ-0))
 (76 2 (:REWRITE O--0))
 (35 26 (:REWRITE DEFAULT-<-2))
 (35 26 (:REWRITE DEFAULT-<-1))
 (32 32 (:REWRITE |a < b & b < c  =>  a < c|))
 (32 32 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (32 32 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (18 18 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (18 18 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (12 6 (:REWRITE O-FIRST-EXPT-O-P))
 (10 10 (:REWRITE DEFAULT-+-2))
 (10 10 (:REWRITE DEFAULT-+-1))
 (8 8 (:REWRITE O-FINP-O-RST))
 (8 8 (:REWRITE NATP-RW))
 )
(|a < 1  <=> a = 0|
 (56 10 (:REWRITE O-FIRST-EXPT-O-INFP))
 (53 2 (:REWRITE O-FIRST-EXPT-<))
 (42 42 (:TYPE-PRESCRIPTION O-FINP))
 (22 8 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (16 3 (:LINEAR O-FIRST-EXPT-<=))
 (14 3 (:REWRITE O-INFP->NEQ-0))
 (10 2 (:REWRITE O-FIRST-EXPT-0-NATP))
 (8 2 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (7 3 (:REWRITE O-P-DEF-O-FINP-1))
 (6 2 (:REWRITE O-FINP-<))
 (6 2 (:REWRITE AC-<))
 (6 1 (:REWRITE O-INFP-O-FINP-O<=))
 (4 2 (:REWRITE DEFAULT-<-1))
 (3 3 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (3 3 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (3 1 (:REWRITE O<=-O-FINP-DEF))
 (2 2 (:REWRITE |a < b & b < c  =>  a < c|))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:REWRITE O-FIRST-EXPT-O-P))
 (2 2 (:REWRITE O-FIRST-COEFF-<))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:META CANCEL_PLUS-LESSP-CORRECT))
 )
(O^-O-FIRST-EXPT-2
 (362 25 (:REWRITE O--0))
 (315 46 (:REWRITE MAKE-ORD-EQUAL-4))
 (307 52 (:REWRITE O-FIRST-EXPT-<))
 (203 4 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (201 49 (:REWRITE O-INFP->NEQ-0))
 (151 151 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (151 151 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (149 51 (:REWRITE O-FIRST-COEFF-<))
 (146 52 (:REWRITE O-FINP-<))
 (146 52 (:REWRITE AC-<))
 (140 34 (:REWRITE O*-O-FINP))
 (125 52 (:REWRITE |a < b & b < c  =>  a < c|))
 (119 22 (:REWRITE DEFAULT-*-2))
 (112 112 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (109 23 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (78 26 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (78 12 (:REWRITE ZIP-OPEN))
 (67 48 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (64 1 (:REWRITE |(o-first-expt a) < a|))
 (62 62 (:REWRITE NATP-RW))
 (59 50 (:REWRITE DEFAULT-+-2))
 (59 50 (:REWRITE DEFAULT-+-1))
 (56 14 (:REWRITE NATP-POSP))
 (44 2 (:REWRITE O-FIRST-EXPT-O--<))
 (44 1 (:REWRITE O-P-O*))
 (42 2 (:REWRITE O+-O-FIRST-EXPT-2))
 (36 9 (:REWRITE <-0-+-NEGATIVE-1))
 (30 5 (:REWRITE O-INFP-O-FINP-O<=))
 (29 25 (:REWRITE O-FINP-O-RST))
 (27 9 (:REWRITE FOLD-CONSTS-IN-+))
 (27 9 (:REWRITE EQUAL-CONSTANT-+))
 (24 2 (:REWRITE O+-O-FIRST-EXPT-1))
 (23 2 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (22 22 (:REWRITE DEFAULT-*-1))
 (22 22 (:META CANCEL_PLUS-LESSP-CORRECT))
 (20 1 (:REWRITE |~(a=0)  =>  (a < b  <=>  a-1 < b-1)|))
 (18 18 (:TYPE-PRESCRIPTION OB+))
 (18 9 (:REWRITE O*-O-FIRST-COEFF))
 (15 5 (:REWRITE O<=-O-FINP-DEF))
 (14 14 (:REWRITE POSP-RW))
 (14 2 (:REWRITE O-INFP-O^-1))
 (13 13 (:REWRITE DEFAULT-<-2))
 (13 13 (:REWRITE DEFAULT-<-1))
 (12 2 (:REWRITE O-FIRST-COEFF-0))
 (11 11 (:REWRITE O^-O-FIRST-EXPT))
 (9 9 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP))
 (9 9 (:REWRITE EXPONENTS-ADD-FOR-NONNEG-EXPONENTS))
 (9 9 (:REWRITE EXPONENTS-ADD))
 (1 1 (:REWRITE |~(a < a)|))
 )
(O^-O-FIRST-EXPT-3
 (138 1 (:DEFINITION OB^))
 (76 38 (:TYPE-PRESCRIPTION O+-O-FINP))
 (70 1 (:REWRITE O*-O-INFP-DEF))
 (53 3 (:REWRITE MAKE-ORD-EQUAL-4))
 (49 24 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (49 11 (:REWRITE O-FIRST-EXPT-O-INFP))
 (49 3 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (46 23 (:TYPE-PRESCRIPTION O^-O-FINP))
 (38 38 (:TYPE-PRESCRIPTION OB+))
 (22 2 (:DEFINITION OMEGA-TERM))
 (14 3 (:REWRITE O-INFP->NEQ-0))
 (13 3 (:REWRITE O-FIRST-COEFF-<))
 (12 12 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (12 12 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (12 4 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (11 9 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (11 1 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (9 4 (:REWRITE O*-O-FINP))
 (8 2 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (8 2 (:LINEAR O-FIRST-EXPT-<=))
 (7 3 (:REWRITE O-FINP-<))
 (7 3 (:REWRITE AC-<))
 (6 6 (:TYPE-PRESCRIPTION NATP))
 (6 3 (:REWRITE O-FIRST-EXPT-<))
 (6 2 (:REWRITE O-FIRST-EXPT-0-NATP))
 (4 2 (:REWRITE O-P-DEF-O-FINP-1))
 (4 1 (:REWRITE NATP-POSP))
 (3 3 (:TYPE-PRESCRIPTION MAKE-ORD))
 (3 3 (:REWRITE |a < b & b < c  =>  a < c|))
 (3 3 (:REWRITE O^-^))
 (3 3 (:REWRITE O+-ATOM-DEF))
 (3 3 (:REWRITE NATP-RW))
 (2 2 (:REWRITE O-FINP-O-RST))
 (1 1 (:REWRITE |a0 = 0|))
 (1 1 (:REWRITE POSP-RW))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|o-first-expt(b) < o-first-expt(c)  =>  (a^b)*(a^c) = a^c|
 (2595 140 (:REWRITE MAKE-ORD-EQUAL-4))
 (749 32 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (640 31 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (541 541 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (541 541 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (538 116 (:REWRITE O-FIRST-EXPT-<))
 (511 113 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (453 15 (:DEFINITION EXPT))
 (407 27 (:REWRITE O--0))
 (395 114 (:REWRITE O-FIRST-COEFF-<))
 (331 4 (:REWRITE O-FIRST-EXPT-<-O+))
 (325 117 (:REWRITE AC-<))
 (283 116 (:REWRITE O-FINP-<))
 (268 134 (:TYPE-PRESCRIPTION O+-O-FINP))
 (196 117 (:REWRITE |a < b & b < c  =>  a < c|))
 (166 83 (:REWRITE O*-O-FIRST-COEFF))
 (163 31 (:REWRITE DEFAULT-*-2))
 (153 4 (:REWRITE |(o-first-expt a) < a|))
 (134 134 (:TYPE-PRESCRIPTION OB+))
 (124 124 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (109 109 (:REWRITE NATP-RW))
 (109 28 (:REWRITE NATP-POSP))
 (105 15 (:REWRITE ZIP-OPEN))
 (104 95 (:REWRITE O-FINP-O-RST))
 (93 15 (:REWRITE COMMUTATIVITY-OF-+))
 (93 7 (:REWRITE O+-O-FIRST-EXPT-2))
 (80 68 (:REWRITE DEFAULT-+-2))
 (80 68 (:REWRITE DEFAULT-+-1))
 (78 1 (:REWRITE LIMITP-DEF))
 (64 7 (:REWRITE O+-O-FIRST-EXPT-1))
 (61 9 (:REWRITE O-INFP-O-FINP-O<=))
 (60 1 (:REWRITE |1a = a|))
 (48 12 (:REWRITE <-0-+-NEGATIVE-1))
 (44 27 (:REWRITE O-FIRST-EXPT-O-P))
 (36 12 (:REWRITE FOLD-CONSTS-IN-+))
 (36 12 (:REWRITE EQUAL-CONSTANT-+))
 (35 31 (:REWRITE DEFAULT-*-1))
 (31 31 (:REWRITE O+-ATOM-DEF))
 (30 2 (:REWRITE O-INFP-O+))
 (28 28 (:REWRITE POSP-RW))
 (28 2 (:REWRITE O-INFP-O+-2))
 (27 27 (:META CANCEL_PLUS-LESSP-CORRECT))
 (25 9 (:REWRITE O<=-O-FINP-DEF))
 (20 1 (:REWRITE |~(a=0)  =>  (a < b  <=>  a-1 < b-1)|))
 (15 15 (:REWRITE DEFAULT-<-2))
 (15 15 (:REWRITE DEFAULT-<-1))
 (15 15 (:DEFINITION FIX))
 (12 12 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP))
 (12 12 (:REWRITE EXPONENTS-ADD-FOR-NONNEG-EXPONENTS))
 (12 12 (:REWRITE EXPONENTS-ADD))
 (9 1 (:REWRITE O^-O-FIRST-EXPT-3))
 (9 1 (:REWRITE O*-O-RST))
 (8 2 (:REWRITE O-INFP-O+-3))
 (4 4 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (3 1 (:REWRITE O*-0))
 (2 2 (:TYPE-PRESCRIPTION LIMITP))
 (2 2 (:REWRITE POSP-O-FIRST-COEFF))
 )
(EXP-IND-1
 (15 15 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (5 1 (:REWRITE O<=-O-FINP-DEF))
 (4 4 (:META CANCEL_PLUS-LESSP-CORRECT))
 (4 1 (:REWRITE NATP-POSP))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE O-INFP-O-FINP-O<=))
 (2 1 (:REWRITE AC-<))
 (1 1 (:REWRITE |a < b & b < c  =>  a < c|))
 (1 1 (:REWRITE POSP-RW))
 (1 1 (:REWRITE NATP-RW))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(|a^(b+c)  =  a^b * a^c :b helper|
 (451 5 (:REWRITE O*-O-FIRST-EXPT-SMASH-1A))
 (269 26 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (175 24 (:REWRITE MAKE-ORD-EQUAL-4))
 (167 167 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (120 120 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (120 120 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (120 2 (:REWRITE O*-O-FIRST-EXPT-SMASH-1B))
 (115 22 (:REWRITE DEFAULT-*-2))
 (110 4 (:REWRITE O*-0))
 (86 2 (:REWRITE O*-O-FIRST-EXPT))
 (80 15 (:REWRITE ZIP-OPEN))
 (60 55 (:REWRITE DEFAULT-+-2))
 (60 55 (:REWRITE DEFAULT-+-1))
 (48 9 (:REWRITE NATP-RW))
 (43 31 (:REWRITE O-FINP-O-RST))
 (24 24 (:META CANCEL_PLUS-LESSP-CORRECT))
 (22 22 (:REWRITE DEFAULT-*-1))
 (20 10 (:REWRITE O*-O-FIRST-COEFF))
 (20 5 (:REWRITE <-0-+-NEGATIVE-1))
 (19 19 (:REWRITE DEFAULT-<-2))
 (19 19 (:REWRITE DEFAULT-<-1))
 (15 5 (:REWRITE FOLD-CONSTS-IN-+))
 (15 5 (:REWRITE EQUAL-CONSTANT-+))
 (12 3 (:REWRITE NATP-POSP))
 (8 2 (:LINEAR EXPT->-1))
 (5 5 (:REWRITE EXPONENTS-ADD-FOR-NONNEG-EXPONENTS))
 (5 5 (:REWRITE EXPONENTS-ADD))
 (4 4 (:LINEAR EXPT-IS-INCREASING-FOR-BASE>1))
 (4 2 (:REWRITE UNICITY-OF-0))
 (3 3 (:REWRITE POSP-RW))
 )
(O^-O-FIRST-EXPT-O-FIRST-EXPT-O<
 (194 40 (:REWRITE O-FIRST-EXPT-O-INFP))
 (135 65 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (108 5 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (68 14 (:REWRITE O-FIRST-EXPT-<))
 (64 2 (:REWRITE |a <= b & c <= d  =>  a+c <= b+d|))
 (60 16 (:REWRITE O-INFP->NEQ-0))
 (55 10 (:REWRITE O-FIRST-COEFF-<))
 (50 35 (:TYPE-PRESCRIPTION O^-O-FINP))
 (48 6 (:REWRITE O-INFP-O-FINP-O<=))
 (40 13 (:LINEAR O-FIRST-EXPT-<=))
 (32 14 (:REWRITE O-FINP-<))
 (32 14 (:REWRITE AC-<))
 (30 2 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (24 12 (:TYPE-PRESCRIPTION O+-O-FINP))
 (17 17 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (17 17 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (16 8 (:REWRITE O-P-DEF-O-FINP-1))
 (14 14 (:REWRITE |a < b & b < c  =>  a < c|))
 (14 6 (:REWRITE O<=-O-FINP-DEF))
 (12 12 (:TYPE-PRESCRIPTION OB+))
 (10 1 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (6 2 (:REWRITE O*-O-FINP))
 (5 5 (:REWRITE O+-ATOM-DEF))
 (4 4 (:TYPE-PRESCRIPTION NATP))
 (3 3 (:REWRITE O^-^))
 (2 2 (:REWRITE NATP-RW))
 )
(|a^(b+c)  =  a^b * a^c :a|
 (2117 100 (:REWRITE MAKE-ORD-EQUAL-4))
 (943 103 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (574 126 (:REWRITE O-INFP->NEQ-0))
 (565 493 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (514 112 (:REWRITE O*-O-FINP))
 (493 493 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (466 27 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (397 106 (:REWRITE O^-^))
 (286 18 (:REWRITE O--0))
 (277 30 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (210 2 (:REWRITE O+-INF))
 (194 32 (:REWRITE NATP-POSP))
 (188 127 (:REWRITE NATP-RW))
 (185 9 (:REWRITE O*-O-FIRST-EXPT))
 (172 54 (:REWRITE O-FIRST-EXPT-<))
 (166 5 (:REWRITE |(o-first-expt a) < a|))
 (153 51 (:REWRITE O-FIRST-COEFF-<))
 (148 74 (:REWRITE O*-O-FIRST-COEFF))
 (138 58 (:REWRITE |a < b & b < c  =>  a < c|))
 (137 118 (:REWRITE DEFAULT-+-2))
 (137 118 (:REWRITE DEFAULT-+-1))
 (136 54 (:REWRITE O-FINP-<))
 (136 54 (:REWRITE AC-<))
 (126 32 (:REWRITE POSP-RW))
 (99 3 (:DEFINITION EXPT))
 (85 1 (:REWRITE O-FIRST-EXPT-<-O+))
 (82 58 (:REWRITE O-FINP-O-RST))
 (62 38 (:REWRITE FOLD-CONSTS-IN-+))
 (58 28 (:REWRITE EQUAL-CONSTANT-+))
 (49 10 (:REWRITE DEFAULT-*-2))
 (48 12 (:REWRITE <-0-+-NEGATIVE-1))
 (46 4 (:REWRITE |o-first-expt(b) < o-first-expt(c)  =>  (a^b)*(a^c) = a^c|))
 (32 32 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (32 1 (:REWRITE |a <= b & c < d  =>  a+c < b+d|))
 (31 5 (:REWRITE O-INFP-O-FINP-O<=))
 (30 30 (:META CANCEL_PLUS-LESSP-CORRECT))
 (26 2 (:REWRITE |~(a=0)  =>  (a < b  <=>  a-1 < b-1)|))
 (24 3 (:REWRITE ZIP-OPEN))
 (24 2 (:REWRITE O*-O-FIRST-EXPT-SMASH-2B))
 (24 1 (:REWRITE O*-0))
 (22 1 (:REWRITE LIMITP-DEF))
 (18 18 (:REWRITE DEFAULT-<-2))
 (18 18 (:REWRITE DEFAULT-<-1))
 (18 9 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (18 2 (:REWRITE O^-O-FIRST-EXPT-3))
 (17 1 (:REWRITE O+-O-FIRST-EXPT-1))
 (15 11 (:REWRITE O-FIRST-EXPT-O-P))
 (14 10 (:REWRITE DEFAULT-*-1))
 (11 1 (:REWRITE |a+0 = a|))
 (10 4 (:TYPE-PRESCRIPTION |0 < a  =>  0^a = 0 :b|))
 (10 1 (:REWRITE |a < b  <=>  c+a < c+b|))
 (9 9 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE))
 (9 9 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONZERO))
 (9 1 (:REWRITE O-INFP-O+-2))
 (4 4 (:REWRITE |~(a<0)|))
 (4 1 (:REWRITE O-INFP-O^-1))
 (4 1 (:REWRITE O-INFP-O+))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP))
 (3 3 (:REWRITE |~(a < a)|))
 (3 3 (:REWRITE EXPONENTS-ADD-FOR-NONNEG-EXPONENTS))
 (3 3 (:REWRITE EXPONENTS-ADD))
 (3 1 (:REWRITE O<=-O-FINP-DEF))
 (2 2 (:TYPE-PRESCRIPTION LIMITP))
 )
(|a^(b+c)  =  a^b * a^c :b|
 (865 4 (:DEFINITION OB^))
 (339 4 (:REWRITE O*-O-INFP-DEF))
 (262 131 (:TYPE-PRESCRIPTION O+-O-FINP))
 (242 24 (:REWRITE MAKE-ORD-EQUAL-4))
 (170 85 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (160 39 (:REWRITE O-FIRST-EXPT-O-INFP))
 (139 20 (:DEFINITION OMEGA-TERM))
 (80 17 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (78 18 (:REWRITE O-INFP->NEQ-0))
 (74 17 (:REWRITE O-FIRST-EXPT-<))
 (69 69 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (69 69 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (64 4 (:REWRITE O--0))
 (57 17 (:REWRITE O-FIRST-COEFF-<))
 (47 17 (:REWRITE O^-^))
 (44 4 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (43 17 (:REWRITE O-FINP-<))
 (43 17 (:REWRITE AC-<))
 (40 38 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (39 17 (:REWRITE O*-O-FINP))
 (36 36 (:TYPE-PRESCRIPTION MAKE-ORD))
 (36 13 (:LINEAR O-FIRST-EXPT-<=))
 (28 17 (:REWRITE |a < b & b < c  =>  a < c|))
 (28 13 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (16 16 (:REWRITE O-FINP-O-RST))
 (16 16 (:REWRITE NATP-RW))
 (15 5 (:REWRITE O-FIRST-EXPT-0-NATP))
 (12 2 (:REWRITE O-INFP-O-FINP-O<=))
 (9 3 (:REWRITE O-P-DEF-O-FINP-1))
 (6 2 (:REWRITE O<=-O-FINP-DEF))
 (5 5 (:REWRITE O+-ATOM-DEF))
 (4 4 (:REWRITE |a0 = 0|))
 (4 1 (:REWRITE NATP-POSP))
 (1 1 (:REWRITE POSP-RW))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(EXP-IND-2
 (67 2 (:DEFINITION ACL2-COUNT))
 (35 6 (:REWRITE O-FIRST-EXPT-O-INFP))
 (24 2 (:REWRITE O-FIRST-EXPT-<))
 (21 10 (:REWRITE DEFAULT-+-2))
 (19 8 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (14 14 (:TYPE-PRESCRIPTION ACL2-COUNT))
 (14 10 (:REWRITE DEFAULT-+-1))
 (12 2 (:REWRITE O-FIRST-COEFF-<))
 (10 2 (:DEFINITION INTEGER-ABS))
 (8 2 (:REWRITE COMMUTATIVITY-OF-+))
 (8 1 (:DEFINITION LENGTH))
 (6 2 (:REWRITE O-P-DEF-O-FINP-1))
 (6 2 (:REWRITE O-FINP-<))
 (6 2 (:REWRITE AC-<))
 (6 1 (:REWRITE O-INFP-O-FINP-O<=))
 (6 1 (:REWRITE O-FIRST-EXPT-0-NATP))
 (6 1 (:LINEAR O-FIRST-EXPT-<=))
 (5 1 (:DEFINITION LEN))
 (4 1 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (4 1 (:REWRITE O-INFP->NEQ-0))
 (3 3 (:REWRITE FOLD-CONSTS-IN-+))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 1 (:REWRITE O<=-O-FINP-DEF))
 (2 2 (:REWRITE |a < b & b < c  =>  a < c|))
 (2 2 (:REWRITE DEFAULT-UNARY-MINUS))
 (2 2 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:META CANCEL_PLUS-LESSP-CORRECT))
 (1 1 (:TYPE-PRESCRIPTION LEN))
 (1 1 (:REWRITE O-FINP-O-RST))
 (1 1 (:REWRITE NUMERATOR-WHEN-INTEGERP))
 (1 1 (:REWRITE INTEGERP==>DENOMINATOR=1))
 (1 1 (:REWRITE DEFAULT-REALPART))
 (1 1 (:REWRITE DEFAULT-NUMERATOR))
 (1 1 (:REWRITE DEFAULT-IMAGPART))
 (1 1 (:REWRITE DEFAULT-DENOMINATOR))
 (1 1 (:REWRITE DEFAULT-COERCE-2))
 (1 1 (:REWRITE DEFAULT-COERCE-1))
 (1 1 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (1 1 (:META CANCEL_PLUS-EQUAL-CORRECT))
 )
(|a^(b+c)  =  a^b * a^c|
 (3089 594 (:REWRITE O-FIRST-EXPT-O-INFP))
 (2450 196 (:REWRITE MAKE-ORD-EQUAL-4))
 (1795 174 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (1203 52 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (976 221 (:REWRITE O-INFP->NEQ-0))
 (905 292 (:REWRITE O-FIRST-COEFF-<))
 (866 293 (:REWRITE |a < b & b < c  =>  a < c|))
 (826 292 (:REWRITE O-FIRST-EXPT-<))
 (800 27 (:REWRITE O+-O-RST-2))
 (724 724 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (724 724 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (691 292 (:REWRITE AC-<))
 (646 292 (:REWRITE O-FINP-<))
 (556 28 (:REWRITE O-INFP-O+-2))
 (527 35 (:REWRITE O--0))
 (372 195 (:REWRITE NATP-RW))
 (365 34 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (300 50 (:REWRITE O-INFP-O-FINP-O<=))
 (255 35 (:REWRITE O+-O-FIRST-EXPT-1))
 (245 5 (:REWRITE O*-0))
 (240 22 (:REWRITE O+-O-FIRST-COEFF-1))
 (222 39 (:REWRITE NATP-POSP))
 (218 28 (:REWRITE O-INFP-O+-3))
 (196 196 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (192 41 (:REWRITE DEFAULT-*-2))
 (177 15 (:REWRITE ZIP-OPEN))
 (147 49 (:REWRITE O<=-O-FINP-DEF))
 (133 133 (:REWRITE O-FINP-O-RST))
 (114 26 (:REWRITE O+-O-FIRST-COEFF-3))
 (109 9 (:REWRITE EQUAL-CONSTANT-+))
 (98 89 (:REWRITE DEFAULT-+-2))
 (98 89 (:REWRITE DEFAULT-+-1))
 (79 9 (:REWRITE |o-first-expt(b) < o-first-expt(c)  =>  (a^b)*(a^c) = a^c|))
 (78 39 (:REWRITE POSP-RW))
 (72 36 (:REWRITE O*-O-FIRST-COEFF))
 (67 41 (:REWRITE DEFAULT-*-1))
 (51 9 (:REWRITE |(a = 0) & ~(b = 0)  <=>  (a^b = 0)|))
 (32 8 (:REWRITE <-0-+-NEGATIVE-1))
 (31 13 (:REWRITE O-FIRST-EXPT-O-P))
 (27 27 (:META CANCEL_PLUS-LESSP-CORRECT))
 (26 10 (:REWRITE FOLD-CONSTS-IN-+))
 (19 19 (:REWRITE DEFAULT-<-2))
 (19 19 (:REWRITE DEFAULT-<-1))
 (10 10 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (8 8 (:REWRITE EXPONENTS-ADD-FOR-NONNEG-EXPONENTS))
 (7 1 (:REWRITE O-INFP-O^-1))
 )
(|(a^b = 1)  <=>  (a = 1) V (b = 0)|
 (252 3 (:REWRITE O*-O-INFP-DEF))
 (195 46 (:REWRITE O-FIRST-EXPT-O-INFP))
 (168 18 (:REWRITE MAKE-ORD-EQUAL-4))
 (121 25 (:REWRITE O-INFP->NEQ-0))
 (93 15 (:DEFINITION OMEGA-TERM))
 (91 91 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (73 16 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (72 3 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (67 67 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (67 67 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (59 17 (:REWRITE O^-^))
 (39 16 (:REWRITE O*-O-FINP))
 (39 3 (:REWRITE O--0))
 (34 13 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (33 3 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (28 28 (:REWRITE NATP-RW))
 (28 7 (:REWRITE NATP-POSP))
 (27 27 (:TYPE-PRESCRIPTION MAKE-ORD))
 (24 12 (:TYPE-PRESCRIPTION O+-O-FINP))
 (24 9 (:REWRITE O-FIRST-COEFF-<))
 (21 9 (:REWRITE O-FINP-<))
 (21 9 (:REWRITE AC-<))
 (21 7 (:REWRITE O-FIRST-EXPT-0-NATP))
 (18 9 (:REWRITE O-FIRST-EXPT-<))
 (12 12 (:TYPE-PRESCRIPTION OB+))
 (12 12 (:REWRITE O-FINP-O-RST))
 (9 9 (:REWRITE |a < b & b < c  =>  a < c|))
 (7 7 (:REWRITE POSP-RW))
 (5 5 (:REWRITE DEFAULT-+-2))
 (5 5 (:REWRITE DEFAULT-+-1))
 (3 3 (:REWRITE |a0 = 0|))
 (3 3 (:REWRITE O+-ATOM-DEF))
 )
(O-+
 (1125 240 (:REWRITE O-FIRST-EXPT-O-INFP))
 (851 106 (:REWRITE O-FIRST-EXPT-<))
 (520 260 (:TYPE-PRESCRIPTION O*-FINITE))
 (484 94 (:REWRITE O-FIRST-COEFF-<))
 (424 23 (:REWRITE MAKE-ORD-EQUAL-4))
 (277 106 (:REWRITE O-FINP-<))
 (277 106 (:REWRITE AC-<))
 (228 38 (:REWRITE O-INFP-O-FINP-O<=))
 (218 42 (:REWRITE O-FIRST-EXPT-0-NATP))
 (167 49 (:REWRITE O-INFP->NEQ-0))
 (140 12 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (120 108 (:REWRITE |a < b & b < c  =>  a < c|))
 (113 113 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (108 36 (:REWRITE O<=-O-FINP-DEF))
 (103 73 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (79 50 (:REWRITE DEFAULT-+-2))
 (78 4 (:REWRITE O-INFP-O+-2))
 (73 3 (:REWRITE O+-O-FIRST-EXPT-2))
 (68 50 (:REWRITE DEFAULT-+-1))
 (55 33 (:REWRITE O-FINP-O-RST))
 (44 2 (:REWRITE O--0))
 (36 4 (:REWRITE O-INFP-O+-3))
 (33 3 (:REWRITE O+-O-FIRST-EXPT-1))
 (20 1 (:REWRITE O+-O-FIRST-COEFF-2))
 (20 1 (:REWRITE O+-O-FIRST-COEFF-1))
 (14 14 (:REWRITE DEFAULT-<-1))
 (12 12 (:REWRITE |~(a < a)|))
 (9 1 (:REWRITE O+-O-FIRST-COEFF-3))
 (3 3 (:REWRITE NATP-RW))
 )
(|a^(bc) = (a^b)^c :a lemma 1a|
 (5297 329 (:REWRITE O-FIRST-EXPT-<))
 (5256 686 (:REWRITE O-FIRST-EXPT-O-INFP))
 (3157 39 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (2900 234 (:REWRITE O-FIRST-EXPT-0-NATP))
 (2747 1342 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (2144 24 (:REWRITE O-FIRST-EXPT-<-O+))
 (1850 326 (:REWRITE O-FIRST-COEFF-<))
 (1598 799 (:TYPE-PRESCRIPTION O+-O-FINP))
 (1562 329 (:REWRITE AC-<))
 (1465 55 (:REWRITE O-INFP-O+))
 (1428 55 (:REWRITE O-INFP-O+-2))
 (1203 46 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (1140 38 (:REWRITE O-FIRST-EXPT-O--<))
 (1038 267 (:REWRITE O-INFP->NEQ-0))
 (1035 73 (:REWRITE O+-O-FIRST-EXPT-2))
 (799 799 (:TYPE-PRESCRIPTION OB+))
 (748 73 (:REWRITE O+-O-FIRST-EXPT-1))
 (691 329 (:REWRITE O-FINP-<))
 (603 603 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (603 603 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (522 17 (:REWRITE |(o-first-expt a) < a|))
 (519 55 (:REWRITE O-INFP-O+-3))
 (398 329 (:REWRITE |a < b & b < c  =>  a < c|))
 (397 41 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (293 293 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (198 60 (:REWRITE O-INFP-O-FINP-O<=))
 (192 60 (:REWRITE O<=-O-FINP-DEF))
 (112 16 (:REWRITE O--0))
 (92 41 (:REWRITE O*-O-FINP))
 (73 28 (:REWRITE O^-^))
 (52 43 (:REWRITE NATP-RW))
 (46 46 (:REWRITE O+-ATOM-DEF))
 (30 30 (:REWRITE O-FINP-O-RST))
 (13 7 (:REWRITE O^-O-FIRST-EXPT-3))
 (12 3 (:REWRITE NATP-POSP))
 (9 3 (:REWRITE O*-O-FIRST-EXPT-SMASH-1A))
 (7 3 (:REWRITE O*-O-FIRST-EXPT-SMASH-2A))
 (4 2 (:REWRITE DEFAULT-CDR))
 (4 2 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE |~(a < a)|))
 (3 3 (:REWRITE POSP-RW))
 (2 2 (:REWRITE POSP-O-FIRST-COEFF))
 (2 2 (:REWRITE O-INFP-O^-1))
 (2 2 (:REWRITE O-FIRST-COEFF-0))
 (1 1 (:REWRITE |0+a = a|))
 )
(|a^(bc) = (a^b)^c :a lemma 1|
 (1558 45 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (1014 39 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (629 629 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (629 629 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (607 15 (:REWRITE |(o-first-expt a) < a|))
 (585 70 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (434 88 (:REWRITE O-FIRST-COEFF-<))
 (419 405 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (348 4 (:REWRITE O-FIRST-EXPT-<-O+))
 (343 88 (:REWRITE O-FIRST-EXPT-<))
 (292 146 (:TYPE-PRESCRIPTION O+-O-FINP))
 (192 88 (:REWRITE O-FINP-<))
 (192 88 (:REWRITE AC-<))
 (178 61 (:REWRITE O^-^))
 (130 10 (:REWRITE O--0))
 (127 101 (:REWRITE NATP-RW))
 (90 90 (:REWRITE |a < b & b < c  =>  a < c|))
 (80 4 (:REWRITE O+-O-FIRST-EXPT-2))
 (64 6 (:REWRITE LIMITP-DEF))
 (49 43 (:REWRITE O-FINP-O-RST))
 (48 6 (:REWRITE O-INFP-O-FINP-O<=))
 (45 45 (:REWRITE O+-ATOM-DEF))
 (44 4 (:REWRITE O+-O-FIRST-EXPT-1))
 (36 36 (:TYPE-PRESCRIPTION NATPART-NATP))
 (24 6 (:REWRITE O^-O-FIRST-EXPT-3))
 (24 6 (:REWRITE O^-O-FIRST-EXPT-2))
 (14 9 (:REWRITE POSP-RW))
 (14 6 (:REWRITE DEFAULT-CDR))
 (14 6 (:REWRITE DEFAULT-CAR))
 (12 12 (:TYPE-PRESCRIPTION LIMITP))
 (12 12 (:REWRITE DEFAULT-+-2))
 (12 12 (:REWRITE DEFAULT-+-1))
 (12 4 (:REWRITE O<=-O-FINP-DEF))
 (8 8 (:REWRITE DEFAULT-*-2))
 (8 8 (:REWRITE DEFAULT-*-1))
 (8 6 (:REWRITE NATPART-DEF-O-FINP))
 (6 6 (:REWRITE POSP-O-FIRST-COEFF))
 (3 3 (:REWRITE O-INFP-O*))
 (3 1 (:REWRITE O*-O-FIRST-EXPT-SMASH-2A))
 (2 1 (:REWRITE O*-O-FIRST-EXPT-SMASH-1A))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:META CANCEL_PLUS-LESSP-CORRECT))
 )
(|a^(bc) = (a^b)^c :a lemma 2|
 (6598 11 (:DEFINITION OB^))
 (2169 426 (:REWRITE O-FIRST-EXPT-O-INFP))
 (1339 468 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (1106 20 (:REWRITE O*-O-INFP-DEF))
 (1036 324 (:REWRITE O-INFP->NEQ-0))
 (956 24 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (775 40 (:REWRITE O*-O-RST))
 (661 76 (:LINEAR O-FIRST-EXPT-<=))
 (617 617 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (617 617 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (516 80 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (498 90 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (496 68 (:REWRITE O-FIRST-EXPT-0-NATP))
 (462 12 (:REWRITE |(o-first-expt a) < a|))
 (390 239 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (301 130 (:REWRITE O-P-DEF-O-FINP-1))
 (285 21 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (238 80 (:REWRITE O*-O-FINP))
 (225 6 (:REWRITE O+-O-FIRST-EXPT-2))
 (200 65 (:REWRITE O-FIRST-COEFF-<))
 (166 55 (:REWRITE O^-^))
 (143 11 (:REWRITE O--0))
 (137 65 (:REWRITE O-FINP-<))
 (137 65 (:REWRITE AC-<))
 (130 65 (:REWRITE O-FIRST-EXPT-<))
 (130 11 (:REWRITE NATP-POSP))
 (126 3 (:REWRITE |(a = 0) & ~(b = 0)  <=>  (a^b = 0)|))
 (124 3 (:REWRITE O-INFP-O+-2))
 (119 76 (:REWRITE NATP-RW))
 (113 3 (:REWRITE |o-first-expt(b) < o-first-expt(c)  =>  (a^b)*(a^c) = a^c|))
 (96 5 (:REWRITE O+-O-FIRST-COEFF-2))
 (94 40 (:REWRITE O-INFP-O*))
 (94 8 (:REWRITE O-P-O+))
 (90 3 (:REWRITE O-INFP-O+-3))
 (84 24 (:REWRITE O+-ATOM-DEF))
 (77 3 (:REWRITE O-INFP-O+))
 (73 40 (:REWRITE O-INFP-O*-2))
 (70 4 (:REWRITE O+-O-RST-2))
 (66 5 (:REWRITE O+-O-FIRST-COEFF-1))
 (65 65 (:REWRITE |a < b & b < c  =>  a < c|))
 (62 32 (:REWRITE O*-O-FIRST-EXPT-<))
 (61 61 (:REWRITE O-FINP-O-RST))
 (60 5 (:REWRITE O+-O-FIRST-COEFF-3))
 (60 3 (:REWRITE O*-0))
 (58 6 (:REWRITE O+-O-FIRST-EXPT-1))
 (54 11 (:REWRITE POSP-RW))
 (43 4 (:REWRITE O+-O-RST-1))
 (42 10 (:REWRITE |a^(bc) = (a^b)^c :a lemma 1|))
 (42 7 (:REWRITE O-INFP-O-FINP-O<=))
 (30 10 (:REWRITE |a^(bc) = (a^b)^c :a lemma 1a|))
 (21 7 (:REWRITE O<=-O-FINP-DEF))
 (11 11 (:REWRITE |a0 = 0|))
 (11 11 (:REWRITE DEFAULT-+-2))
 (11 11 (:REWRITE DEFAULT-+-1))
 )
(|a^(bc) = (a^b)^c :a lemma 3|
 (5378 125 (:REWRITE MAKE-ORD-EQUAL-4))
 (2124 396 (:REWRITE O-FIRST-EXPT-O-INFP))
 (1588 740 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (1541 47 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (1509 44 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (1205 25 (:REWRITE O*-O-FIRST-EXPT))
 (779 21 (:REWRITE |(o-first-expt a) < a|))
 (746 746 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (746 746 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (695 148 (:REWRITE O-INFP->NEQ-0))
 (688 8 (:REWRITE O-FIRST-EXPT-<-O+))
 (645 139 (:REWRITE O-FIRST-EXPT-<))
 (641 139 (:REWRITE O-FIRST-COEFF-<))
 (593 553 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (544 272 (:REWRITE O*-O-FIRST-COEFF))
 (543 96 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (488 96 (:REWRITE O^-^))
 (454 227 (:TYPE-PRESCRIPTION O+-O-FINP))
 (349 24 (:REWRITE O--0))
 (328 139 (:REWRITE O-FINP-<))
 (296 100 (:REWRITE O*-O-FINP))
 (227 227 (:TYPE-PRESCRIPTION OB+))
 (207 150 (:REWRITE NATP-RW))
 (199 30 (:REWRITE O^-O-FIRST-EXPT))
 (185 140 (:REWRITE |a < b & b < c  =>  a < c|))
 (161 11 (:REWRITE O+-O-FIRST-EXPT-2))
 (126 11 (:REWRITE O+-O-FIRST-EXPT-1))
 (83 80 (:REWRITE O-FINP-O-RST))
 (76 19 (:REWRITE NATP-POSP))
 (68 2 (:DEFINITION EXPT))
 (48 13 (:REWRITE O^-O-FIRST-EXPT-3))
 (46 18 (:REWRITE O-INFP-O^-1))
 (46 13 (:REWRITE O^-O-FIRST-EXPT-2))
 (44 44 (:REWRITE O+-ATOM-DEF))
 (30 6 (:REWRITE DEFAULT-*-2))
 (30 2 (:REWRITE O-INFP-O+))
 (28 2 (:REWRITE O-INFP-O+-2))
 (27 25 (:REWRITE DEFAULT-+-2))
 (27 25 (:REWRITE DEFAULT-+-1))
 (26 5 (:REWRITE O-INFP-O-FINP-O<=))
 (22 22 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (19 19 (:REWRITE POSP-RW))
 (16 2 (:REWRITE ZIP-OPEN))
 (14 2 (:REWRITE COMMUTATIVITY-OF-+))
 (13 5 (:REWRITE O<=-O-FINP-DEF))
 (12 6 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (8 2 (:REWRITE O-INFP-O+-3))
 (8 2 (:REWRITE <-0-+-NEGATIVE-1))
 (6 6 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE))
 (6 6 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONZERO))
 (6 6 (:REWRITE DEFAULT-*-1))
 (6 2 (:REWRITE FOLD-CONSTS-IN-+))
 (6 2 (:REWRITE EQUAL-CONSTANT-+))
 (4 4 (:META CANCEL_PLUS-LESSP-CORRECT))
 (2 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP))
 (2 2 (:REWRITE EXPONENTS-ADD-FOR-NONNEG-EXPONENTS))
 (2 2 (:REWRITE EXPONENTS-ADD))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:DEFINITION FIX))
 )
(|a^(bc) = (a^b)^c :a|
 (4870 157 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (3808 128 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (3653 3653 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (3653 3653 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (2448 60 (:REWRITE |(o-first-expt a) < a|))
 (2036 409 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (1778 15 (:REWRITE O-FIRST-EXPT-<-O+))
 (1549 376 (:REWRITE O-FIRST-EXPT-<))
 (1364 674 (:TYPE-PRESCRIPTION O+-O-FINP))
 (1326 82 (:REWRITE O--0))
 (1317 376 (:REWRITE O-FIRST-COEFF-<))
 (1024 376 (:REWRITE O-FINP-<))
 (839 577 (:REWRITE NATP-RW))
 (534 82 (:REWRITE NATP-POSP))
 (509 24 (:REWRITE O+-O-FIRST-EXPT-2))
 (442 385 (:REWRITE |a < b & b < c  =>  a < c|))
 (376 319 (:REWRITE O-FINP-O-RST))
 (321 11 (:REWRITE O-+))
 (289 64 (:REWRITE O^-O-FIRST-EXPT))
 (286 92 (:REWRITE O-INFP-O*))
 (224 18 (:REWRITE O+-O-FIRST-EXPT-1))
 (216 58 (:REWRITE O^-O-FIRST-EXPT-3))
 (188 67 (:REWRITE DEFAULT-*-2))
 (185 82 (:REWRITE POSP-RW))
 (170 43 (:REWRITE |a^(bc) = (a^b)^c :a lemma 1a|))
 (157 157 (:REWRITE O+-ATOM-DEF))
 (142 13 (:REWRITE O-INFP-O-FINP-O<=))
 (130 2 (:REWRITE |o-first-expt(b) < o-first-expt(c)  =>  (a^b)*(a^c) = a^c|))
 (127 58 (:REWRITE O^-O-FIRST-EXPT-2))
 (124 67 (:REWRITE DEFAULT-*-1))
 (95 95 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (92 8 (:REWRITE O*-0))
 (85 80 (:REWRITE DEFAULT-+-1))
 (83 80 (:REWRITE DEFAULT-+-2))
 (70 2 (:REWRITE |(ab)c = a(bc)|))
 (66 6 (:REWRITE |~(a<0)|))
 (53 53 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (34 3 (:REWRITE ZIP-OPEN))
 (30 2 (:REWRITE O-INFP-O+))
 (28 2 (:REWRITE O-INFP-O+-2))
 (27 5 (:REWRITE COMMUTATIVITY-OF-+))
 (24 4 (:REWRITE MAKE-ORD-EQUAL-2))
 (20 11 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP))
 (19 7 (:REWRITE O<=-O-FINP-DEF))
 (19 3 (:REWRITE EQUAL-CONSTANT-+))
 (18 3 (:REWRITE LIMITP-DEF))
 (16 8 (:REWRITE DEFAULT-CDR))
 (16 8 (:REWRITE DEFAULT-CAR))
 (15 9 (:REWRITE O-INFP-O^-1))
 (14 14 (:REWRITE |0+a = a|))
 (12 3 (:REWRITE <-0-+-NEGATIVE-1))
 (11 11 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE))
 (11 11 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONZERO))
 (10 2 (:REWRITE |(a = 1) & (b = 1)  <=>  ab = 1|))
 (9 3 (:REWRITE FOLD-CONSTS-IN-+))
 (8 2 (:REWRITE O-INFP-O+-3))
 (8 2 (:REWRITE O*-O-FIRST-EXPT-<))
 (6 6 (:TYPE-PRESCRIPTION LIMITP))
 (6 6 (:META CANCEL_PLUS-LESSP-CORRECT))
 (5 5 (:DEFINITION FIX))
 (4 4 (:REWRITE /R-WHEN-ABS-NUMERATOR=1))
 (4 2 (:REWRITE MINUS-CANCELLATION-ON-LEFT))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP))
 (3 3 (:REWRITE EXPONENTS-ADD-FOR-NONNEG-EXPONENTS))
 (3 3 (:REWRITE EXPONENTS-ADD))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-UNARY-/))
 (2 2 (:REWRITE |1a = a|))
 )
(|a^(bc) = (a^b)^c :b|
 (1497 96 (:REWRITE MAKE-ORD-EQUAL-4))
 (1282 16 (:REWRITE O*-O-INFP-DEF))
 (1267 5 (:REWRITE |a^(bc) = (a^b)^c :a|))
 (1261 249 (:REWRITE O-FIRST-EXPT-O-INFP))
 (1155 80 (:DEFINITION OMEGA-TERM))
 (494 34 (:REWRITE O*-O-FIRST-COEFF))
 (482 28 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (451 90 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (447 109 (:REWRITE O-INFP->NEQ-0))
 (406 406 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (359 32 (:REWRITE O*-O-FIRST-EXPT))
 (348 20 (:REWRITE O*-O-RST))
 (322 78 (:LINEAR O-FIRST-EXPT-<=))
 (310 85 (:REWRITE O^-^))
 (292 292 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (292 292 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (248 78 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (235 90 (:REWRITE O*-O-FINP))
 (208 16 (:REWRITE O--0))
 (185 46 (:REWRITE O-FIRST-EXPT-0-NATP))
 (173 8 (:REWRITE DISTRIBUTIVITY))
 (159 112 (:REWRITE NATP-RW))
 (144 144 (:TYPE-PRESCRIPTION MAKE-ORD))
 (140 50 (:REWRITE O-FIRST-COEFF-<))
 (135 32 (:REWRITE COMMUTATIVITY-OF-*))
 (130 50 (:REWRITE O-FINP-<))
 (130 50 (:REWRITE AC-<))
 (110 10 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (108 17 (:REWRITE NATP-POSP))
 (100 50 (:REWRITE O-FIRST-EXPT-<))
 (97 2 (:REWRITE |o-first-expt(b) < o-first-expt(c)  =>  (a^b)*(a^c) = a^c|))
 (95 72 (:REWRITE DEFAULT-*-2))
 (87 72 (:REWRITE DEFAULT-*-1))
 (85 8 (:REWRITE FUNCTIONAL-COMMUTATIVITY-OF-MINUS-*-RIGHT))
 (68 64 (:REWRITE O-FINP-O-RST))
 (64 11 (:REWRITE O-INFP-O*))
 (60 12 (:REWRITE |a+0 = a|))
 (50 50 (:REWRITE |a < b & b < c  =>  a < c|))
 (48 12 (:LINEAR X*Y>1-POSITIVE))
 (47 19 (:REWRITE EQUAL-CONSTANT-+))
 (42 17 (:REWRITE POSP-RW))
 (41 41 (:REWRITE DEFAULT-+-2))
 (41 41 (:REWRITE DEFAULT-+-1))
 (38 38 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (28 28 (:REWRITE O+-ATOM-DEF))
 (24 8 (:REWRITE UNICITY-OF-1))
 (24 8 (:REWRITE COMMUTATIVITY-OF-+))
 (20 20 (:TYPE-PRESCRIPTION |x < y  =>  0 < y-x|))
 (20 11 (:REWRITE O-INFP-O*-2))
 (16 16 (:REWRITE |a0 = 0|))
 (16 8 (:DEFINITION FIX))
 (14 14 (:REWRITE O-FIRST-EXPT-O-P))
 (14 14 (:META CANCEL_PLUS-LESSP-CORRECT))
 (13 13 (:REWRITE DEFAULT-<-2))
 (13 13 (:REWRITE DEFAULT-<-1))
 (12 2 (:REWRITE O^-O-FIRST-EXPT))
 (8 8 (:REWRITE DEFAULT-UNARY-MINUS))
 (4 1 (:REWRITE <-0-+-NEGATIVE-1))
 (3 1 (:REWRITE FOLD-CONSTS-IN-+))
 (1 1 (:REWRITE ZP-OPEN))
 )
(EXP-IND-3
 (444 2 (:DEFINITION OB^))
 (155 24 (:REWRITE O-FIRST-EXPT-O-INFP))
 (114 57 (:TYPE-PRESCRIPTION O^-O-FINP))
 (92 10 (:DEFINITION OMEGA-TERM))
 (87 15 (:REWRITE O-INFP->NEQ-0))
 (82 10 (:REWRITE MAKE-ORD-EQUAL-4))
 (68 44 (:REWRITE O-P-DEF-O-FINP-1))
 (67 2 (:DEFINITION ACL2-COUNT))
 (46 10 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (46 9 (:LINEAR O-FIRST-EXPT-<=))
 (42 18 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (42 2 (:REWRITE O*-O-INFP-DEF))
 (40 9 (:REWRITE O-FIRST-EXPT-0-NATP))
 (34 10 (:REWRITE O^-^))
 (30 9 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (26 2 (:REWRITE O--0))
 (24 10 (:REWRITE O*-O-FINP))
 (23 12 (:REWRITE DEFAULT-+-2))
 (22 22 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (22 22 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (18 18 (:TYPE-PRESCRIPTION MAKE-ORD))
 (16 12 (:REWRITE DEFAULT-+-1))
 (14 14 (:TYPE-PRESCRIPTION ACL2-COUNT))
 (12 12 (:REWRITE NATP-RW))
 (10 2 (:DEFINITION INTEGER-ABS))
 (8 4 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (8 2 (:REWRITE NATP-POSP))
 (8 2 (:REWRITE COMMUTATIVITY-OF-+))
 (8 1 (:DEFINITION LENGTH))
 (7 7 (:REWRITE O-FINP-O-RST))
 (7 1 (:REWRITE O-INFP-O^-1))
 (6 2 (:REWRITE O-FINP-<))
 (6 2 (:REWRITE AC-<))
 (6 1 (:REWRITE |(a^b = 1)  <=>  (a = 1) V (b = 0)|))
 (6 1 (:REWRITE |(a = 0) & ~(b = 0)  <=>  (a^b = 0)|))
 (5 1 (:DEFINITION LEN))
 (4 2 (:REWRITE O-FIRST-EXPT-<))
 (4 1 (:REWRITE O^-O-FIRST-EXPT))
 (3 3 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (3 3 (:REWRITE FOLD-CONSTS-IN-+))
 (3 3 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE |a < b & b < c  =>  a < c|))
 (2 2 (:REWRITE POSP-RW))
 (2 2 (:REWRITE O-FIRST-COEFF-<))
 (2 2 (:REWRITE DEFAULT-UNARY-MINUS))
 (2 2 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:META CANCEL_PLUS-LESSP-CORRECT))
 (1 1 (:TYPE-PRESCRIPTION LEN))
 (1 1 (:REWRITE NUMERATOR-WHEN-INTEGERP))
 (1 1 (:REWRITE INTEGERP==>DENOMINATOR=1))
 (1 1 (:REWRITE DEFAULT-REALPART))
 (1 1 (:REWRITE DEFAULT-NUMERATOR))
 (1 1 (:REWRITE DEFAULT-IMAGPART))
 (1 1 (:REWRITE DEFAULT-DENOMINATOR))
 (1 1 (:REWRITE DEFAULT-COERCE-2))
 (1 1 (:REWRITE DEFAULT-COERCE-1))
 )
(|a^(bc) = (a^b)^c helper1|
 (550 275 (:TYPE-PRESCRIPTION O*-FINITE))
 (243 1 (:DEFINITION OB^))
 (84 1 (:REWRITE O*-O-INFP-DEF))
 (58 14 (:REWRITE O-FIRST-EXPT-O-INFP))
 (56 6 (:REWRITE MAKE-ORD-EQUAL-4))
 (54 12 (:REWRITE O^-^))
 (44 22 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (39 8 (:REWRITE O-INFP->NEQ-0))
 (33 7 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (31 5 (:DEFINITION OMEGA-TERM))
 (24 1 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (20 11 (:REWRITE NATP-RW))
 (19 19 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (19 19 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (18 7 (:REWRITE O*-O-FINP))
 (14 1 (:REWRITE |a^(bc) = (a^b)^c :b|))
 (13 1 (:REWRITE O--0))
 (12 4 (:REWRITE O-P-DEF-O-FINP-1))
 (11 1 (:REWRITE |a^(bc) = (a^b)^c :a|))
 (11 1 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (10 8 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (10 4 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (9 9 (:TYPE-PRESCRIPTION MAKE-ORD))
 (8 4 (:TYPE-PRESCRIPTION O+-O-FINP))
 (8 3 (:REWRITE O-FIRST-COEFF-<))
 (7 3 (:REWRITE O-FINP-<))
 (7 3 (:REWRITE AC-<))
 (6 3 (:REWRITE O-FIRST-EXPT-<))
 (6 2 (:REWRITE O-FIRST-EXPT-0-NATP))
 (4 4 (:TYPE-PRESCRIPTION OB+))
 (4 4 (:REWRITE O-FINP-O-RST))
 (4 1 (:REWRITE NATP-POSP))
 (3 3 (:REWRITE |a < b & b < c  =>  a < c|))
 (1 1 (:REWRITE |a0 = 0|))
 (1 1 (:REWRITE POSP-RW))
 (1 1 (:REWRITE O+-ATOM-DEF))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(POSP-O-INFP-0)
(O*-POSP-O-INFP-0
 (186 93 (:TYPE-PRESCRIPTION O*-FINITE))
 )
(|a^(bc) = (a^b)^c|
 (7199 448 (:REWRITE MAKE-ORD-EQUAL-4))
 (5154 1152 (:REWRITE O-FIRST-EXPT-O-INFP))
 (2392 85 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (1923 391 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (1754 450 (:REWRITE O-INFP->NEQ-0))
 (1484 1484 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (1484 1484 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (1283 380 (:REWRITE O^-^))
 (1162 40 (:REWRITE O*-O-RST))
 (1013 43 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (1007 77 (:REWRITE O*-O-FIRST-EXPT))
 (998 391 (:REWRITE O*-O-FINP))
 (987 75 (:REWRITE O--0))
 (840 202 (:REWRITE O-FIRST-EXPT-0-NATP))
 (737 208 (:REWRITE O-FIRST-COEFF-<))
 (675 675 (:TYPE-PRESCRIPTION MAKE-ORD))
 (638 18 (:REWRITE |(o-first-expt a) < a|))
 (622 505 (:REWRITE NATP-RW))
 (572 208 (:REWRITE O-FIRST-EXPT-<))
 (550 208 (:REWRITE O-FINP-<))
 (550 208 (:REWRITE AC-<))
 (519 24 (:REWRITE DISTRIBUTIVITY))
 (466 466 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (464 232 (:TYPE-PRESCRIPTION O+-O-FINP))
 (386 77 (:REWRITE NATP-POSP))
 (340 4 (:REWRITE O-FIRST-EXPT-<-O+))
 (301 301 (:REWRITE O-FINP-O-RST))
 (275 178 (:REWRITE DEFAULT-*-2))
 (255 24 (:REWRITE FUNCTIONAL-COMMUTATIVITY-OF-MINUS-*-RIGHT))
 (251 178 (:REWRITE DEFAULT-*-1))
 (232 232 (:TYPE-PRESCRIPTION OB+))
 (219 208 (:REWRITE |a < b & b < c  =>  a < c|))
 (204 4 (:REWRITE |o-first-expt(b) < o-first-expt(c)  =>  (a^b)*(a^c) = a^c|))
 (170 170 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (140 28 (:REWRITE O-P-O*))
 (128 128 (:REWRITE DEFAULT-+-2))
 (128 128 (:REWRITE DEFAULT-+-1))
 (124 24 (:REWRITE O^-O-FIRST-EXPT))
 (121 77 (:REWRITE POSP-RW))
 (104 52 (:TYPE-PRESCRIPTION |0 < a  =>  0^a = 0 :b|))
 (104 52 (:TYPE-PRESCRIPTION |0 < a  =>  0^a = 0 :a|))
 (102 44 (:REWRITE EQUAL-CONSTANT-+))
 (85 85 (:REWRITE O+-ATOM-DEF))
 (81 33 (:REWRITE O-INFP-O*))
 (72 24 (:REWRITE UNICITY-OF-1))
 (72 24 (:REWRITE COMMUTATIVITY-OF-+))
 (68 4 (:REWRITE O+-O-FIRST-EXPT-1))
 (66 33 (:REWRITE O-INFP-O*-2))
 (64 4 (:REWRITE O+-O-FIRST-EXPT-2))
 (60 60 (:TYPE-PRESCRIPTION |x < y  =>  0 < y-x|))
 (48 24 (:DEFINITION FIX))
 (34 15 (:REWRITE O-INFP-O^-1))
 (34 4 (:REWRITE ZP-OPEN))
 (32 32 (:REWRITE O-FIRST-EXPT-O-P))
 (32 8 (:REWRITE O^-O-FIRST-EXPT-3))
 (32 8 (:REWRITE O^-O-FIRST-EXPT-2))
 (24 24 (:REWRITE DEFAULT-UNARY-MINUS))
 (16 4 (:REWRITE <-0-+-NEGATIVE-1))
 (11 11 (:META CANCEL_PLUS-LESSP-CORRECT))
 (7 7 (:REWRITE DEFAULT-<-2))
 (7 7 (:REWRITE DEFAULT-<-1))
 (3 1 (:REWRITE FOLD-CONSTS-IN-+))
 )
(|0 < w^a|
 (151 1 (:DEFINITION OB^))
 (83 1 (:REWRITE O*-O-INFP-DEF))
 (76 1 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (63 9 (:REWRITE O-FIRST-EXPT-O-INFP))
 (36 4 (:REWRITE O-FIRST-EXPT-0-NATP))
 (29 11 (:REWRITE O-P-DEF-O-FINP-1))
 (27 4 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (20 10 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (19 3 (:LINEAR O-FIRST-EXPT-<=))
 (12 4 (:REWRITE O-INFP->NEQ-0))
 (10 6 (:REWRITE O-FIRST-EXPT-O-P))
 (10 2 (:DEFINITION OMEGA-TERM))
 (9 3 (:REWRITE MAKE-ORD-EQUAL-4))
 (6 6 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (6 6 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (6 3 (:REWRITE O^-^))
 (6 2 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (5 3 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (4 4 (:TYPE-PRESCRIPTION NATP))
 (4 2 (:REWRITE O*-O-FINP))
 (4 1 (:REWRITE NATP-POSP))
 (4 1 (:REWRITE |0+a = a|))
 (3 3 (:TYPE-PRESCRIPTION MAKE-ORD))
 (3 3 (:REWRITE NATP-RW))
 (2 2 (:REWRITE O-FINP-O-RST))
 (1 1 (:REWRITE POSP-RW))
 (1 1 (:REWRITE OMEGA-O-FIRST-EXPT))
 (1 1 (:REWRITE O+-ATOM-DEF))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(O^-OMEGA-O-FIRST-EXPT
 (151 1 (:DEFINITION OB^))
 (83 1 (:REWRITE O*-O-INFP-DEF))
 (76 1 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (71 1 (:REWRITE |0 < a  =  ~(a = 0)|))
 (66 10 (:REWRITE O-FIRST-EXPT-O-INFP))
 (36 4 (:REWRITE O-FIRST-EXPT-0-NATP))
 (27 10 (:REWRITE O-P-DEF-O-FINP-1))
 (27 4 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (24 12 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (19 3 (:LINEAR O-FIRST-EXPT-<=))
 (15 3 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (12 4 (:REWRITE O-INFP->NEQ-0))
 (10 6 (:REWRITE O-FIRST-EXPT-O-P))
 (10 2 (:DEFINITION OMEGA-TERM))
 (9 3 (:REWRITE MAKE-ORD-EQUAL-4))
 (7 3 (:REWRITE O*-O-FINP))
 (6 6 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (6 6 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (6 3 (:REWRITE O^-^))
 (6 1 (:REWRITE LIMITP-DEF))
 (5 3 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (4 4 (:TYPE-PRESCRIPTION NATP))
 (4 1 (:REWRITE NATP-POSP))
 (4 1 (:REWRITE |0+a = a|))
 (3 3 (:TYPE-PRESCRIPTION MAKE-ORD))
 (3 3 (:REWRITE NATP-RW))
 (2 2 (:TYPE-PRESCRIPTION LIMITP))
 (2 2 (:REWRITE O-FINP-O-RST))
 (1 1 (:REWRITE POSP-RW))
 (1 1 (:REWRITE O+-ATOM-DEF))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(O^-O-RST
 (357 22 (:REWRITE MAKE-ORD-EQUAL-4))
 (195 45 (:REWRITE O-INFP->NEQ-0))
 (152 2 (:REWRITE O*-O-FIRST-EXPT))
 (140 2 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (128 8 (:REWRITE O--0))
 (128 2 (:REWRITE |(o-first-expt a) < a|))
 (124 27 (:REWRITE O-FINP-O-RST))
 (106 4 (:DEFINITION EXPT))
 (104 104 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (104 104 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (96 20 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (96 20 (:REWRITE O-FIRST-EXPT-0-NATP))
 (52 17 (:REWRITE O*-O-FINP))
 (45 39 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (45 15 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (44 2 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (36 12 (:REWRITE O-FINP-<))
 (36 12 (:REWRITE AC-<))
 (34 12 (:REWRITE |a < b & b < c  =>  a < c|))
 (32 6 (:REWRITE DEFAULT-*-2))
 (25 25 (:REWRITE NATP-RW))
 (24 12 (:REWRITE O-FIRST-EXPT-<))
 (24 4 (:REWRITE ZIP-OPEN))
 (22 12 (:REWRITE O-FIRST-COEFF-<))
 (20 20 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (20 10 (:REWRITE O*-O-FIRST-COEFF))
 (20 4 (:REWRITE COMMUTATIVITY-OF-+))
 (18 4 (:REWRITE O-INFP-O^-1))
 (14 12 (:REWRITE DEFAULT-+-2))
 (14 12 (:REWRITE DEFAULT-+-1))
 (12 6 (:TYPE-PRESCRIPTION O+-O-FINP))
 (8 2 (:REWRITE NATP-POSP))
 (8 2 (:REWRITE <-0-+-NEGATIVE-1))
 (6 6 (:TYPE-PRESCRIPTION OB+))
 (6 6 (:REWRITE DEFAULT-*-1))
 (6 6 (:META CANCEL_PLUS-LESSP-CORRECT))
 (6 2 (:REWRITE FOLD-CONSTS-IN-+))
 (6 2 (:REWRITE EQUAL-CONSTANT-+))
 (4 4 (:REWRITE O-FIRST-EXPT-O-P))
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (4 4 (:DEFINITION FIX))
 (3 3 (:REWRITE O^-O-FIRST-EXPT))
 (2 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP))
 (2 2 (:REWRITE POSP-RW))
 (2 2 (:REWRITE O+-ATOM-DEF))
 (2 2 (:REWRITE EXPONENTS-ADD-FOR-NONNEG-EXPONENTS))
 (2 2 (:REWRITE EXPONENTS-ADD))
 )
(O^-LIMITP-O-RST
 (653 131 (:REWRITE O-FIRST-EXPT-O-INFP))
 (351 75 (:REWRITE O-INFP->NEQ-0))
 (307 8 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (233 11 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (231 4 (:REWRITE O*-O-FIRST-EXPT))
 (217 5 (:REWRITE |(o-first-expt a) < a|))
 (180 180 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (180 180 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (161 38 (:REWRITE O-FINP-O-RST))
 (111 16 (:REWRITE LIMITP-DEF))
 (104 27 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (102 6 (:REWRITE O--0))
 (90 82 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (85 23 (:REWRITE O-FIRST-EXPT-<))
 (85 1 (:REWRITE O-FIRST-EXPT-<-O+))
 (79 29 (:REWRITE O*-O-FINP))
 (74 37 (:TYPE-PRESCRIPTION O+-O-FINP))
 (73 23 (:REWRITE O-FIRST-COEFF-<))
 (57 23 (:REWRITE O-FINP-<))
 (57 23 (:REWRITE AC-<))
 (52 26 (:REWRITE O*-O-FIRST-COEFF))
 (45 23 (:REWRITE |a < b & b < c  =>  a < c|))
 (37 37 (:TYPE-PRESCRIPTION OB+))
 (35 7 (:REWRITE O-INFP-O^-1))
 (30 30 (:REWRITE NATP-RW))
 (28 6 (:REWRITE O^-O-FIRST-EXPT))
 (27 5 (:REWRITE DEFAULT-*-2))
 (24 6 (:REWRITE NATP-POSP))
 (23 23 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (20 3 (:REWRITE ZIP-OPEN))
 (17 3 (:REWRITE COMMUTATIVITY-OF-+))
 (17 1 (:REWRITE O+-O-FIRST-EXPT-1))
 (16 1 (:REWRITE O+-O-FIRST-EXPT-2))
 (14 12 (:REWRITE DEFAULT-+-2))
 (14 12 (:REWRITE DEFAULT-+-1))
 (8 8 (:REWRITE O+-ATOM-DEF))
 (8 2 (:REWRITE <-0-+-NEGATIVE-1))
 (6 6 (:REWRITE POSP-RW))
 (6 2 (:REWRITE NATPART-DEF-O-FINP))
 (6 2 (:REWRITE FOLD-CONSTS-IN-+))
 (6 2 (:REWRITE EQUAL-CONSTANT-+))
 (5 5 (:REWRITE DEFAULT-*-1))
 (5 5 (:META CANCEL_PLUS-LESSP-CORRECT))
 (4 2 (:TYPE-PRESCRIPTION |0 < a  =>  0^a = 0 :a|))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (3 3 (:DEFINITION FIX))
 (2 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP))
 (2 2 (:REWRITE POSP-O-FIRST-COEFF))
 (2 2 (:REWRITE EXPONENTS-ADD-FOR-NONNEG-EXPONENTS))
 (2 2 (:REWRITE EXPONENTS-ADD))
 )
(O^-LIMITP-O-RST-2
 (655 139 (:REWRITE O-FIRST-EXPT-O-INFP))
 (374 70 (:REWRITE O-INFP->NEQ-0))
 (287 11 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (244 14 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (214 214 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (214 214 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (146 43 (:REWRITE O-FINP-O-RST))
 (137 33 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (136 68 (:REWRITE O*-O-FIRST-COEFF))
 (102 51 (:TYPE-PRESCRIPTION O+-O-FINP))
 (89 3 (:REWRITE |(o-first-expt a) < a|))
 (88 23 (:REWRITE O-FIRST-COEFF-<))
 (85 23 (:REWRITE O-FIRST-EXPT-<))
 (85 1 (:REWRITE O-FIRST-EXPT-<-O+))
 (79 2 (:REWRITE O*-O-FIRST-EXPT))
 (71 33 (:REWRITE O*-O-FINP))
 (65 7 (:REWRITE O^-LIMITP-O-RST))
 (51 51 (:TYPE-PRESCRIPTION OB+))
 (50 5 (:REWRITE O^-O-FIRST-EXPT))
 (47 23 (:REWRITE O-FINP-<))
 (47 23 (:REWRITE AC-<))
 (47 10 (:REWRITE O^-O-RST))
 (43 43 (:TYPE-PRESCRIPTION NATP))
 (36 9 (:REWRITE NATP-POSP))
 (33 5 (:REWRITE O-INFP-O^-1))
 (29 23 (:REWRITE O^-^))
 (26 7 (:REWRITE LIMITP-DEF))
 (23 23 (:REWRITE |a < b & b < c  =>  a < c|))
 (22 22 (:REWRITE NATP-RW))
 (17 1 (:REWRITE O+-O-FIRST-EXPT-1))
 (16 1 (:REWRITE O+-O-FIRST-EXPT-2))
 (14 14 (:TYPE-PRESCRIPTION LIMITP))
 (11 11 (:REWRITE O+-ATOM-DEF))
 (9 9 (:REWRITE POSP-RW))
 (8 8 (:REWRITE DEFAULT-+-2))
 (8 8 (:REWRITE DEFAULT-+-1))
 (3 3 (:REWRITE O-INFP-O^))
 (2 2 (:REWRITE MAKE-ORD-O-FIRST-EXPT))
 )
(O^-O-INFP
 (247 1 (:DEFINITION OB^))
 (149 26 (:REWRITE O-FIRST-EXPT-O-INFP))
 (84 1 (:REWRITE O*-O-INFP-DEF))
 (78 28 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (56 6 (:REWRITE MAKE-ORD-EQUAL-4))
 (51 11 (:REWRITE O-INFP->NEQ-0))
 (35 6 (:LINEAR O-FIRST-EXPT-<=))
 (31 5 (:DEFINITION OMEGA-TERM))
 (28 6 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (25 25 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (25 25 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (24 1 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (23 5 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (19 4 (:REWRITE O-FIRST-EXPT-0-NATP))
 (17 5 (:REWRITE O^-^))
 (13 1 (:REWRITE O--0))
 (12 5 (:REWRITE O*-O-FINP))
 (12 2 (:REWRITE O^-O-FIRST-EXPT))
 (11 3 (:REWRITE O-INFP-O^-1))
 (11 1 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (10 8 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (9 9 (:TYPE-PRESCRIPTION MAKE-ORD))
 (8 8 (:REWRITE NATP-RW))
 (8 4 (:TYPE-PRESCRIPTION O+-O-FINP))
 (8 4 (:TYPE-PRESCRIPTION |0 < a  =>  0^a = 0 :b|))
 (8 4 (:TYPE-PRESCRIPTION |0 < a  =>  0^a = 0 :a|))
 (8 3 (:REWRITE O-FIRST-COEFF-<))
 (7 3 (:REWRITE O-FINP-<))
 (7 3 (:REWRITE AC-<))
 (6 3 (:REWRITE O-FIRST-EXPT-<))
 (6 2 (:REWRITE O-P-DEF-O-FINP-1))
 (4 4 (:TYPE-PRESCRIPTION POSP))
 (4 4 (:TYPE-PRESCRIPTION OB+))
 (4 4 (:REWRITE O-FINP-O-RST))
 (4 1 (:REWRITE O-INFP-O^))
 (4 1 (:REWRITE NATP-POSP))
 (3 3 (:REWRITE |a < b & b < c  =>  a < c|))
 (1 1 (:REWRITE |a0 = 0|))
 (1 1 (:REWRITE POSP-RW))
 (1 1 (:REWRITE O+-ATOM-DEF))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(O^-LIMITP-O-FIRST-COEFF
 (2704 1493 (:TYPE-PRESCRIPTION O*-FINITE))
 (1420 42 (:REWRITE MAKE-ORD-EQUAL-4))
 (1093 227 (:REWRITE O-FIRST-EXPT-O-INFP))
 (498 33 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (478 18 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (468 110 (:REWRITE O-INFP->NEQ-0))
 (382 65 (:REWRITE O-FIRST-EXPT-<))
 (358 65 (:REWRITE O-FIRST-COEFF-<))
 (311 311 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (311 311 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (294 68 (:REWRITE AC-<))
 (292 146 (:TYPE-PRESCRIPTION O+-O-FINP))
 (178 6 (:REWRITE |(o-first-expt a) < a|))
 (170 2 (:REWRITE O-FIRST-EXPT-<-O+))
 (162 65 (:REWRITE O-FINP-<))
 (158 4 (:REWRITE O*-O-FIRST-EXPT))
 (146 146 (:TYPE-PRESCRIPTION OB+))
 (139 88 (:REWRITE O-FIRST-EXPT-O-P))
 (132 40 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (98 11 (:REWRITE NOT-LIMITP-NATP))
 (96 6 (:REWRITE O-INFP-O+-2))
 (95 11 (:REWRITE O+-O-FIRST-EXPT-2))
 (90 6 (:REWRITE O-INFP-O+))
 (85 11 (:REWRITE O+-O-FIRST-EXPT-1))
 (84 40 (:REWRITE O*-O-FINP))
 (68 68 (:REWRITE |a < b & b < c  =>  a < c|))
 (67 19 (:REWRITE NATP-POSP))
 (65 65 (:TYPE-PRESCRIPTION NATP))
 (47 5 (:REWRITE LIMITP-DEF))
 (42 42 (:REWRITE O-FINP-O-RST))
 (39 33 (:REWRITE O^-^))
 (36 36 (:REWRITE NATP-RW))
 (28 2 (:REWRITE DEFAULT-*-2))
 (24 6 (:REWRITE O-INFP-O+-3))
 (19 19 (:REWRITE POSP-RW))
 (18 18 (:REWRITE O+-ATOM-DEF))
 (18 2 (:REWRITE O*-O-RST))
 (16 4 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (14 4 (:REWRITE O*-0))
 (11 11 (:REWRITE DEFAULT-+-2))
 (11 11 (:REWRITE DEFAULT-+-1))
 (10 10 (:TYPE-PRESCRIPTION LIMITP))
 (8 2 (:REWRITE O^-O-FIRST-EXPT))
 (6 6 (:REWRITE POSP-O-FIRST-COEFF))
 (6 3 (:REWRITE O<=-O-FINP-DEF))
 (6 3 (:REWRITE O-INFP-O-FINP-O<=))
 (2 2 (:REWRITE MAKE-ORD-O-FIRST-EXPT))
 (2 2 (:REWRITE DEFAULT-*-1))
 (1 1 (:REWRITE NATPART-O-FINP))
 )
(O^-W-O-FIRST-EXPT
 (118 29 (:REWRITE O-FIRST-EXPT-O-INFP))
 (112 13 (:REWRITE O-FIRST-EXPT-<))
 (78 9 (:REWRITE O-FIRST-COEFF-<))
 (54 27 (:TYPE-PRESCRIPTION O*-FINITE))
 (53 7 (:REWRITE O-INFP-O-FINP-O<=))
 (35 13 (:REWRITE O-FINP-<))
 (35 13 (:REWRITE AC-<))
 (32 9 (:REWRITE O-INFP->NEQ-0))
 (30 6 (:REWRITE O<=-O-FINP-DEF))
 (21 14 (:REWRITE |a < b & b < c  =>  a < c|))
 (16 3 (:REWRITE NOT-LIMITP-NATP))
 (15 4 (:LINEAR O-FIRST-EXPT-<=))
 (14 14 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (14 14 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (14 9 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (14 4 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (12 4 (:REWRITE O-FIRST-EXPT-0-NATP))
 (10 6 (:REWRITE O-FINP-O-RST))
 (9 3 (:REWRITE NATPART-DEF-O-FINP))
 (5 3 (:REWRITE DEFAULT-<-1))
 (4 2 (:REWRITE O^-^))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:META CANCEL_PLUS-LESSP-CORRECT))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1 1 (:REWRITE NATP-RW))
 )
(|b < w^a  =>  b + w^a = w^a|
 (755 5 (:DEFINITION OB^))
 (415 5 (:REWRITE O*-O-INFP-DEF))
 (362 58 (:REWRITE O-FIRST-EXPT-O-INFP))
 (355 5 (:REWRITE |0 < a  =  ~(a = 0)|))
 (183 21 (:REWRITE O-FIRST-EXPT-0-NATP))
 (159 75 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (137 21 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (125 45 (:REWRITE O-P-DEF-O-FINP-1))
 (72 18 (:REWRITE |a < b & b < c  =>  a < c|))
 (70 24 (:REWRITE O-INFP->NEQ-0))
 (65 14 (:REWRITE O-FIRST-COEFF-<))
 (60 18 (:REWRITE O-FINP-<))
 (60 18 (:REWRITE AC-<))
 (50 30 (:REWRITE O-FIRST-EXPT-O-P))
 (50 10 (:DEFINITION OMEGA-TERM))
 (45 15 (:REWRITE MAKE-ORD-EQUAL-4))
 (37 5 (:REWRITE O<=-O-FINP-DEF))
 (36 18 (:REWRITE O^-^))
 (36 5 (:REWRITE O-INFP-O-FINP-O<=))
 (35 35 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (35 35 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (30 10 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (25 15 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (20 10 (:REWRITE O*-O-FINP))
 (20 5 (:REWRITE NATP-POSP))
 (20 5 (:REWRITE |0+a = a|))
 (15 15 (:TYPE-PRESCRIPTION MAKE-ORD))
 (15 15 (:REWRITE NATP-RW))
 (10 10 (:REWRITE O-FINP-O-RST))
 (9 1 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (7 7 (:REWRITE O+-ATOM-DEF))
 (5 5 (:REWRITE POSP-RW))
 (5 5 (:REWRITE OMEGA-O-FIRST-EXPT))
 (5 5 (:REWRITE DEFAULT-+-2))
 (5 5 (:REWRITE DEFAULT-+-1))
 (4 1 (:REWRITE O-INFP-O^-1))
 (3 3 (:REWRITE |~(a < a)|))
 )
(|a < b  =>  c^a < c^b :l1|
 (836 292 (:TYPE-PRESCRIPTION O^-O-FINP))
 (681 3 (:DEFINITION OB^))
 (264 132 (:TYPE-PRESCRIPTION O+-O-FINP))
 (252 3 (:REWRITE O*-O-INFP-DEF))
 (168 18 (:REWRITE MAKE-ORD-EQUAL-4))
 (141 31 (:REWRITE O-FIRST-EXPT-O-INFP))
 (132 132 (:TYPE-PRESCRIPTION OB+))
 (116 57 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (104 16 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (93 15 (:DEFINITION OMEGA-TERM))
 (72 3 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (48 16 (:REWRITE O*-O-FINP))
 (45 15 (:REWRITE O^-^))
 (45 12 (:REWRITE O-INFP->NEQ-0))
 (42 42 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (42 42 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (42 6 (:REWRITE O--0))
 (36 12 (:LINEAR O-FIRST-EXPT-<=))
 (33 3 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (30 24 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (30 12 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (30 10 (:REWRITE O-FIRST-COEFF-<))
 (29 20 (:REWRITE NATP-RW))
 (27 27 (:TYPE-PRESCRIPTION MAKE-ORD))
 (24 10 (:REWRITE O-FINP-<))
 (24 10 (:REWRITE AC-<))
 (24 1 (:REWRITE |o-first-expt(b) < o-first-expt(c)  =>  (a^b)*(a^c) = a^c|))
 (20 10 (:REWRITE O-FIRST-EXPT-<))
 (18 6 (:REWRITE O-FIRST-EXPT-0-NATP))
 (12 12 (:REWRITE O-FINP-O-RST))
 (12 3 (:REWRITE NATP-POSP))
 (10 10 (:REWRITE |a < b & b < c  =>  a < c|))
 (9 3 (:REWRITE O-P-DEF-O-FINP-1))
 (4 4 (:REWRITE O+-ATOM-DEF))
 (3 3 (:REWRITE |a0 = 0|))
 (3 3 (:REWRITE POSP-RW))
 (3 3 (:REWRITE DEFAULT-+-2))
 (3 3 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE |(a = 0) & ~(b = 0)  <=>  (a^b = 0)|))
 )
(|a < b  =>  c^a < c^b|
 (2491 11 (:DEFINITION OB^))
 (1136 568 (:TYPE-PRESCRIPTION O^-O-FINP))
 (924 11 (:REWRITE O*-O-INFP-DEF))
 (616 66 (:REWRITE MAKE-ORD-EQUAL-4))
 (563 125 (:REWRITE O-FIRST-EXPT-O-INFP))
 (439 217 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (341 55 (:DEFINITION OMEGA-TERM))
 (323 57 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (264 11 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (175 47 (:REWRITE O-INFP->NEQ-0))
 (160 55 (:REWRITE O^-^))
 (159 159 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (159 159 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (156 57 (:REWRITE O*-O-FINP))
 (153 40 (:REWRITE O-FIRST-COEFF-<))
 (148 16 (:REWRITE O--0))
 (135 45 (:LINEAR O-FIRST-EXPT-<=))
 (121 11 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (117 42 (:REWRITE O-FIRST-EXPT-<))
 (112 45 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (111 42 (:REWRITE O-FINP-<))
 (111 42 (:REWRITE AC-<))
 (110 88 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (99 99 (:TYPE-PRESCRIPTION MAKE-ORD))
 (88 70 (:REWRITE NATP-RW))
 (88 44 (:TYPE-PRESCRIPTION O+-O-FINP))
 (69 23 (:REWRITE O-FIRST-EXPT-0-NATP))
 (62 42 (:REWRITE |a < b & b < c  =>  a < c|))
 (52 3 (:REWRITE O-INFP-O-FINP-O<=))
 (48 2 (:REWRITE |o-first-expt(b) < o-first-expt(c)  =>  (a^b)*(a^c) = a^c|))
 (44 44 (:TYPE-PRESCRIPTION OB+))
 (44 44 (:REWRITE O-FINP-O-RST))
 (44 11 (:REWRITE NATP-POSP))
 (18 3 (:REWRITE O<=-O-FINP-DEF))
 (14 2 (:REWRITE O-INFP-O^-1))
 (11 11 (:REWRITE |a0 = 0|))
 (11 11 (:REWRITE POSP-RW))
 (11 11 (:REWRITE O+-ATOM-DEF))
 (11 11 (:REWRITE DEFAULT-+-2))
 (11 11 (:REWRITE DEFAULT-+-1))
 (9 3 (:REWRITE O-P-DEF-O-FINP-1))
 (8 2 (:REWRITE O^-O-FIRST-EXPT))
 (2 2 (:REWRITE |~(a < a)|))
 )
(|a < b  <=>  c^a < c^b helper|
 (1756 8 (:DEFINITION OB^))
 (1434 717 (:TYPE-PRESCRIPTION O^-O-FINP))
 (675 117 (:REWRITE O-FIRST-EXPT-O-INFP))
 (631 99 (:REWRITE O-FIRST-EXPT-<))
 (626 8 (:REWRITE O*-O-INFP-DEF))
 (570 93 (:REWRITE O-FIRST-COEFF-<))
 (520 172 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (402 48 (:REWRITE MAKE-ORD-EQUAL-4))
 (395 6 (:REWRITE O-INFP-O-FINP-O<=))
 (375 6 (:REWRITE O*-O-FIRST-EXPT))
 (367 99 (:REWRITE O-FINP-<))
 (367 99 (:REWRITE AC-<))
 (333 48 (:REWRITE O-INFP->NEQ-0))
 (324 44 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (251 8 (:REWRITE O-INFP-O*))
 (248 40 (:DEFINITION OMEGA-TERM))
 (238 8 (:REWRITE O-INFP-O*-2))
 (192 8 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (186 99 (:REWRITE |a < b & b < c  =>  a < c|))
 (144 44 (:REWRITE O*-O-FINP))
 (125 57 (:REWRITE O-P-DEF-O-FINP-1))
 (124 12 (:REWRITE O--0))
 (121 121 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (121 121 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (118 40 (:REWRITE O^-^))
 (96 31 (:LINEAR O-FIRST-EXPT-<=))
 (90 54 (:REWRITE NATP-RW))
 (76 31 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (74 58 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (72 72 (:TYPE-PRESCRIPTION MAKE-ORD))
 (70 6 (:REWRITE O<=-O-FINP-DEF))
 (68 2 (:REWRITE O*-O-FIRST-EXPT-SMASH-1A))
 (66 6 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (54 32 (:REWRITE O-FINP-O-RST))
 (54 1 (:REWRITE |~(a=0) & b>1  <=>  a < ab|))
 (48 24 (:TYPE-PRESCRIPTION O+-O-FINP))
 (47 15 (:REWRITE O-FIRST-EXPT-0-NATP))
 (42 6 (:REWRITE O*-0))
 (32 8 (:REWRITE NATP-POSP))
 (24 24 (:TYPE-PRESCRIPTION OB+))
 (24 2 (:REWRITE O*-O-FIRST-EXPT-SMASH-2A))
 (21 1 (:REWRITE O-P-O*))
 (16 14 (:REWRITE |(a = 0) & ~(b = 0)  <=>  (a^b = 0)|))
 (16 4 (:REWRITE O^-O-FIRST-EXPT))
 (15 10 (:REWRITE O-P-O^))
 (14 2 (:REWRITE O^-LIMITP-O-RST))
 (12 2 (:REWRITE O^-O-RST))
 (12 2 (:REWRITE O^-LIMITP-O-RST-2))
 (10 4 (:REWRITE O-INFP-O^-1))
 (8 8 (:TYPE-PRESCRIPTION OMEGA))
 (8 8 (:REWRITE |a0 = 0|))
 (8 8 (:REWRITE POSP-RW))
 (8 8 (:REWRITE OMEGA-O-P))
 (8 8 (:REWRITE O+-ATOM-DEF))
 (8 8 (:REWRITE DEFAULT-+-2))
 (8 8 (:REWRITE DEFAULT-+-1))
 (8 2 (:REWRITE |o-first-expt(b) < o-first-expt(c)  =>  (a^b)*(a^c) = a^c|))
 (8 2 (:REWRITE LIMITP-DEF))
 (6 6 (:REWRITE |~(a < a)|))
 (4 4 (:TYPE-PRESCRIPTION LIMITP))
 (2 2 (:REWRITE O-FIRST-EXPT-O--<))
 (2 1 (:REWRITE O^-O-FIRST-EXPT-2))
 (1 1 (:REWRITE O^-O-FIRST-EXPT-3))
 )
(|a < b  <=>  c^a < c^b|
 (3572 16 (:DEFINITION OB^))
 (1680 840 (:TYPE-PRESCRIPTION O^-O-FINP))
 (1275 16 (:REWRITE O*-O-INFP-DEF))
 (1148 236 (:REWRITE O-FIRST-EXPT-O-INFP))
 (912 364 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (862 143 (:REWRITE O-FIRST-COEFF-<))
 (827 96 (:REWRITE MAKE-ORD-EQUAL-4))
 (808 160 (:REWRITE O-FIRST-EXPT-<))
 (578 86 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (537 160 (:REWRITE O-FINP-<))
 (537 160 (:REWRITE AC-<))
 (496 80 (:DEFINITION OMEGA-TERM))
 (453 95 (:REWRITE O-INFP->NEQ-0))
 (384 16 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (272 5 (:REWRITE O*-O-FIRST-EXPT))
 (264 86 (:REWRITE O*-O-FINP))
 (250 250 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (250 250 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (239 80 (:REWRITE O^-^))
 (232 24 (:REWRITE O--0))
 (208 67 (:LINEAR O-FIRST-EXPT-<=))
 (201 160 (:REWRITE |a < b & b < c  =>  a < c|))
 (179 68 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (170 5 (:REWRITE O-INFP-O*-2))
 (168 77 (:REWRITE O-P-DEF-O-FINP-1))
 (161 107 (:REWRITE NATP-RW))
 (159 5 (:REWRITE O-INFP-O*))
 (151 119 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (144 144 (:TYPE-PRESCRIPTION MAKE-ORD))
 (143 13 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (138 14 (:REWRITE O-INFP-O-FINP-O<=))
 (120 14 (:REWRITE O<=-O-FINP-DEF))
 (104 52 (:TYPE-PRESCRIPTION O+-O-FINP))
 (85 63 (:REWRITE O-FINP-O-RST))
 (79 2 (:REWRITE O*-O-FIRST-EXPT-SMASH-1A))
 (64 16 (:REWRITE NATP-POSP))
 (52 52 (:TYPE-PRESCRIPTION OB+))
 (36 8 (:REWRITE O^-O-FIRST-EXPT))
 (36 7 (:REWRITE O-INFP-O^-1))
 (36 4 (:REWRITE |o-first-expt(b) < o-first-expt(c)  =>  (a^b)*(a^c) = a^c|))
 (24 2 (:REWRITE O*-O-FIRST-EXPT-SMASH-2A))
 (23 2 (:REWRITE O^-O-RST))
 (21 1 (:REWRITE O-P-O*))
 (16 16 (:TYPE-PRESCRIPTION OMEGA))
 (16 16 (:REWRITE |a0 = 0|))
 (16 16 (:REWRITE POSP-RW))
 (16 16 (:REWRITE OMEGA-O-P))
 (16 16 (:REWRITE O+-ATOM-DEF))
 (16 16 (:REWRITE DEFAULT-+-2))
 (16 16 (:REWRITE DEFAULT-+-1))
 (14 2 (:REWRITE O^-LIMITP-O-RST))
 (13 7 (:REWRITE O-P-O^))
 (12 2 (:REWRITE O^-LIMITP-O-RST-2))
 (8 2 (:REWRITE LIMITP-DEF))
 (8 1 (:REWRITE |a < b  =>  c^a < c^b|))
 (4 4 (:TYPE-PRESCRIPTION LIMITP))
 (2 2 (:REWRITE O-FIRST-EXPT-O--<))
 )
(|a <= b  =>  c^a <= c^b|
 (1378 6 (:DEFINITION OB^))
 (550 275 (:TYPE-PRESCRIPTION O^-O-FINP))
 (504 6 (:REWRITE O*-O-INFP-DEF))
 (392 97 (:REWRITE O-FIRST-EXPT-O-INFP))
 (363 149 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (336 36 (:REWRITE MAKE-ORD-EQUAL-4))
 (262 33 (:REWRITE O-FIRST-EXPT-<))
 (186 30 (:DEFINITION OMEGA-TERM))
 (175 31 (:REWRITE O-FIRST-COEFF-<))
 (144 6 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (138 30 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (122 31 (:REWRITE O-INFP->NEQ-0))
 (117 8 (:REWRITE O-INFP-O-FINP-O<=))
 (114 33 (:REWRITE O-FINP-<))
 (114 33 (:REWRITE AC-<))
 (107 107 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (107 107 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (101 32 (:REWRITE O^-^))
 (78 6 (:REWRITE O--0))
 (72 30 (:REWRITE O*-O-FINP))
 (66 6 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (60 48 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (60 24 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (54 54 (:TYPE-PRESCRIPTION MAKE-ORD))
 (51 8 (:REWRITE O<=-O-FINP-DEF))
 (48 24 (:TYPE-PRESCRIPTION O+-O-FINP))
 (44 9 (:REWRITE O^-O-FIRST-EXPT))
 (41 41 (:REWRITE NATP-RW))
 (36 12 (:REWRITE O-FIRST-EXPT-0-NATP))
 (35 5 (:REWRITE O-INFP-O^-1))
 (33 33 (:REWRITE |a < b & b < c  =>  a < c|))
 (33 11 (:REWRITE O-P-DEF-O-FINP-1))
 (24 24 (:TYPE-PRESCRIPTION OB+))
 (24 24 (:REWRITE O-FINP-O-RST))
 (24 6 (:REWRITE NATP-POSP))
 (9 3 (:REWRITE |a < b  <=>  c^a < c^b|))
 (6 6 (:REWRITE |a0 = 0|))
 (6 6 (:REWRITE POSP-RW))
 (6 6 (:REWRITE O+-ATOM-DEF))
 (6 6 (:REWRITE DEFAULT-+-2))
 (6 6 (:REWRITE DEFAULT-+-1))
 (2 1 (:REWRITE O^-O-FIRST-EXPT-2))
 (1 1 (:REWRITE O^-O-FIRST-EXPT-3))
 )
(|a < b  <=>  w^a + w^b = w^b|
 (620 5 (:DEFINITION OB^))
 (280 5 (:REWRITE O*-O-INFP-DEF))
 (260 55 (:REWRITE O-FIRST-EXPT-O-INFP))
 (260 5 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (235 5 (:REWRITE |0 < a  =  ~(a = 0)|))
 (132 64 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (105 20 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (100 20 (:REWRITE O-FIRST-EXPT-0-NATP))
 (60 20 (:REWRITE O-INFP->NEQ-0))
 (55 15 (:LINEAR O-FIRST-EXPT-<=))
 (50 10 (:DEFINITION OMEGA-TERM))
 (50 5 (:REWRITE O-FIRST-EXPT-<))
 (45 15 (:REWRITE MAKE-ORD-EQUAL-4))
 (30 30 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (30 30 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (30 15 (:REWRITE O^-^))
 (30 10 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (25 15 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (25 9 (:REWRITE O-P-DEF-O-FINP-1))
 (24 4 (:REWRITE O-FIRST-COEFF-<))
 (20 10 (:REWRITE O*-O-FINP))
 (20 5 (:REWRITE NATP-POSP))
 (15 15 (:TYPE-PRESCRIPTION MAKE-ORD))
 (15 5 (:REWRITE |a < b & b < c  =>  a < c|))
 (15 5 (:REWRITE O-FINP-<))
 (15 5 (:REWRITE AC-<))
 (10 10 (:TYPE-PRESCRIPTION NATP))
 (10 10 (:REWRITE O-FINP-O-RST))
 (6 1 (:REWRITE O-INFP-O-FINP-O<=))
 (5 5 (:REWRITE POSP-RW))
 (5 5 (:REWRITE OMEGA-O-FIRST-EXPT))
 (5 5 (:REWRITE O-FIRST-EXPT-O-P))
 (5 5 (:REWRITE O+-ATOM-DEF))
 (5 5 (:REWRITE NATP-RW))
 (5 5 (:REWRITE DEFAULT-+-2))
 (5 5 (:REWRITE DEFAULT-+-1))
 (5 5 (:REWRITE |0+a = a|))
 (3 1 (:REWRITE O<=-O-FINP-DEF))
 (1 1 (:REWRITE |~(a < a)|))
 )
(|b-1 <= a+b|
 (4997 1109 (:REWRITE O-FIRST-EXPT-O-INFP))
 (4776 2388 (:TYPE-PRESCRIPTION O*-FINITE))
 (1611 642 (:REWRITE |a < b & b < c  =>  a < c|))
 (1086 258 (:REWRITE O-INFP->NEQ-0))
 (1063 718 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (1019 189 (:REWRITE O-INFP-O-FINP-O<=))
 (962 216 (:REWRITE O-FIRST-EXPT-0-NATP))
 (829 9 (:REWRITE O-FIRST-EXPT-<-O+))
 (815 73 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (718 718 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (460 10 (:REWRITE O-INFP-O+))
 (297 297 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (290 20 (:REWRITE O-INFP-O+-3))
 (261 166 (:REWRITE DEFAULT-+-1))
 (247 166 (:REWRITE DEFAULT-+-2))
 (203 20 (:REWRITE O-INFP-O+-2))
 (202 28 (:REWRITE O--0))
 (200 184 (:REWRITE O-FINP-O-RST))
 (200 12 (:REWRITE O+-O-FIRST-COEFF-2))
 (197 17 (:REWRITE O+-O-FIRST-EXPT-1))
 (135 12 (:REWRITE O+-O-FIRST-COEFF-1))
 (77 53 (:REWRITE DEFAULT-<-2))
 (68 53 (:REWRITE DEFAULT-<-1))
 (63 12 (:REWRITE O+-O-FIRST-COEFF-3))
 (60 55 (:META CANCEL_PLUS-LESSP-CORRECT))
 (32 32 (:REWRITE NATP-RW))
 (27 27 (:REWRITE EQUAL-CONSTANT-+))
 (12 8 (:REWRITE DEFAULT-CDR))
 (12 8 (:REWRITE DEFAULT-CAR))
 (8 2 (:REWRITE NATP-POSP))
 (4 4 (:REWRITE O-FIRST-COEFF-0))
 (2 2 (:REWRITE |a < b  <=>  c+a < c+b :l1|))
 (2 2 (:REWRITE POSP-RW))
 )
(|b-1 <= a+b:1|
 (220 110 (:TYPE-PRESCRIPTION O+-O-FINP))
 (110 110 (:TYPE-PRESCRIPTION OB+))
 )
(EXP-IND-4
 (67 2 (:DEFINITION ACL2-COUNT))
 (26 3 (:REWRITE O-FIRST-EXPT-O-INFP))
 (21 10 (:REWRITE DEFAULT-+-2))
 (14 14 (:TYPE-PRESCRIPTION ACL2-COUNT))
 (14 10 (:REWRITE DEFAULT-+-1))
 (10 2 (:DEFINITION INTEGER-ABS))
 (8 2 (:REWRITE COMMUTATIVITY-OF-+))
 (8 1 (:DEFINITION LENGTH))
 (6 2 (:REWRITE O-P-DEF-O-FINP-1))
 (6 1 (:REWRITE O-FIRST-EXPT-0-NATP))
 (6 1 (:LINEAR O-FIRST-EXPT-<=))
 (5 1 (:DEFINITION LEN))
 (4 1 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (4 1 (:REWRITE O-INFP->NEQ-0))
 (3 3 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (3 3 (:REWRITE FOLD-CONSTS-IN-+))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 1 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (2 2 (:REWRITE DEFAULT-UNARY-MINUS))
 (2 2 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:META CANCEL_PLUS-LESSP-CORRECT))
 (1 1 (:TYPE-PRESCRIPTION LEN))
 (1 1 (:REWRITE O-FINP-O-RST))
 (1 1 (:REWRITE NUMERATOR-WHEN-INTEGERP))
 (1 1 (:REWRITE INTEGERP==>DENOMINATOR=1))
 (1 1 (:REWRITE DEFAULT-REALPART))
 (1 1 (:REWRITE DEFAULT-NUMERATOR))
 (1 1 (:REWRITE DEFAULT-IMAGPART))
 (1 1 (:REWRITE DEFAULT-DENOMINATOR))
 (1 1 (:REWRITE DEFAULT-COERCE-2))
 (1 1 (:REWRITE DEFAULT-COERCE-1))
 (1 1 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (1 1 (:META CANCEL_PLUS-EQUAL-CORRECT))
 )
(|a <= b  =>  a^c <= b^c :l1|
 (5975 150 (:REWRITE MAKE-ORD-EQUAL-4))
 (2425 260 (:REWRITE O-FIRST-EXPT-<))
 (2211 81 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (2011 50 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (1492 41 (:REWRITE |(o-first-expt a) < a|))
 (1454 25 (:REWRITE O*-O-FIRST-EXPT))
 (1253 13 (:REWRITE O-FIRST-EXPT-<-O+))
 (1216 252 (:REWRITE O-FIRST-COEFF-<))
 (1040 260 (:REWRITE O-FINP-<))
 (993 993 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (993 993 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (674 337 (:TYPE-PRESCRIPTION O+-O-FINP))
 (525 30 (:REWRITE O--0))
 (522 295 (:REWRITE |a < b & b < c  =>  a < c|))
 (433 123 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (416 208 (:REWRITE O*-O-FIRST-COEFF))
 (331 331 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (313 59 (:REWRITE DEFAULT-*-2))
 (284 19 (:REWRITE O+-O-FIRST-EXPT-2))
 (265 19 (:REWRITE O+-O-FIRST-EXPT-1))
 (204 3 (:REWRITE O-FIRST-EXPT-O+-<))
 (176 22 (:REWRITE ZIP-OPEN))
 (166 166 (:REWRITE NATP-RW))
 (152 130 (:REWRITE DEFAULT-+-2))
 (152 130 (:REWRITE DEFAULT-+-1))
 (150 130 (:REWRITE O-FINP-O-RST))
 (137 29 (:REWRITE O^-O-FIRST-EXPT))
 (106 67 (:REWRITE DEFAULT-<-2))
 (98 67 (:REWRITE DEFAULT-<-1))
 (96 24 (:REWRITE <-0-+-NEGATIVE-1))
 (91 91 (:META CANCEL_PLUS-LESSP-CORRECT))
 (73 73 (:REWRITE O-FIRST-EXPT-O-P))
 (72 3 (:REWRITE |(a <= b) & (c < d)  =>  ac < bd|))
 (68 2 (:LINEAR X*Y>1-POSITIVE))
 (66 22 (:REWRITE FOLD-CONSTS-IN-+))
 (66 22 (:REWRITE EQUAL-CONSTANT-+))
 (63 59 (:REWRITE DEFAULT-*-1))
 (50 50 (:REWRITE O+-ATOM-DEF))
 (47 6 (:REWRITE O*-0))
 (38 38 (:REWRITE POSP-RW))
 (29 5 (:REWRITE O^-O-FIRST-EXPT-2))
 (23 1 (:REWRITE |a <= b & c < d  =>  a+c < b+d|))
 (22 22 (:REWRITE EXPONENTS-ADD-FOR-NONNEG-EXPONENTS))
 (22 22 (:REWRITE EXPONENTS-ADD))
 (16 4 (:REWRITE X*Y>1-POSITIVE-LEMMA))
 (16 4 (:REWRITE *-PRESERVES->-FOR-NONNEGATIVES-1))
 (16 1 (:REWRITE O-INFP-O+-2))
 (16 1 (:REWRITE O-INFP-O+))
 (14 14 (:LINEAR EXPT-IS-INCREASING-FOR-BASE>1))
 (12 12 (:REWRITE MAKE-ORD-O-FIRST-COEFF))
 (12 5 (:REWRITE O^-O-FIRST-EXPT-3))
 (9 9 (:REWRITE MAKE-ORD-O-FIRST-EXPT))
 (8 4 (:REWRITE DEFAULT-CDR))
 (8 4 (:REWRITE DEFAULT-CAR))
 (8 2 (:REWRITE *-PRESERVES->=-FOR-NONNEGATIVES))
 (6 6 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (4 1 (:REWRITE O-INFP-O+-3))
 )
(|a <= b  =>  a^c <= b^c|
 (2390 289 (:REWRITE O-FIRST-EXPT-O-INFP))
 (1979 55 (:REWRITE O-FIRST-EXPT-<))
 (400 55 (:REWRITE O-FIRST-COEFF-<))
 (393 42 (:REWRITE O-FIRST-EXPT-0-NATP))
 (333 42 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (242 55 (:REWRITE O-FINP-<))
 (234 54 (:REWRITE O-INFP->NEQ-0))
 (232 55 (:REWRITE AC-<))
 (229 27 (:REWRITE O^-O-FIRST-EXPT-3))
 (214 41 (:REWRITE O^-O-FIRST-EXPT))
 (201 201 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (201 201 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (150 15 (:REWRITE NATP-POSP))
 (147 31 (:REWRITE O-INFP-O^-1))
 (146 23 (:REWRITE O<=-O-FINP-DEF))
 (135 15 (:REWRITE POSP-RW))
 (104 27 (:REWRITE O^-O-FIRST-EXPT-2))
 (89 56 (:REWRITE DEFAULT-<-1))
 (88 25 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (79 79 (:REWRITE NATP-RW))
 (75 56 (:REWRITE DEFAULT-<-2))
 (72 72 (:META CANCEL_PLUS-LESSP-CORRECT))
 (64 16 (:REWRITE <-0-+-NEGATIVE-1))
 (63 63 (:REWRITE |a < b & b < c  =>  a < c|))
 (62 39 (:REWRITE O-FIRST-EXPT-O-P))
 (58 56 (:REWRITE DEFAULT-+-2))
 (57 56 (:REWRITE DEFAULT-+-1))
 (51 17 (:REWRITE FOLD-CONSTS-IN-+))
 (45 45 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (32 8 (:REWRITE O^-LIMITP-O-FIRST-COEFF))
 (22 22 (:REWRITE O-FINP-O-RST))
 (20 5 (:REWRITE DEFAULT-*-2))
 (16 4 (:REWRITE O^-LIMITP-O-RST-2))
 (12 3 (:LINEAR X*Y>1-POSITIVE))
 (11 1 (:REWRITE O*-O-FIRST-EXPT))
 (8 4 (:REWRITE O^-O-RST))
 (7 2 (:REWRITE |(a = 0) & ~(b = 0)  <=>  (a^b = 0)|))
 (7 1 (:REWRITE COMMUTATIVITY-OF-+))
 (5 5 (:REWRITE ZP-OPEN))
 (5 5 (:REWRITE DEFAULT-*-1))
 (2 2 (:REWRITE EXPONENTS-ADD-FOR-NONNEG-EXPONENTS))
 (2 2 (:REWRITE EXPONENTS-ADD))
 (1 1 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP))
 (1 1 (:DEFINITION FIX))
 )
(|a <= b & c < d  =>  a^c < b^d|
 (1876 8 (:DEFINITION OB^))
 (672 8 (:REWRITE O*-O-INFP-DEF))
 (448 48 (:REWRITE MAKE-ORD-EQUAL-4))
 (417 95 (:REWRITE O-FIRST-EXPT-O-INFP))
 (322 157 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (294 147 (:TYPE-PRESCRIPTION O^-O-FINP))
 (248 40 (:DEFINITION OMEGA-TERM))
 (192 8 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (184 40 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (164 40 (:REWRITE O-INFP->NEQ-0))
 (126 126 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (126 126 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (118 40 (:REWRITE O^-^))
 (105 27 (:REWRITE O-FIRST-COEFF-<))
 (104 8 (:REWRITE O--0))
 (96 40 (:REWRITE O*-O-FINP))
 (96 32 (:LINEAR O-FIRST-EXPT-<=))
 (88 8 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (80 64 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (80 32 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (77 28 (:REWRITE O-FINP-<))
 (77 28 (:REWRITE AC-<))
 (75 28 (:REWRITE O-FIRST-EXPT-<))
 (72 72 (:TYPE-PRESCRIPTION MAKE-ORD))
 (64 32 (:TYPE-PRESCRIPTION O+-O-FINP))
 (50 50 (:REWRITE NATP-RW))
 (48 16 (:REWRITE O-FIRST-EXPT-0-NATP))
 (38 28 (:REWRITE |a < b & b < c  =>  a < c|))
 (35 2 (:REWRITE O-INFP-O-FINP-O<=))
 (32 32 (:TYPE-PRESCRIPTION OB+))
 (32 32 (:REWRITE O-FINP-O-RST))
 (32 8 (:REWRITE NATP-POSP))
 (15 2 (:REWRITE O<=-O-FINP-DEF))
 (14 2 (:REWRITE O-INFP-O^-1))
 (8 8 (:REWRITE |a0 = 0|))
 (8 8 (:REWRITE POSP-RW))
 (8 8 (:REWRITE O+-ATOM-DEF))
 (8 8 (:REWRITE DEFAULT-+-2))
 (8 8 (:REWRITE DEFAULT-+-1))
 (8 2 (:REWRITE O^-O-FIRST-EXPT))
 (1 1 (:REWRITE |~(a < a)|))
 (1 1 (:REWRITE |a <= b  =>  c^a <= c^b|))
 )
(|a <= b & c <= d  =>  a^c <= b^d|
 (1414 6 (:DEFINITION OB^))
 (536 268 (:TYPE-PRESCRIPTION O^-O-FINP))
 (504 6 (:REWRITE O*-O-INFP-DEF))
 (408 103 (:REWRITE O-FIRST-EXPT-O-INFP))
 (358 157 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (336 36 (:REWRITE MAKE-ORD-EQUAL-4))
 (240 35 (:REWRITE O-FIRST-EXPT-<))
 (194 35 (:REWRITE O-FIRST-COEFF-<))
 (186 30 (:DEFINITION OMEGA-TERM))
 (154 36 (:REWRITE O-INFP->NEQ-0))
 (144 6 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (138 30 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (109 35 (:REWRITE O-FINP-<))
 (109 35 (:REWRITE AC-<))
 (104 104 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (104 104 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (102 30 (:REWRITE O^-^))
 (101 10 (:REWRITE O-INFP-O-FINP-O<=))
 (78 6 (:REWRITE O--0))
 (72 30 (:REWRITE O*-O-FINP))
 (66 6 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (60 48 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (60 24 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (54 54 (:TYPE-PRESCRIPTION MAKE-ORD))
 (48 24 (:TYPE-PRESCRIPTION O+-O-FINP))
 (46 10 (:REWRITE O<=-O-FINP-DEF))
 (42 42 (:REWRITE NATP-RW))
 (36 12 (:REWRITE O-P-DEF-O-FINP-1))
 (36 12 (:REWRITE O-FIRST-EXPT-0-NATP))
 (35 35 (:REWRITE |a < b & b < c  =>  a < c|))
 (28 6 (:REWRITE O^-O-FIRST-EXPT))
 (28 4 (:REWRITE O-INFP-O^-1))
 (24 24 (:TYPE-PRESCRIPTION OB+))
 (24 24 (:REWRITE O-FINP-O-RST))
 (24 6 (:REWRITE NATP-POSP))
 (6 6 (:REWRITE |a0 = 0|))
 (6 6 (:REWRITE POSP-RW))
 (6 6 (:REWRITE O+-ATOM-DEF))
 (6 6 (:REWRITE DEFAULT-+-2))
 (6 6 (:REWRITE DEFAULT-+-1))
 (2 1 (:REWRITE O^-O-FIRST-EXPT-2))
 (1 1 (:REWRITE O^-O-FIRST-EXPT-3))
 )
(O^1C-L1
 (7208 4 (:DEFINITION OB^))
 (4607 17 (:DEFINITION OB+))
 (2596 75 (:REWRITE MAKE-ORD-EQUAL-4))
 (1254 27 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (997 115 (:REWRITE O-INFP->NEQ-0))
 (901 129 (:REWRITE O-FIRST-EXPT-<))
 (853 5 (:REWRITE O*-O-FIRST-EXPT))
 (550 414 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (523 128 (:REWRITE O-FIRST-COEFF-<))
 (511 50 (:REWRITE O-FIRST-EXPT-0-NATP))
 (474 22 (:REWRITE O--0))
 (470 10 (:REWRITE OCMP-GT))
 (414 414 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (387 129 (:REWRITE AC-<))
 (376 14 (:DEFINITION OMEGA-TERM))
 (363 129 (:REWRITE O-FINP-<))
 (357 13 (:REWRITE OCMP-LT))
 (329 129 (:REWRITE |a < b & b < c  =>  a < c|))
 (313 57 (:REWRITE O^-O-FIRST-EXPT-3))
 (258 129 (:REWRITE O*-O-FIRST-COEFF))
 (204 163 (:REWRITE O-FINP-O-RST))
 (168 28 (:REWRITE O-INFP-O-FINP-O<=))
 (144 8 (:REWRITE |0 < a  =  ~(a = 0)|))
 (140 5 (:REWRITE |(o-first-expt a) < a|))
 (137 25 (:REWRITE O-INFP-O^-1))
 (135 6 (:DEFINITION EXPT))
 (128 8 (:REWRITE |0+a = a|))
 (108 108 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (108 60 (:REWRITE NATP-RW))
 (88 4 (:REWRITE O-FIRST-EXPT-O--<))
 (84 28 (:REWRITE O<=-O-FINP-DEF))
 (82 48 (:REWRITE DEFAULT-+-2))
 (78 48 (:REWRITE DEFAULT-+-1))
 (64 64 (:REWRITE O^-O-FIRST-EXPT))
 (64 8 (:REWRITE |(a = 0) & ~(b = 0)  <=>  (a^b = 0)|))
 (57 19 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (56 14 (:REWRITE COMMUTATIVITY-OF-+))
 (56 12 (:LINEAR EXPT->-1))
 (55 16 (:REWRITE DEFAULT-*-2))
 (38 19 (:REWRITE O*-O-FINP))
 (36 36 (:REWRITE EQUAL-CONSTANT-+))
 (31 27 (:REWRITE O+-ATOM-DEF))
 (26 18 (:REWRITE DEFAULT-<-2))
 (25 25 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP))
 (25 6 (:REWRITE ZIP-OPEN))
 (24 24 (:LINEAR EXPT-IS-INCREASING-FOR-BASE>1))
 (23 23 (:TYPE-PRESCRIPTION OCMP))
 (19 2 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (18 18 (:REWRITE DEFAULT-<-1))
 (18 18 (:META CANCEL_PLUS-LESSP-CORRECT))
 (16 16 (:REWRITE DEFAULT-*-1))
 (16 8 (:TYPE-PRESCRIPTION O+-O-FINP))
 (16 4 (:REWRITE NATP-POSP))
 (12 4 (:REWRITE UNICITY-OF-0))
 (10 10 (:REWRITE O^-LIMITP-O-FIRST-COEFF))
 (9 9 (:REWRITE O^-LIMITP-O-RST-2))
 (8 8 (:TYPE-PRESCRIPTION OB+))
 (6 6 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (4 4 (:REWRITE POSP-RW))
 (4 4 (:REWRITE POSP-O-FIRST-COEFF))
 (2 2 (:REWRITE /R-WHEN-ABS-NUMERATOR=1))
 (1 1 (:REWRITE |~(a < a)|))
 (1 1 (:REWRITE DEFAULT-UNARY-/))
 )
(O^1C
 (3761 19 (:DEFINITION OB+))
 (1996 65 (:REWRITE MAKE-ORD-EQUAL-4))
 (1468 28 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (1248 6 (:REWRITE O+-INF))
 (968 132 (:REWRITE O-INFP->NEQ-0))
 (958 7 (:REWRITE O*-O-FIRST-EXPT))
 (786 114 (:REWRITE O-FIRST-EXPT-<))
 (669 6 (:REWRITE MAKE-ORD-O-P))
 (579 73 (:REWRITE O-FIRST-EXPT-0-NATP))
 (477 93 (:REWRITE O-P-O^))
 (458 356 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (435 111 (:REWRITE O-FIRST-COEFF-<))
 (424 28 (:REWRITE O--0))
 (412 13 (:REWRITE |(o-first-expt a) < a|))
 (364 76 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (356 356 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (351 75 (:REWRITE O-FIRST-EXPT-O-P))
 (348 114 (:REWRITE AC-<))
 (333 9 (:REWRITE OCMP-GT))
 (312 114 (:REWRITE O-FINP-<))
 (309 114 (:REWRITE |a < b & b < c  =>  a < c|))
 (276 54 (:REWRITE O^-O-FIRST-EXPT-2))
 (270 54 (:REWRITE O^-O-FIRST-EXPT-3))
 (263 16 (:REWRITE OCMP-LT))
 (218 109 (:TYPE-PRESCRIPTION O*-FINITE))
 (183 6 (:REWRITE |(b > 1)  =>  (a < b  <=>  a-1 < b-1|))
 (174 134 (:REWRITE O-FINP-O-RST))
 (159 12 (:REWRITE |0 < a  =  ~(a = 0)|))
 (150 12 (:REWRITE |~(a=0)  =>  (a < b  <=>  a-1 < b-1)|))
 (138 24 (:REWRITE O-INFP-O-FINP-O<=))
 (137 32 (:REWRITE DEFAULT-*-2))
 (135 27 (:REWRITE O-INFP-O^-1))
 (120 9 (:REWRITE |0+a = a|))
 (117 117 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (116 58 (:REWRITE O*-O-FIRST-COEFF))
 (110 73 (:REWRITE DEFAULT-+-2))
 (107 73 (:REWRITE DEFAULT-+-1))
 (107 71 (:REWRITE NATP-RW))
 (88 88 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (81 9 (:REWRITE O^-O-RST))
 (72 24 (:REWRITE O<=-O-FINP-DEF))
 (71 11 (:REWRITE ZIP-OPEN))
 (68 2 (:LINEAR X*Y>1-POSITIVE))
 (66 3 (:REWRITE O-FIRST-EXPT-O--<))
 (64 10 (:REWRITE |(a = 0) & ~(b = 0)  <=>  (a^b = 0)|))
 (59 59 (:REWRITE O^-O-FIRST-EXPT))
 (57 19 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (48 12 (:REWRITE NATP-POSP))
 (42 26 (:REWRITE EQUAL-CONSTANT-+))
 (40 10 (:REWRITE <-0-+-NEGATIVE-1))
 (34 28 (:REWRITE O+-ATOM-DEF))
 (33 6 (:REWRITE |(a-1 = 0)  <=>  a <= 1|))
 (32 32 (:REWRITE DEFAULT-*-1))
 (27 27 (:META CANCEL_PLUS-LESSP-CORRECT))
 (25 25 (:TYPE-PRESCRIPTION OCMP))
 (25 17 (:REWRITE DEFAULT-<-2))
 (24 8 (:REWRITE FOLD-CONSTS-IN-+))
 (17 17 (:REWRITE DEFAULT-<-1))
 (14 14 (:REWRITE O^-LIMITP-O-FIRST-COEFF))
 (12 12 (:REWRITE POSP-RW))
 (10 10 (:LINEAR EXPT-IS-INCREASING-FOR-BASE>1))
 (9 9 (:REWRITE O^-LIMITP-O-RST-2))
 (9 3 (:REWRITE UNICITY-OF-0))
 (8 8 (:REWRITE EXPONENTS-ADD-FOR-NONNEG-EXPONENTS))
 (8 8 (:REWRITE EXPONENTS-ADD))
 (6 6 (:REWRITE POSP-O-FIRST-COEFF))
 (4 2 (:REWRITE DEFAULT-CDR))
 (4 2 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE |~(a < a)|))
 (2 2 (:REWRITE /R-WHEN-ABS-NUMERATOR=1))
 (1 1 (:REWRITE DEFAULT-UNARY-/))
 )
(O^1
 (202 101 (:TYPE-PRESCRIPTION O*-FINITE))
 (165 1 (:DEFINITION OB^))
 (149 5 (:REWRITE MAKE-ORD-EQUAL-4))
 (76 1 (:REWRITE O*-O-FIRST-EXPT))
 (73 5 (:REWRITE O--0))
 (70 1 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (64 1 (:REWRITE |(o-first-expt a) < a|))
 (52 11 (:REWRITE O-INFP->NEQ-0))
 (49 4 (:REWRITE O^-^))
 (48 9 (:REWRITE O-FIRST-EXPT-0-NATP))
 (47 10 (:REWRITE O-FIRST-EXPT-<))
 (47 9 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (40 20 (:TYPE-PRESCRIPTION O^-O-FINP))
 (36 3 (:DEFINITION OMEGA-TERM))
 (34 10 (:REWRITE |a < b & b < c  =>  a < c|))
 (33 1 (:DEFINITION EXPT))
 (31 9 (:REWRITE O-FIRST-COEFF-<))
 (29 29 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (29 29 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (28 13 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (24 10 (:REWRITE O-FINP-<))
 (24 10 (:REWRITE AC-<))
 (22 1 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (20 1 (:REWRITE |~(a=0)  =>  (a < b  <=>  a-1 < b-1)|))
 (16 4 (:REWRITE NATP-POSP))
 (15 3 (:REWRITE O*-O-FINP))
 (11 3 (:REWRITE O-INFP-O^-1))
 (11 2 (:REWRITE DEFAULT-*-2))
 (9 9 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (8 8 (:REWRITE NATP-RW))
 (8 4 (:REWRITE O*-O-FIRST-COEFF))
 (8 1 (:REWRITE ZIP-OPEN))
 (7 1 (:REWRITE COMMUTATIVITY-OF-+))
 (6 3 (:TYPE-PRESCRIPTION O+-O-FINP))
 (6 2 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (6 1 (:REWRITE O-INFP-O-FINP-O<=))
 (5 5 (:REWRITE O^-O-FIRST-EXPT))
 (5 4 (:REWRITE DEFAULT-+-2))
 (5 4 (:REWRITE DEFAULT-+-1))
 (4 4 (:REWRITE POSP-RW))
 (4 4 (:REWRITE O-FINP-O-RST))
 (4 1 (:REWRITE O^-O-FIRST-EXPT-3))
 (4 1 (:REWRITE <-0-+-NEGATIVE-1))
 (3 3 (:TYPE-PRESCRIPTION OB+))
 (3 1 (:REWRITE O<=-O-FINP-DEF))
 (3 1 (:REWRITE FOLD-CONSTS-IN-+))
 (3 1 (:REWRITE EQUAL-CONSTANT-+))
 (2 2 (:REWRITE DEFAULT-*-1))
 (2 2 (:META CANCEL_PLUS-LESSP-CORRECT))
 (1 1 (:REWRITE |~(a < a)|))
 (1 1 (:REWRITE O^-LIMITP-O-FIRST-COEFF))
 (1 1 (:REWRITE O+-ATOM-DEF))
 (1 1 (:REWRITE EXPONENTS-ADD-FOR-NONNEG-EXPONENTS))
 (1 1 (:REWRITE EXPONENTS-ADD))
 (1 1 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:DEFINITION FIX))
 )
(O^2C-L1-L1
 (122 9 (:REWRITE MAKE-ORD-EQUAL-4))
 (48 10 (:REWRITE O-FIRST-EXPT-O-INFP))
 (40 40 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (32 1 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (31 24 (:REWRITE DEFAULT-*-2))
 (26 24 (:REWRITE DEFAULT-*-1))
 (20 4 (:REWRITE O-FIRST-EXPT-<))
 (18 2 (:REWRITE LIMITP-DEF))
 (16 14 (:REWRITE DEFAULT-+-2))
 (16 14 (:REWRITE DEFAULT-+-1))
 (12 6 (:REWRITE DEFAULT-CDR))
 (12 6 (:REWRITE DEFAULT-CAR))
 (11 11 (:REWRITE EQUAL-CONSTANT-+))
 (10 10 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (10 4 (:REWRITE O-INFP->NEQ-0))
 (9 9 (:REWRITE DEFAULT-UNARY-MINUS))
 (8 4 (:REWRITE O-FINP-<))
 (8 4 (:REWRITE AC-<))
 (8 2 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (8 2 (:LINEAR X*Y>1-POSITIVE))
 (7 2 (:REWRITE O-INFP-O-FINP-O<=))
 (6 3 (:REWRITE O*-O-FIRST-COEFF))
 (6 2 (:REWRITE O-FIRST-EXPT-0-NATP))
 (4 4 (:REWRITE |a < b & b < c  =>  a < c|))
 (4 4 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (4 3 (:REWRITE O-FINP-O-RST))
 (4 2 (:REWRITE O<=-O-FINP-DEF))
 (2 2 (:REWRITE NATP-RW))
 (2 2 (:REWRITE FOLD-CONSTS-IN-+))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:META CANCEL_PLUS-LESSP-CORRECT))
 (1 1 (:REWRITE NATPART-DEF-O-FINP))
 )
(O^2C-L1
 (245 2 (:REWRITE O*-O-FIRST-EXPT-SMASH-1A))
 (78 2 (:REWRITE O*-O-FIRST-EXPT))
 (46 12 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (41 27 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (32 2 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (26 6 (:REWRITE MAKE-ORD-EQUAL-4))
 (24 6 (:REWRITE O-FIRST-EXPT-<))
 (23 23 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (23 23 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (22 12 (:REWRITE O*-O-FINP))
 (16 6 (:REWRITE O-INFP->NEQ-0))
 (15 2 (:REWRITE |a+0 = a|))
 (14 6 (:REWRITE O-FINP-<))
 (14 6 (:REWRITE AC-<))
 (12 1 (:REWRITE LIMITP-DEF))
 (10 8 (:REWRITE O-FIRST-EXPT-O-P))
 (9 8 (:REWRITE DEFAULT-+-2))
 (8 8 (:REWRITE DEFAULT-+-1))
 (6 6 (:REWRITE |a < b & b < c  =>  a < c|))
 (6 6 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (6 3 (:LINEAR O-FIRST-EXPT-<=))
 (6 2 (:REWRITE O-FIRST-EXPT-O-INFP))
 (5 5 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (4 4 (:REWRITE |~(a < a)|))
 (4 4 (:REWRITE NATP-RW))
 (4 2 (:REWRITE O-FINP-O-RST))
 (4 2 (:REWRITE O*-O-FIRST-COEFF))
 (2 2 (:REWRITE O-FIRST-COEFF-<))
 (2 2 (:REWRITE O+-ATOM-DEF))
 (2 2 (:REWRITE O*-O-FIRST-EXPT-SMASH-2A))
 (2 2 (:REWRITE MAKE-ORD-O-RST))
 (2 2 (:REWRITE MAKE-ORD-O-FIRST-EXPT))
 (1 1 (:REWRITE NATPART-DEF-O-FINP))
 )
(O^2C
 (99 22 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (76 8 (:REWRITE MAKE-ORD-EQUAL-4))
 (46 24 (:REWRITE O*-O-FINP))
 (38 38 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (38 38 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (30 10 (:REWRITE O-FIRST-EXPT-O-INFP))
 (26 6 (:REWRITE O-INFP->NEQ-0))
 (13 11 (:REWRITE DEFAULT-+-2))
 (12 6 (:REWRITE O*-O-FIRST-COEFF))
 (11 11 (:REWRITE DEFAULT-+-1))
 (10 10 (:REWRITE O^-^))
 (9 9 (:REWRITE NATP-RW))
 (8 4 (:LINEAR O-FIRST-EXPT-<=))
 (8 2 (:REWRITE POSP-RW))
 (8 2 (:REWRITE O^-LIMITP-O-FIRST-COEFF))
 (8 2 (:REWRITE NATP-POSP))
 (7 7 (:META CANCEL_PLUS-LESSP-CORRECT))
 (5 5 (:REWRITE DEFAULT-<-2))
 (5 5 (:REWRITE DEFAULT-<-1))
 (4 4 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (2 2 (:REWRITE O-FINP-O-RST))
 )
(O^2
 (84 16 (:REWRITE O-FIRST-EXPT-O-INFP))
 (27 11 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (16 4 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (16 4 (:REWRITE O-INFP->NEQ-0))
 (16 4 (:LINEAR O-FIRST-EXPT-<=))
 (12 12 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (12 12 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (12 4 (:REWRITE O-FIRST-EXPT-0-NATP))
 (12 3 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (9 3 (:REWRITE O*-O-FINP))
 (4 4 (:REWRITE ZP-OPEN))
 (4 4 (:REWRITE DEFAULT-+-2))
 (4 4 (:REWRITE DEFAULT-+-1))
 (4 1 (:REWRITE MAKE-ORD-EQUAL-4))
 (3 3 (:REWRITE NATP-RW))
 (1 1 (:TYPE-PRESCRIPTION MAKE-ORD))
 (1 1 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 )
(O^2-O-INFP
 (107 12 (:REWRITE O-FIRST-EXPT-O-INFP))
 (29 9 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (25 4 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (25 4 (:LINEAR O-FIRST-EXPT-<=))
 (22 4 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (21 3 (:REWRITE O-FIRST-EXPT-0-NATP))
 (18 4 (:REWRITE O-INFP->NEQ-0))
 (10 10 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (10 10 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (10 4 (:REWRITE O*-O-FINP))
 (8 2 (:REWRITE NATP-POSP))
 (8 2 (:REWRITE MAKE-ORD-EQUAL-4))
 (4 4 (:REWRITE NATP-RW))
 (2 2 (:REWRITE POSP-RW))
 (2 2 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(O-FIRST-EXPT-O^2
 (264 132 (:TYPE-PRESCRIPTION O*-FINITE))
 (17 3 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (17 1 (:DEFINITION OB^))
 (9 7 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (7 2 (:REWRITE O-INFP->NEQ-0))
 (6 2 (:REWRITE O-FIRST-EXPT-O-INFP))
 (6 1 (:REWRITE LIMITP-DEF))
 (5 3 (:REWRITE O*-O-FINP))
 (4 1 (:REWRITE POSP-RW))
 (4 1 (:REWRITE NATP-POSP))
 (2 2 (:REWRITE O^-^))
 (2 2 (:REWRITE NATP-RW))
 (2 2 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (2 2 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (2 1 (:LINEAR O-FIRST-EXPT-<=))
 (1 1 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (1 1 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 (1 1 (:META CANCEL_PLUS-LESSP-CORRECT))
 )
(O-LAST-EXPT-O^2
 (195 5 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (99 99 (:TYPE-PRESCRIPTION OB+))
 (85 34 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (77 18 (:REWRITE O-FIRST-EXPT-O-INFP))
 (58 3 (:REWRITE O*-O-FIRST-EXPT))
 (41 6 (:REWRITE O-LAST-EXPT-DEF-O-INFP-1))
 (38 6 (:REWRITE O-FIRST-EXPT-<))
 (32 6 (:REWRITE O-LAST-EXPT-DEF-O-INFP-2))
 (29 5 (:REWRITE O+-ATOM-DEF))
 (26 6 (:REWRITE O-FIRST-COEFF-<))
 (25 3 (:REWRITE O-FIRST-EXPT-0-NATP))
 (21 3 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (19 6 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (19 1 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (18 7 (:REWRITE O-FINP-O-RST))
 (18 3 (:REWRITE LIMITP-DEF))
 (16 2 (:REWRITE MAKE-ORD-EQUAL-4))
 (14 14 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (14 14 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (14 6 (:REWRITE O-FINP-<))
 (14 6 (:REWRITE O*-O-FINP))
 (14 6 (:REWRITE AC-<))
 (11 2 (:LINEAR O-FIRST-EXPT-<=))
 (10 10 (:TYPE-PRESCRIPTION NATP))
 (8 3 (:REWRITE O-INFP->NEQ-0))
 (8 2 (:REWRITE NATP-POSP))
 (6 6 (:REWRITE |a < b & b < c  =>  a < c|))
 (6 1 (:REWRITE |a+0 = a|))
 (5 5 (:REWRITE NATP-RW))
 (4 4 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (4 4 (:REWRITE DEFAULT-+-2))
 (4 4 (:REWRITE DEFAULT-+-1))
 (4 2 (:REWRITE O-FIRST-EXPT-O-P))
 (4 2 (:REWRITE O*-O-FIRST-COEFF))
 (3 1 (:REWRITE EQUAL-CONSTANT-+))
 (2 2 (:REWRITE POSP-RW))
 )
(O-P-O^2
 (16 2 (:REWRITE MAKE-ORD-EQUAL-4))
 (14 4 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (12 2 (:REWRITE LIMITP-DEF))
 (10 4 (:REWRITE O*-O-FINP))
 (8 8 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (8 8 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (6 4 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (6 2 (:REWRITE O-FIRST-EXPT-O-INFP))
 (4 4 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (4 2 (:REWRITE O*-O-FIRST-COEFF))
 (3 3 (:REWRITE NATP-RW))
 (2 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(|a(b-1)+a = ab|
 (273 273 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (40 1 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (22 4 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (11 3 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (7 2 (:REWRITE O-INFP->NEQ-0))
 (6 2 (:REWRITE O-FIRST-EXPT-O-INFP))
 (6 1 (:REWRITE O-FIRST-COEFF-<))
 (5 4 (:REWRITE DEFAULT-+-1))
 (5 3 (:REWRITE O*-O-FINP))
 (4 4 (:REWRITE DEFAULT-+-2))
 (4 1 (:REWRITE O*-O-FIRST-EXPT))
 (3 1 (:REWRITE O-FINP-<))
 (3 1 (:REWRITE AC-<))
 (2 2 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (2 2 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (2 1 (:REWRITE O-FIRST-EXPT-<))
 (1 1 (:REWRITE |a < b & b < c  =>  a < c|))
 )
(|a(b-2)+a = a(b-1)|
 (45 45 (:TYPE-PRESCRIPTION OB+))
 (40 1 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (22 4 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (13 1 (:REWRITE O+-ATOM-DEF))
 (10 2 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (7 2 (:REWRITE O-INFP->NEQ-0))
 (6 5 (:REWRITE DEFAULT-+-2))
 (6 2 (:REWRITE O-FIRST-EXPT-O-INFP))
 (6 1 (:REWRITE O-FIRST-COEFF-<))
 (5 5 (:REWRITE DEFAULT-+-1))
 (4 2 (:REWRITE O*-O-FINP))
 (4 1 (:REWRITE O*-O-FIRST-EXPT))
 (3 1 (:REWRITE O-P-DEF-O-FINP-1))
 (3 1 (:REWRITE O-FINP-<))
 (3 1 (:REWRITE AC-<))
 (2 2 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (2 2 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (2 1 (:REWRITE O-FIRST-EXPT-<))
 (1 1 (:REWRITE |a < b & b < c  =>  a < c|))
 )
(O^2-COUNT
 (298 37 (:REWRITE MAKE-ORD-EQUAL-4))
 (267 92 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (261 136 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (218 102 (:REWRITE O*-O-FINP))
 (186 8 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (179 25 (:REWRITE O-FIRST-EXPT-<))
 (173 173 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (173 173 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (159 39 (:REWRITE O-FIRST-EXPT-O-INFP))
 (144 4 (:REWRITE |(a <= b) & (c <= d)  =>  ac <= bd|))
 (132 14 (:REWRITE O-FIRST-COEFF-<))
 (123 51 (:REWRITE NATP-RW))
 (102 102 (:TYPE-PRESCRIPTION NATP))
 (80 33 (:REWRITE AC-<))
 (78 39 (:REWRITE O*-O-FIRST-COEFF))
 (74 74 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (72 56 (:REWRITE DEFAULT-+-2))
 (72 12 (:REWRITE LIMITP-DEF))
 (56 56 (:REWRITE DEFAULT-+-1))
 (54 15 (:REWRITE O<=-O-FINP-DEF))
 (54 15 (:REWRITE O-INFP-O-FINP-O<=))
 (33 33 (:REWRITE |a < b & b < c  =>  a < c|))
 (32 3 (:REWRITE O-LAST-EXPT-DEF-O-INFP-1))
 (26 3 (:REWRITE O-LAST-EXPT-DEF-O-INFP-2))
 (25 14 (:REWRITE O-FINP-O-RST))
 (24 6 (:REWRITE NATP-POSP))
 (20 8 (:REWRITE O+-ATOM-DEF))
 (17 3 (:REWRITE |a+0 = a|))
 (17 2 (:REWRITE O-FIRST-EXPT-0-NATP))
 (15 15 (:META CANCEL_PLUS-LESSP-CORRECT))
 (7 7 (:REWRITE DEFAULT-<-2))
 (7 7 (:REWRITE DEFAULT-<-1))
 (7 2 (:LINEAR O-FIRST-EXPT-<=))
 (6 6 (:REWRITE POSP-RW))
 (6 2 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (6 2 (:REWRITE O-INFP->NEQ-0))
 (6 1 (:REWRITE O-INFP-O*))
 (3 3 (:REWRITE O-FIRST-EXPT-O-P))
 )
(O^3H-O-FIRST-EXPT
 (2364 8 (:REWRITE PADD-O+))
 (1983 7 (:DEFINITION COUNT1))
 (883 77 (:REWRITE O-FIRST-EXPT-O-INFP))
 (352 36 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (308 14 (:REWRITE O-LAST-EXPT-O-FIRST-EXPT-COUNT))
 (234 9 (:LINEAR O-FIRST-EXPT-<=))
 (218 31 (:REWRITE O-INFP->NEQ-0))
 (199 19 (:REWRITE O-FIRST-EXPT-<))
 (197 8 (:REWRITE O*-O-RST))
 (142 7 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (141 36 (:REWRITE O*-O-FINP))
 (98 10 (:REWRITE O-INFP-O-FINP-O<=))
 (87 17 (:REWRITE O-FIRST-COEFF-<))
 (85 85 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (85 85 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (75 21 (:REWRITE O-FINP-<))
 (71 21 (:REWRITE AC-<))
 (63 15 (:REWRITE NAT-COUNT))
 (60 15 (:REWRITE NATP-POSP))
 (55 46 (:REWRITE NATP-RW))
 (51 9 (:REWRITE MAKE-ORD-EQUAL-4))
 (48 3 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (47 1 (:REWRITE |(a <= b) & (c <= d)  =>  ac <= bd|))
 (43 43 (:TYPE-PRESCRIPTION COUNT1))
 (38 27 (:REWRITE DEFAULT-+-2))
 (33 7 (:REWRITE O-FIRST-EXPT-0-NATP))
 (30 30 (:TYPE-PRESCRIPTION PADD))
 (30 10 (:REWRITE O<=-O-FINP-DEF))
 (27 27 (:REWRITE DEFAULT-+-1))
 (24 1 (:REWRITE |(a <= b) & (c < d)  =>  ac < bd|))
 (21 21 (:REWRITE |a < b & b < c  =>  a < c|))
 (16 8 (:REWRITE DEFAULT-<-1))
 (15 15 (:REWRITE POSP-RW))
 (15 5 (:REWRITE EQUAL-CONSTANT-+))
 (14 1 (:REWRITE O*-O-INFP-DEF))
 (12 12 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (12 6 (:REWRITE O*-O-FIRST-COEFF))
 (12 4 (:REWRITE FOLD-CONSTS-IN-+))
 (9 9 (:META CANCEL_PLUS-LESSP-CORRECT))
 (8 8 (:REWRITE O-FINP-O-RST))
 (8 8 (:REWRITE DEFAULT-<-2))
 (6 1 (:REWRITE NOT-LIMITP-NATP))
 (5 5 (:REWRITE ZP-OPEN))
 (4 4 (:TYPE-PRESCRIPTION OLEN))
 (4 2 (:REWRITE NATPART-DEF-O-FINP))
 (4 1 (:REWRITE O*-O-FIRST-EXPT-SMASH-1A))
 (4 1 (:REWRITE O*-LEN-2))
 (3 3 (:REWRITE O+-ATOM-DEF))
 (2 2 (:REWRITE |~(a < a)|))
 (2 1 (:REWRITE O*-O-FIRST-EXPT-SMASH-2A))
 (1 1 (:REWRITE O*-LEN-1))
 )
(LIMIT-O-RST-P-O*
 (750 164 (:REWRITE O-FIRST-EXPT-O-INFP))
 (599 28 (:REWRITE MAKE-ORD-EQUAL-4))
 (432 18 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (377 26 (:REWRITE NOT-LIMITP-NATP))
 (348 94 (:REWRITE O-INFP->NEQ-0))
 (198 18 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (195 143 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (144 72 (:TYPE-PRESCRIPTION O+-O-FINP))
 (137 137 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (126 36 (:REWRITE O-FIRST-COEFF-<))
 (100 25 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (100 25 (:LINEAR O-FIRST-EXPT-<=))
 (97 22 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (75 25 (:REWRITE O-FIRST-EXPT-0-NATP))
 (72 72 (:TYPE-PRESCRIPTION OB+))
 (72 36 (:REWRITE O-FIRST-EXPT-<))
 (72 36 (:REWRITE O-FINP-<))
 (72 36 (:REWRITE AC-<))
 (59 7 (:REWRITE O-INFP-O*))
 (37 4 (:REWRITE LIMITP-DEF))
 (36 36 (:REWRITE |a < b & b < c  =>  a < c|))
 (33 33 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (32 7 (:REWRITE O-INFP-O*-2))
 (28 7 (:REWRITE O*-O-FIRST-EXPT))
 (24 13 (:REWRITE DEFAULT-*-2))
 (24 13 (:REWRITE DEFAULT-*-1))
 (18 18 (:TYPE-PRESCRIPTION NATP))
 (18 18 (:REWRITE O-FINP-O-RST))
 (18 18 (:REWRITE O+-ATOM-DEF))
 (12 12 (:REWRITE NATP-RW))
 (11 6 (:DEFINITION FIX))
 (8 8 (:TYPE-PRESCRIPTION LIMITP))
 (6 6 (:REWRITE O-FIRST-COEFF-0))
 (4 4 (:REWRITE NATPART-O-FINP))
 )
(O-P-O^3H
 (1993 5 (:DEFINITION COUNT1))
 (819 69 (:REWRITE O-FIRST-EXPT-O-INFP))
 (514 24 (:REWRITE O*-O-FIRST-EXPT))
 (377 91 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (328 29 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (320 6 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (303 24 (:REWRITE O-FIRST-EXPT-<))
 (227 6 (:REWRITE O-INFP-O-FINP-O<=))
 (203 33 (:REWRITE O-INFP->NEQ-0))
 (202 7 (:LINEAR O-FIRST-EXPT-<=))
 (126 7 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (124 29 (:REWRITE O*-O-FINP))
 (123 7 (:REWRITE O*-O-RST))
 (122 24 (:REWRITE O-FINP-<))
 (121 24 (:REWRITE AC-<))
 (112 17 (:REWRITE O-INFP-O*-2))
 (103 103 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (103 103 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (91 13 (:REWRITE NATP-POSP))
 (86 23 (:REWRITE O-FIRST-COEFF-<))
 (67 13 (:REWRITE POSP-RW))
 (51 17 (:REWRITE EQUAL-CONSTANT-+))
 (48 6 (:REWRITE MAKE-ORD-EQUAL-4))
 (46 37 (:REWRITE NATP-RW))
 (46 1 (:REWRITE |(a <= b) & (c < d)  =>  ac < bd|))
 (39 6 (:REWRITE O+-ATOM-DEF))
 (38 8 (:REWRITE LIMITP-DEF))
 (31 7 (:REWRITE O-FIRST-EXPT-0-NATP))
 (30 21 (:REWRITE DEFAULT-+-2))
 (29 1 (:REWRITE |(a < b) & ~(c = 0)  <=>  ca < cb|))
 (28 1 (:REWRITE O-LAST-EXPT-DEF-O-INFP-1))
 (24 24 (:REWRITE |a < b & b < c  =>  a < c|))
 (22 11 (:REWRITE DEFAULT-<-2))
 (21 21 (:REWRITE DEFAULT-+-1))
 (18 6 (:REWRITE O<=-O-FINP-DEF))
 (16 11 (:REWRITE DEFAULT-<-1))
 (16 1 (:REWRITE O-LAST-EXPT-DEF-O-INFP-2))
 (12 12 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (12 12 (:META CANCEL_PLUS-LESSP-CORRECT))
 (12 6 (:REWRITE O*-O-FIRST-COEFF))
 (12 4 (:REWRITE NATPART-DEF-O-FINP))
 (12 4 (:REWRITE FOLD-CONSTS-IN-+))
 (8 8 (:REWRITE O-FINP-O-RST))
 (8 3 (:REWRITE |a+0 = a|))
 (4 4 (:REWRITE ZP-OPEN))
 (4 2 (:REWRITE POSP-NATP))
 (4 1 (:REWRITE O*-O-FIRST-EXPT-SMASH-1A))
 (4 1 (:REWRITE O*-LIMITP-2))
 (3 3 (:TYPE-PRESCRIPTION PADD))
 (3 1 (:REWRITE |a(b-1)+a = ab|))
 (2 1 (:REWRITE O*-O-FIRST-EXPT-SMASH-2A))
 (1 1 (:REWRITE |~(a < a)|))
 (1 1 (:REWRITE O-FIRST-EXPT-O-P))
 )
(O^3H
 (1695 4 (:DEFINITION COUNT1))
 (1438 3 (:REWRITE PADD-O+))
 (896 98 (:REWRITE O-FIRST-EXPT-O-INFP))
 (514 36 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (379 107 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (356 17 (:REWRITE O*-O-FIRST-EXPT))
 (297 64 (:REWRITE O-INFP->NEQ-0))
 (235 32 (:LINEAR O-FIRST-EXPT-<=))
 (232 12 (:REWRITE O-FIRST-EXPT-<))
 (204 4 (:REWRITE O-INFP-O-FINP-O<=))
 (157 32 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (150 36 (:REWRITE O*-O-FINP))
 (142 142 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (142 142 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (130 10 (:REWRITE NOT-LIMITP-NATP))
 (108 14 (:REWRITE O-INFP-O*-2))
 (100 6 (:REWRITE O*-O-RST))
 (95 15 (:REWRITE NATP-POSP))
 (85 2 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (82 12 (:REWRITE O-FINP-<))
 (82 12 (:REWRITE AC-<))
 (62 12 (:REWRITE O-FIRST-COEFF-<))
 (60 15 (:REWRITE POSP-RW))
 (55 15 (:REWRITE O-FIRST-EXPT-0-NATP))
 (52 34 (:REWRITE NATP-RW))
 (45 15 (:REWRITE EQUAL-CONSTANT-+))
 (36 9 (:REWRITE MAKE-ORD-EQUAL-4))
 (35 25 (:REWRITE DEFAULT-+-2))
 (32 24 (:REWRITE NATPART-DEF-O-FINP))
 (31 1 (:REWRITE O-LAST-EXPT-DEF-O-INFP-1))
 (25 25 (:REWRITE DEFAULT-+-1))
 (24 13 (:REWRITE DEFAULT-<-2))
 (24 10 (:REWRITE ZP-OPEN))
 (19 13 (:REWRITE DEFAULT-<-1))
 (18 6 (:REWRITE FOLD-CONSTS-IN-+))
 (16 1 (:REWRITE O-LAST-EXPT-DEF-O-INFP-2))
 (15 15 (:META CANCEL_PLUS-LESSP-CORRECT))
 (14 2 (:REWRITE O+-ATOM-DEF))
 (12 12 (:REWRITE |a < b & b < c  =>  a < c|))
 (12 4 (:REWRITE O<=-O-FINP-DEF))
 (9 9 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (8 8 (:REWRITE O-FINP-O-RST))
 (8 2 (:REWRITE O*-O-FIRST-EXPT-SMASH-1A))
 (8 2 (:REWRITE <-0-+-NEGATIVE-1))
 (6 3 (:REWRITE POSP-NATP))
 (6 1 (:REWRITE |a+0 = a|))
 (4 2 (:REWRITE O*-O-FIRST-EXPT-SMASH-2A))
 (4 1 (:REWRITE O*-LIMITP-2))
 (1 1 (:REWRITE O-FIRST-EXPT-O-P))
 )
(O^3SUM
 (20 10 (:TYPE-PRESCRIPTION NATPART-NATP))
 (10 10 (:TYPE-PRESCRIPTION O-P))
 (1 1 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 )
(O^3SUM-DEF-0
 (22 11 (:TYPE-PRESCRIPTION NATPART-NATP))
 (11 11 (:TYPE-PRESCRIPTION O-P))
 (6 2 (:REWRITE NATPART-DEF-O-FINP))
 (4 4 (:TYPE-PRESCRIPTION O-FINP))
 )
(O-P-O^3SUM
 (510 6 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (469 20 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (287 45 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (207 6 (:REWRITE O*-O-FIRST-EXPT))
 (190 22 (:REWRITE O-INFP->NEQ-0))
 (172 34 (:REWRITE O-FIRST-EXPT-O-INFP))
 (165 6 (:REWRITE O+-ATOM-DEF))
 (142 20 (:REWRITE O*-O-FINP))
 (46 46 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (46 46 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (36 6 (:REWRITE O-FIRST-COEFF-<))
 (33 3 (:TYPE-PRESCRIPTION O+-O-FINP))
 (26 8 (:LINEAR O-FIRST-EXPT-<=))
 (25 10 (:REWRITE NATP-RW))
 (24 6 (:REWRITE MAKE-ORD-EQUAL-4))
 (23 8 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (20 16 (:REWRITE DEFAULT-+-2))
 (18 6 (:REWRITE O-FINP-<))
 (18 6 (:REWRITE AC-<))
 (16 16 (:REWRITE DEFAULT-+-1))
 (15 5 (:REWRITE O-FIRST-EXPT-0-NATP))
 (13 1 (:REWRITE NOT-LIMITP-NATP))
 (12 6 (:REWRITE O-FIRST-EXPT-<))
 (12 4 (:REWRITE FOLD-CONSTS-IN-+))
 (11 1 (:REWRITE O*-O-FIRST-EXPT-SMASH-1A))
 (10 10 (:REWRITE NATPART-DEF-O-FINP))
 (10 1 (:REWRITE LIMITP-DEF))
 (9 7 (:REWRITE LIMITPART-DEF-O-FINP))
 (6 6 (:REWRITE |a < b & b < c  =>  a < c|))
 (6 6 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (6 2 (:REWRITE EQUAL-CONSTANT-+))
 (5 1 (:REWRITE LIMITPART-O-RST))
 (4 4 (:REWRITE ZP-OPEN))
 (4 4 (:REWRITE LIMITPART-O-FINP))
 (3 3 (:TYPE-PRESCRIPTION OB+))
 (2 2 (:TYPE-PRESCRIPTION LIMITP))
 (2 1 (:REWRITE O*-O-FIRST-EXPT-SMASH-2A))
 (1 1 (:REWRITE O-FINP-O-RST))
 )
(O^3SUM-O-FIRST-EXPT
 (3452 63 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (1554 65 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (1191 139 (:REWRITE O-FIRST-EXPT-<))
 (839 839 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (510 63 (:REWRITE O+-ATOM-DEF))
 (438 65 (:REWRITE O*-O-FINP))
 (424 139 (:REWRITE O-FINP-<))
 (424 139 (:REWRITE AC-<))
 (402 127 (:REWRITE O-FIRST-COEFF-<))
 (385 98 (:REWRITE O-FIRST-EXPT-O-INFP))
 (348 81 (:REWRITE NATP-RW))
 (179 139 (:REWRITE |a < b & b < c  =>  a < c|))
 (165 30 (:REWRITE O^-^))
 (135 3 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (122 122 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (122 122 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (103 9 (:REWRITE NOT-LIMITP-NATP))
 (88 4 (:REWRITE O-INFP-O-FINP-O<=))
 (80 2 (:REWRITE O+-O-FIRST-EXPT-1))
 (74 58 (:REWRITE DEFAULT-+-2))
 (73 17 (:REWRITE ZP-OPEN))
 (72 8 (:REWRITE LIMITP-DEF))
 (65 43 (:REWRITE NATPART-DEF-O-FINP))
 (58 58 (:REWRITE DEFAULT-+-1))
 (54 1 (:REWRITE O-FIRST-EXPT-O+-<))
 (51 17 (:REWRITE FOLD-CONSTS-IN-+))
 (46 11 (:REWRITE O-FIRST-EXPT-0-NATP))
 (45 1 (:REWRITE O*-O-FIRST-EXPT-SMASH-1A))
 (38 11 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (36 9 (:REWRITE <-0-+-NEGATIVE-1))
 (22 17 (:REWRITE LIMITPART-DEF-O-FINP))
 (22 5 (:REWRITE O-FINP-O-RST))
 (18 18 (:META CANCEL_PLUS-LESSP-CORRECT))
 (18 3 (:REWRITE NATP-POSP))
 (17 1 (:REWRITE O-INFP-O*))
 (15 1 (:REWRITE O^-LIMITP-O-RST-2))
 (12 12 (:REWRITE |~(a < a)|))
 (12 4 (:REWRITE O<=-O-FINP-DEF))
 (11 3 (:REWRITE POSP-RW))
 (9 9 (:REWRITE DEFAULT-<-2))
 (9 9 (:REWRITE DEFAULT-<-1))
 (7 1 (:REWRITE O^-LIMITP-O-RST))
 (6 6 (:REWRITE MAKE-ORD-O-FIRST-EXPT))
 (5 1 (:REWRITE O*-O-FIRST-EXPT-SMASH-2A))
 (5 1 (:REWRITE LIMITPART-O-RST))
 (3 3 (:REWRITE MAKE-ORD-EQUAL-4))
 (3 1 (:REWRITE EQUAL-CONSTANT-+))
 (2 1 (:REWRITE O^-O-RST))
 (1 1 (:REWRITE O-INFP-O*-2))
 )
(O^3SUM-O-FIRST-COEFF
 (2432 39 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (765 90 (:REWRITE O-FIRST-EXPT-<))
 (698 61 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (652 83 (:REWRITE O-FIRST-COEFF-<))
 (636 6 (:REWRITE O+-O-FIRST-COEFF-3))
 (582 98 (:REWRITE O-FIRST-EXPT-O-INFP))
 (373 4 (:REWRITE O+-O-FIRST-COEFF-1))
 (303 39 (:REWRITE O+-ATOM-DEF))
 (258 91 (:REWRITE AC-<))
 (255 61 (:REWRITE O*-O-FINP))
 (207 207 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (207 207 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (155 23 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (141 91 (:REWRITE |a < b & b < c  =>  a < c|))
 (111 12 (:TYPE-PRESCRIPTION O+-O-FINP))
 (107 12 (:REWRITE NOT-LIMITP-NATP))
 (85 18 (:REWRITE O-FIRST-EXPT-0-NATP))
 (62 17 (:LINEAR O-FIRST-EXPT-<=))
 (59 41 (:REWRITE NATPART-DEF-O-FINP))
 (55 55 (:TYPE-PRESCRIPTION NATP))
 (54 27 (:REWRITE NATP-RW))
 (52 13 (:REWRITE MAKE-ORD-EQUAL-4))
 (50 5 (:REWRITE LIMITP-DEF))
 (47 4 (:REWRITE O*-O-FIRST-EXPT-SMASH-1A))
 (42 32 (:REWRITE DEFAULT-+-2))
 (42 14 (:REWRITE EQUAL-CONSTANT-+))
 (32 32 (:REWRITE DEFAULT-+-1))
 (30 10 (:REWRITE FOLD-CONSTS-IN-+))
 (29 1 (:REWRITE |(a < b) & ~(c = 0)  <=>  ca < cb|))
 (26 16 (:REWRITE LIMITPART-DEF-O-FINP))
 (24 8 (:REWRITE O-INFP-O*-2))
 (24 6 (:REWRITE NATP-POSP))
 (24 3 (:REWRITE O-INFP-O-FINP-O<=))
 (23 4 (:REWRITE LIMITPART-O-RST))
 (20 15 (:REWRITE O-FINP-O-RST))
 (12 12 (:TYPE-PRESCRIPTION OB+))
 (11 11 (:REWRITE DEFAULT-*-2))
 (11 11 (:REWRITE DEFAULT-*-1))
 (11 1 (:REWRITE |ab = ac  <=>  (b=c) V (a = 0)|))
 (10 10 (:TYPE-PRESCRIPTION LIMITP))
 (8 4 (:REWRITE O*-O-FIRST-EXPT-SMASH-2A))
 (8 2 (:LINEAR X*Y>1-POSITIVE))
 (8 1 (:REWRITE ZP-OPEN))
 (7 3 (:REWRITE O<=-O-FINP-DEF))
 (6 6 (:REWRITE POSP-RW))
 (6 6 (:REWRITE NATPART-O-FINP))
 (5 5 (:META CANCEL_PLUS-LESSP-CORRECT))
 (4 2 (:REWRITE POSP-NATP))
 (4 1 (:REWRITE <-0-+-NEGATIVE-1))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 )
(O^3H-PADD-O+
 (536 7 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (531 2 (:DEFINITION O^3SUM))
 (273 21 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (249 7 (:REWRITE O*-O-FIRST-EXPT))
 (136 37 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (111 17 (:REWRITE O-INFP->NEQ-0))
 (110 16 (:REWRITE O-FIRST-EXPT-O-INFP))
 (106 11 (:REWRITE O-FIRST-COEFF-<))
 (89 21 (:REWRITE O*-O-FINP))
 (88 7 (:REWRITE O+-ATOM-DEF))
 (58 58 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (58 58 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (57 12 (:REWRITE O-FIRST-EXPT-<))
 (51 51 (:TYPE-PRESCRIPTION PADD))
 (51 51 (:TYPE-PRESCRIPTION OB+))
 (46 1 (:REWRITE O-LAST-EXPT-DEF-O-INFP-2))
 (46 1 (:REWRITE |(a <= b) & (c < d)  =>  ac < bd|))
 (37 1 (:REWRITE O-LAST-EXPT-DEF-O-INFP-1))
 (32 4 (:REWRITE MAKE-ORD-EQUAL-4))
 (29 1 (:REWRITE |(a < b) & ~(c = 0)  <=>  ca < cb|))
 (28 12 (:REWRITE O-FINP-<))
 (28 4 (:REWRITE O-INFP-O*-2))
 (27 12 (:REWRITE AC-<))
 (24 9 (:REWRITE NATP-RW))
 (24 8 (:REWRITE NATPART-DEF-O-FINP))
 (22 2 (:REWRITE O*-O-RST))
 (20 20 (:TYPE-PRESCRIPTION NATP))
 (18 6 (:REWRITE EQUAL-CONSTANT-+))
 (17 1 (:REWRITE O-INFP-O-FINP-O<=))
 (17 1 (:REWRITE O*-LIMITP-2))
 (16 12 (:REWRITE DEFAULT-+-2))
 (13 1 (:REWRITE NOT-LIMITP-NATP))
 (12 12 (:REWRITE |a < b & b < c  =>  a < c|))
 (12 12 (:REWRITE DEFAULT-+-1))
 (12 4 (:REWRITE FOLD-CONSTS-IN-+))
 (12 3 (:REWRITE LIMITP-DEF))
 (12 2 (:REWRITE O*-O-FIRST-EXPT-SMASH-1A))
 (11 3 (:REWRITE LIMITPART-O-RST))
 (11 3 (:LINEAR O-FIRST-EXPT-<=))
 (10 3 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (9 7 (:REWRITE LIMITPART-DEF-O-FINP))
 (9 3 (:REWRITE O-FIRST-EXPT-0-NATP))
 (8 8 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (8 4 (:REWRITE O*-O-FIRST-COEFF))
 (7 2 (:REWRITE |a+0 = a|))
 (4 4 (:REWRITE O-FINP-O-RST))
 (4 2 (:REWRITE POSP-NATP))
 (4 2 (:REWRITE O*-O-FIRST-EXPT-SMASH-2A))
 (4 1 (:REWRITE NATP-POSP))
 (4 1 (:REWRITE NAT-COUNT))
 (3 1 (:REWRITE |a(b-1)+a = ab|))
 (3 1 (:REWRITE O<=-O-FINP-DEF))
 (2 2 (:META CANCEL_PLUS-LESSP-CORRECT))
 (1 1 (:REWRITE |~(a < a)|))
 (1 1 (:REWRITE POSP-RW))
 (1 1 (:REWRITE O-FIRST-EXPT-O-P))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 )
(O^3HC
 (8646 14 (:DEFINITION COUNT1))
 (3920 72 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (3724 381 (:REWRITE O-FIRST-EXPT-O-INFP))
 (3686 125 (:REWRITE O*-O-FIRST-EXPT))
 (2440 648 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (2295 159 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (1897 5 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (1807 278 (:REWRITE O-INFP->NEQ-0))
 (1773 161 (:REWRITE O-FIRST-COEFF-<))
 (1536 176 (:REWRITE O-FIRST-EXPT-<))
 (1201 5 (:REWRITE PADD-O-FIRST-EXPT))
 (938 74 (:LINEAR O-FIRST-EXPT-<=))
 (923 62 (:REWRITE O-INFP-O*-2))
 (836 159 (:REWRITE O*-O-FINP))
 (823 25 (:REWRITE O*-O-RST))
 (753 72 (:REWRITE O+-ATOM-DEF))
 (551 551 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (551 551 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (545 176 (:REWRITE O-FINP-<))
 (544 176 (:REWRITE AC-<))
 (459 77 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (418 60 (:REWRITE O-FIRST-EXPT-0-NATP))
 (417 25 (:REWRITE O-INFP-O-FINP-O<=))
 (383 7 (:REWRITE O^3H-O-FIRST-EXPT))
 (328 176 (:REWRITE |a < b & b < c  =>  a < c|))
 (231 30 (:REWRITE NOT-LIMITP-NATP))
 (220 4 (:REWRITE O-LAST-EXPT-DEF-O-INFP-2))
 (214 94 (:REWRITE NATP-RW))
 (212 151 (:REWRITE DEFAULT-+-2))
 (191 191 (:TYPE-PRESCRIPTION NATP))
 (186 3 (:REWRITE O-INFP-O+))
 (178 22 (:REWRITE NATP-POSP))
 (172 4 (:REWRITE |(a <= b) & (c < d)  =>  ac < bd|))
 (156 96 (:REWRITE NATPART-DEF-O-FINP))
 (151 151 (:REWRITE DEFAULT-+-1))
 (150 50 (:REWRITE EQUAL-CONSTANT-+))
 (138 22 (:REWRITE POSP-RW))
 (137 47 (:REWRITE MAKE-ORD-EQUAL-4))
 (132 44 (:REWRITE FOLD-CONSTS-IN-+))
 (126 25 (:REWRITE O<=-O-FINP-DEF))
 (116 37 (:REWRITE |a+0 = a|))
 (105 4 (:REWRITE O-LAST-EXPT-DEF-O-INFP-1))
 (98 17 (:REWRITE LIMITP-DEF))
 (96 3 (:REWRITE O-INFP-O+-3))
 (88 62 (:REWRITE LIMITPART-DEF-O-FINP))
 (84 4 (:REWRITE O*-LIMITP-2))
 (75 3 (:REWRITE O+-O-FIRST-EXPT-2))
 (68 15 (:REWRITE LIMITPART-O-RST))
 (68 4 (:REWRITE |(a < b) & ~(c = 0)  <=>  ca < cb|))
 (66 3 (:REWRITE O-INFP-O+-2))
 (63 3 (:REWRITE O+-O-FIRST-EXPT-1))
 (62 54 (:REWRITE O-FINP-O-RST))
 (52 32 (:REWRITE O-FIRST-EXPT-O-P))
 (51 8 (:REWRITE O*-O-FIRST-EXPT-SMASH-1A))
 (50 27 (:REWRITE DEFAULT-<-2))
 (41 27 (:REWRITE DEFAULT-<-1))
 (39 13 (:REWRITE |a(b-1)+a = ab|))
 (30 30 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (29 29 (:META CANCEL_PLUS-LESSP-CORRECT))
 (16 8 (:REWRITE O*-O-FIRST-EXPT-SMASH-2A))
 (15 15 (:REWRITE |~(a < a)|))
 (14 14 (:REWRITE NATPART-O-FINP))
 (14 7 (:REWRITE POSP-NATP))
 (13 12 (:REWRITE OLEN-POSP))
 (4 1 (:REWRITE <-0-+-NEGATIVE-1))
 )
(O^3
 (1412 5 (:DEFINITION O^3SUM))
 (1400 3 (:DEFINITION COUNT1))
 (1136 61 (:REWRITE O-FIRST-COEFF-<))
 (1031 22 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (770 117 (:REWRITE O-FIRST-EXPT-O-INFP))
 (751 32 (:REWRITE O*-O-FIRST-EXPT))
 (671 225 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (557 65 (:REWRITE O-FIRST-EXPT-<))
 (402 33 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (353 76 (:REWRITE O-INFP->NEQ-0))
 (239 6 (:REWRITE O-INFP-O+))
 (228 3 (:REWRITE O*-O-RST))
 (202 22 (:REWRITE O+-ATOM-DEF))
 (187 10 (:REWRITE O-INFP-O*-2))
 (181 65 (:REWRITE AC-<))
 (171 65 (:REWRITE O-FINP-<))
 (155 155 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (155 155 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (153 33 (:REWRITE O*-O-FINP))
 (108 30 (:TYPE-PRESCRIPTION O+-O-FINP))
 (106 6 (:REWRITE O-INFP-O+-3))
 (105 65 (:REWRITE |a < b & b < c  =>  a < c|))
 (97 21 (:REWRITE O-FIRST-EXPT-0-NATP))
 (81 30 (:LINEAR O-FIRST-EXPT-<=))
 (75 4 (:REWRITE O+-O-FIRST-EXPT-2))
 (73 7 (:REWRITE O-INFP-O*))
 (72 6 (:REWRITE O-INFP-O+-2))
 (65 13 (:REWRITE |a+0 = a|))
 (63 4 (:REWRITE O+-O-FIRST-EXPT-1))
 (60 4 (:REWRITE O-LAST-EXPT-DEF-O-INFP-2))
 (57 4 (:REWRITE O-LAST-EXPT-DEF-O-INFP-1))
 (53 11 (:REWRITE LIMITPART-O-RST))
 (48 8 (:REWRITE O<=-O-FINP-DEF))
 (46 33 (:REWRITE DEFAULT-+-2))
 (43 23 (:REWRITE NATPART-DEF-O-FINP))
 (39 15 (:REWRITE MAKE-ORD-EQUAL-4))
 (36 20 (:REWRITE LIMITPART-DEF-O-FINP))
 (36 8 (:REWRITE O-INFP-O-FINP-O<=))
 (33 33 (:REWRITE DEFAULT-+-1))
 (30 30 (:TYPE-PRESCRIPTION OB+))
 (30 10 (:REWRITE FOLD-CONSTS-IN-+))
 (30 3 (:REWRITE LIMITP-DEF))
 (28 7 (:REWRITE NAT-COUNT))
 (24 20 (:REWRITE O-FINP-O-RST))
 (24 8 (:REWRITE EQUAL-CONSTANT-+))
 (23 23 (:REWRITE NATP-RW))
 (23 3 (:REWRITE |a(b-1)+a = ab|))
 (9 1 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (8 8 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (8 4 (:REWRITE DEFAULT-<-2))
 (8 4 (:REWRITE DEFAULT-<-1))
 (7 7 (:REWRITE NATPART-O-FINP))
 (6 1 (:REWRITE |a+b = 0  <=>  a=0 & b=0|))
 (4 4 (:REWRITE |~(a < a)|))
 (4 4 (:META CANCEL_PLUS-LESSP-CORRECT))
 (4 1 (:REWRITE NATPART-MAKE-ORD))
 (2 1 (:REWRITE POSP-NATP))
 (2 1 (:REWRITE O-P-O+))
 (1 1 (:REWRITE POSP-RW))
 )
(O^3RW
 (2187 8 (:DEFINITION O^3SUM))
 (2108 27 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (1182 39 (:REWRITE O*-O-FIRST-EXPT))
 (951 74 (:REWRITE O-FIRST-COEFF-<))
 (860 263 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (651 117 (:REWRITE O-FIRST-EXPT-O-INFP))
 (636 56 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (625 85 (:REWRITE O-FIRST-EXPT-<))
 (532 2 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (427 72 (:REWRITE O-INFP->NEQ-0))
 (333 27 (:REWRITE O+-ATOM-DEF))
 (292 2 (:REWRITE PADD-O-FIRST-EXPT))
 (246 85 (:REWRITE AC-<))
 (243 85 (:REWRITE O-FINP-<))
 (242 56 (:REWRITE O*-O-FINP))
 (237 5 (:REWRITE O-INFP-O+))
 (167 167 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (167 167 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (137 137 (:TYPE-PRESCRIPTION OB+))
 (130 3 (:REWRITE |(a <= b) & (c < d)  =>  ac < bd|))
 (125 85 (:REWRITE |a < b & b < c  =>  a < c|))
 (112 7 (:REWRITE O-INFP-O*-2))
 (104 5 (:REWRITE O-INFP-O+-3))
 (88 88 (:TYPE-PRESCRIPTION PADD))
 (75 4 (:REWRITE O+-O-FIRST-EXPT-2))
 (70 5 (:REWRITE O-INFP-O+-2))
 (69 8 (:REWRITE O-INFP-O-FINP-O<=))
 (66 50 (:REWRITE DEFAULT-+-2))
 (63 4 (:REWRITE O+-O-FIRST-EXPT-1))
 (62 23 (:LINEAR O-FIRST-EXPT-<=))
 (61 25 (:REWRITE MAKE-ORD-EQUAL-4))
 (60 14 (:REWRITE O-FIRST-EXPT-0-NATP))
 (60 4 (:REWRITE O-LAST-EXPT-DEF-O-INFP-2))
 (57 31 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (57 4 (:REWRITE O-LAST-EXPT-DEF-O-INFP-1))
 (55 3 (:REWRITE |(a < b) & ~(c = 0)  <=>  ca < cb|))
 (53 10 (:REWRITE |a+0 = a|))
 (51 29 (:REWRITE NATPART-DEF-O-FINP))
 (50 50 (:REWRITE DEFAULT-+-1))
 (48 16 (:REWRITE FOLD-CONSTS-IN-+))
 (42 14 (:REWRITE EQUAL-CONSTANT-+))
 (40 32 (:REWRITE O-FIRST-EXPT-O-P))
 (40 4 (:REWRITE LIMITP-DEF))
 (38 8 (:REWRITE |a(b-1)+a = ab|))
 (38 8 (:REWRITE LIMITPART-O-RST))
 (36 24 (:REWRITE LIMITPART-DEF-O-FINP))
 (33 5 (:REWRITE O-INFP-O*))
 (26 20 (:REWRITE O-FINP-O-RST))
 (26 3 (:REWRITE NATP-POSP))
 (25 25 (:REWRITE NATP-RW))
 (21 8 (:REWRITE O<=-O-FINP-DEF))
 (21 3 (:REWRITE POSP-RW))
 (16 4 (:REWRITE NAT-COUNT))
 (12 12 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (12 7 (:REWRITE DEFAULT-<-2))
 (11 11 (:REWRITE |~(a < a)|))
 (10 7 (:REWRITE DEFAULT-<-1))
 (8 8 (:REWRITE NATPART-O-FINP))
 (8 8 (:META CANCEL_PLUS-LESSP-CORRECT))
 (6 2 (:REWRITE NATPART-MAKE-ORD))
 (4 2 (:REWRITE POSP-NATP))
 (2 2 (:REWRITE OLEN-POSP))
 (2 1 (:REWRITE O-P-O+))
 )
(O^3C1
 (1403 18 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (987 15 (:REWRITE O*-O-FIRST-EXPT))
 (533 26 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (497 7 (:REWRITE MAKE-ORD-O-P))
 (490 1 (:REWRITE PADD-O+))
 (481 183 (:TYPE-PRESCRIPTION O*-FINITE))
 (437 1 (:DEFINITION COUNT1))
 (433 34 (:REWRITE O-FIRST-EXPT-<))
 (406 18 (:REWRITE O*-0))
 (386 51 (:REWRITE O-FIRST-EXPT-O-INFP))
 (379 121 (:REWRITE O-P-DEF-O-FINP-1))
 (264 59 (:REWRITE O-INFP->NEQ-0))
 (263 116 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (250 2 (:REWRITE |(ab)c = a(bc)|))
 (245 7 (:REWRITE |0 < a  =  ~(a = 0)|))
 (188 20 (:REWRITE O-P-O*))
 (183 183 (:TYPE-PRESCRIPTION OB*))
 (167 1 (:REWRITE O*-O-RST))
 (162 2 (:REWRITE O+-O-FIRST-EXPT-2))
 (154 154 (:TYPE-PRESCRIPTION MAKE-ORD))
 (127 34 (:REWRITE O-FINP-<))
 (127 34 (:REWRITE AC-<))
 (118 118 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (118 118 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (117 18 (:REWRITE O+-ATOM-DEF))
 (106 28 (:REWRITE O*-O-FINP))
 (106 18 (:LINEAR O-FIRST-EXPT-<=))
 (101 30 (:REWRITE O-FIRST-COEFF-<))
 (79 32 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (62 62 (:TYPE-PRESCRIPTION PADD))
 (61 3 (:REWRITE O^3SUM-O-FIRST-EXPT))
 (56 20 (:REWRITE NATP-RW))
 (55 9 (:REWRITE |a+0 = a|))
 (50 25 (:REWRITE POSP-NATP))
 (50 8 (:REWRITE O-FIRST-EXPT-0-NATP))
 (45 45 (:TYPE-PRESCRIPTION OB+))
 (45 2 (:REWRITE O-LAST-EXPT-O-FIRST-EXPT-COUNT))
 (40 4 (:REWRITE LIMITP-DEF))
 (38 38 (:TYPE-PRESCRIPTION NATP))
 (35 35 (:REWRITE |a < b & b < c  =>  a < c|))
 (33 3 (:REWRITE O-INFP-O-FINP-O<=))
 (30 23 (:REWRITE DEFAULT-+-2))
 (28 7 (:REWRITE MAKE-ORD-EQUAL-4))
 (27 2 (:REWRITE |a(b-2)+a = a(b-1)|))
 (23 23 (:REWRITE DEFAULT-+-1))
 (22 2 (:REWRITE O*-O-FIRST-EXPT-SMASH-1A))
 (20 20 (:REWRITE LIMITPART-O-FINP))
 (20 16 (:REWRITE NATPART-DEF-O-FINP))
 (20 2 (:REWRITE O-INFP-O*-2))
 (17 17 (:REWRITE LIMITPART-O-P))
 (17 1 (:REWRITE |a(b-1)+a = ab|))
 (14 10 (:REWRITE LIMITPART-DEF-O-FINP))
 (13 1 (:REWRITE O^3H-O-FIRST-EXPT))
 (10 2 (:REWRITE O-INFP-O*))
 (10 2 (:REWRITE LIMITPART-O-RST))
 (8 2 (:REWRITE NATP-POSP))
 (8 2 (:REWRITE NAT-COUNT))
 (7 7 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (6 6 (:TYPE-PRESCRIPTION COUNT1))
 (6 2 (:REWRITE O<=-O-FINP-DEF))
 (5 5 (:REWRITE O-FINP-O-RST))
 (4 4 (:REWRITE |~(a < a)|))
 (4 2 (:REWRITE O*-O-FIRST-EXPT-SMASH-2A))
 (4 1 (:REWRITE |~(a<0)|))
 (3 3 (:REWRITE MAKE-ORD-O-FIRST-EXPT))
 (2 2 (:REWRITE POSP-RW))
 (2 2 (:REWRITE NATPART-O-FINP))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1 1 (:META CANCEL_PLUS-LESSP-CORRECT))
 )
(O^-ALT-DEF-L1
 (317 317 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (150 15 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (119 10 (:REWRITE NATP-POSP))
 (74 10 (:REWRITE POSP-RW))
 (59 7 (:REWRITE POSP-NATP))
 (57 9 (:REWRITE O-FIRST-EXPT-O-INFP))
 (53 4 (:REWRITE O-P-DEF-O-FINP-1))
 (49 2 (:REWRITE |(a = 0) & ~(b = 0)  <=>  (a^b = 0)|))
 (44 3 (:REWRITE O-INFP->NEQ-0))
 (37 15 (:REWRITE O*-O-FINP))
 (32 8 (:REWRITE <-0-+-NEGATIVE-1))
 (31 6 (:REWRITE NATP-RW))
 (24 8 (:REWRITE EQUAL-CONSTANT-+))
 (23 23 (:REWRITE DEFAULT-+-2))
 (23 23 (:REWRITE DEFAULT-+-1))
 (22 22 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (22 22 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (20 20 (:META CANCEL_PLUS-LESSP-CORRECT))
 (16 16 (:REWRITE O^-^))
 (13 13 (:TYPE-PRESCRIPTION NATP))
 (10 10 (:REWRITE DEFAULT-<-2))
 (10 10 (:REWRITE DEFAULT-<-1))
 (9 1 (:REWRITE O^-O-FIRST-EXPT))
 (9 1 (:REWRITE O-INFP-O^-1))
 (8 2 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (8 2 (:REWRITE O*-O-FIRST-EXPT-SMASH-1A))
 (8 2 (:REWRITE <-+-NEGATIVE-0-1))
 (8 2 (:LINEAR O-FIRST-EXPT-<=))
 (6 2 (:REWRITE O-FIRST-EXPT-0-NATP))
 (2 2 (:REWRITE O-FINP-O-RST))
 (2 2 (:REWRITE O*-O-FIRST-EXPT-SMASH-2A))
 )
(O^-ALT-DEF-L2
 (1215 1215 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (929 64 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (584 42 (:REWRITE NATP-POSP))
 (362 42 (:REWRITE POSP-RW))
 (360 12 (:REWRITE O-INFP->NEQ-0))
 (303 47 (:REWRITE NATP-RW))
 (226 12 (:REWRITE |(a = 0) & ~(b = 0)  <=>  (a^b = 0)|))
 (224 64 (:REWRITE O*-O-FINP))
 (184 18 (:REWRITE O-FIRST-EXPT-O-INFP))
 (160 40 (:REWRITE <-0-+-NEGATIVE-1))
 (146 130 (:REWRITE DEFAULT-+-2))
 (138 138 (:META CANCEL_PLUS-LESSP-CORRECT))
 (130 130 (:REWRITE DEFAULT-+-1))
 (116 29 (:REWRITE <-+-NEGATIVE-0-1))
 (90 10 (:REWRITE O-INFP-O^-1))
 (82 10 (:REWRITE O^-O-FIRST-EXPT))
 (81 81 (:TYPE-PRESCRIPTION NATP))
 (81 81 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (81 81 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (81 27 (:REWRITE EQUAL-CONSTANT-+))
 (72 72 (:REWRITE O^-^))
 (69 69 (:REWRITE DEFAULT-<-2))
 (69 69 (:REWRITE DEFAULT-<-1))
 (23 1 (:REWRITE O*-0))
 (10 1 (:REWRITE LIMITP-DEF))
 (8 2 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (8 2 (:LINEAR O-FIRST-EXPT-<=))
 (6 6 (:TYPE-PRESCRIPTION NATPART-NATP))
 (6 2 (:REWRITE O-FIRST-EXPT-0-NATP))
 (5 2 (:REWRITE O*-O-FIRST-EXPT-SMASH-1A))
 (2 2 (:TYPE-PRESCRIPTION LIMITP))
 (2 2 (:REWRITE O*-O-FIRST-EXPT-SMASH-2A))
 (1 1 (:REWRITE O-FINP-O-RST))
 (1 1 (:REWRITE NATPART-DEF-O-FINP))
 )
(O^-ALT-DEF
 (379 14 (:REWRITE O^-ALT-DEF-L1))
 (312 20 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (134 14 (:REWRITE NATP-POSP))
 (119 6 (:REWRITE O-INFP->NEQ-0))
 (107 15 (:REWRITE O-FIRST-EXPT-O-INFP))
 (97 18 (:REWRITE NATP-RW))
 (86 14 (:REWRITE POSP-RW))
 (80 11 (:REWRITE O-P-DEF-O-FINP-1))
 (72 20 (:REWRITE O*-O-FINP))
 (66 5 (:REWRITE |(a = 0) & ~(b = 0)  <=>  (a^b = 0)|))
 (38 33 (:REWRITE DEFAULT-+-2))
 (36 9 (:REWRITE <-0-+-NEGATIVE-1))
 (34 34 (:META CANCEL_PLUS-LESSP-CORRECT))
 (33 33 (:REWRITE DEFAULT-+-1))
 (32 8 (:REWRITE <-+-NEGATIVE-0-1))
 (30 30 (:TYPE-PRESCRIPTION NATP))
 (27 3 (:REWRITE O-INFP-O^-1))
 (26 3 (:REWRITE O^-O-FIRST-EXPT))
 (25 7 (:REWRITE POSP-NATP))
 (23 23 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (23 23 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (21 21 (:REWRITE O^-^))
 (17 17 (:REWRITE DEFAULT-<-2))
 (17 17 (:REWRITE DEFAULT-<-1))
 (15 5 (:REWRITE EQUAL-CONSTANT-+))
 (12 3 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (12 3 (:LINEAR O-FIRST-EXPT-<=))
 (10 1 (:REWRITE LIMITP-DEF))
 (9 3 (:REWRITE O-FIRST-EXPT-0-NATP))
 (6 6 (:TYPE-PRESCRIPTION NATPART-NATP))
 (2 2 (:TYPE-PRESCRIPTION LIMITP))
 (1 1 (:REWRITE NATPART-DEF-O-FINP))
 )
(POSP-<-1)
(O^3C2-L1-L1
 (5814 63 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (5437 20 (:DEFINITION O^3SUM))
 (5112 176 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (1989 191 (:REWRITE O-FIRST-EXPT-<))
 (1948 527 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (1477 11 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (1415 11 (:REWRITE |a+b = 0  <=>  a=0 & b=0|))
 (1337 207 (:REWRITE O-FIRST-EXPT-O-INFP))
 (886 176 (:REWRITE O*-O-FINP))
 (768 63 (:REWRITE O+-ATOM-DEF))
 (666 178 (:REWRITE O-FIRST-COEFF-<))
 (631 191 (:REWRITE AC-<))
 (630 191 (:REWRITE O-FINP-<))
 (434 434 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (434 434 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (299 64 (:REWRITE NATP-RW))
 (293 11 (:REWRITE O-INFP-O-FINP-O<=))
 (292 192 (:REWRITE |a < b & b < c  =>  a < c|))
 (261 24 (:REWRITE O-FIRST-EXPT-0-NATP))
 (256 5 (:REWRITE O+-O-FIRST-EXPT-1))
 (238 73 (:REWRITE MAKE-ORD-EQUAL-4))
 (237 22 (:LINEAR O-FIRST-EXPT-<=))
 (220 4 (:REWRITE O-INFP-O+-3))
 (218 171 (:REWRITE DEFAULT-+-2))
 (199 29 (:REWRITE NOT-LIMITP-NATP))
 (171 171 (:REWRITE DEFAULT-+-1))
 (162 4 (:REWRITE O-INFP-O+-2))
 (143 77 (:REWRITE NATPART-DEF-O-FINP))
 (130 24 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (111 23 (:REWRITE |a+0 = a|))
 (110 55 (:REWRITE POSP-NATP))
 (94 78 (:REWRITE LIMITPART-DEF-O-FINP))
 (80 8 (:REWRITE LIMITP-DEF))
 (80 2 (:REWRITE |(a <= b) & (c < d)  =>  ac < bd|))
 (72 2 (:REWRITE |(a < b) & ~(c = 0)  <=>  ca < cb|))
 (56 7 (:REWRITE ZP-OPEN))
 (53 21 (:REWRITE O-FIRST-EXPT-O-P))
 (48 6 (:REWRITE O-INFP-O*))
 (42 34 (:REWRITE O-FINP-O-RST))
 (40 40 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (32 8 (:REWRITE NATP-POSP))
 (28 7 (:REWRITE <-0-+-NEGATIVE-1))
 (22 22 (:REWRITE NATPART-O-FINP))
 (16 16 (:META CANCEL_PLUS-LESSP-CORRECT))
 (16 5 (:REWRITE NATPART-MAKE-ORD))
 (8 8 (:REWRITE POSP-RW))
 (7 7 (:REWRITE |a < b  <=>  c+a < c+b :l1|))
 (7 7 (:REWRITE DEFAULT-<-2))
 (7 7 (:REWRITE DEFAULT-<-1))
 )
(O^3C2-L1-L2
 (1607 6 (:DEFINITION O^3SUM))
 (1340 41 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (1264 18 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (559 32 (:REWRITE O-INFP->NEQ-0))
 (554 13 (:REWRITE O*-O-FIRST-EXPT))
 (431 111 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (315 38 (:REWRITE O-FIRST-EXPT-<))
 (284 50 (:REWRITE O-FIRST-EXPT-O-INFP))
 (269 16 (:REWRITE O^3SUM-O-FIRST-EXPT))
 (262 41 (:REWRITE O*-O-FINP))
 (231 18 (:REWRITE O+-ATOM-DEF))
 (231 4 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (195 4 (:REWRITE |a+b = 0  <=>  a=0 & b=0|))
 (148 4 (:REWRITE MAKE-ORD-O-P))
 (138 42 (:REWRITE O-P-DEF-O-FINP-1))
 (131 38 (:REWRITE AC-<))
 (127 38 (:REWRITE O-FINP-<))
 (110 38 (:REWRITE O-FIRST-COEFF-<))
 (104 8 (:REWRITE |0 < a  =  ~(a = 0)|))
 (90 9 (:REWRITE O*-0))
 (81 81 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (81 81 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (78 10 (:REWRITE O-P-O*))
 (70 2 (:REWRITE O-INFP-O+-3))
 (61 46 (:REWRITE DEFAULT-+-2))
 (60 18 (:REWRITE NATP-RW))
 (53 10 (:REWRITE NOT-LIMITP-NATP))
 (50 2 (:REWRITE O-INFP-O+))
 (48 12 (:REWRITE MAKE-ORD-EQUAL-4))
 (46 46 (:REWRITE DEFAULT-+-1))
 (46 2 (:REWRITE O-INFP-O+-2))
 (43 25 (:REWRITE NATPART-DEF-O-FINP))
 (40 4 (:REWRITE LIMITP-DEF))
 (38 38 (:TYPE-PRESCRIPTION NATP))
 (38 38 (:REWRITE |a < b & b < c  =>  a < c|))
 (35 6 (:REWRITE |a+0 = a|))
 (35 3 (:REWRITE O-FIRST-EXPT-O^2))
 (32 4 (:REWRITE ZP-OPEN))
 (32 2 (:REWRITE O+-O-FIRST-EXPT-2))
 (26 5 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (24 24 (:REWRITE LIMITPART-DEF-O-FINP))
 (24 3 (:REWRITE O^2-O-INFP))
 (24 2 (:REWRITE O+-O-FIRST-EXPT-1))
 (16 5 (:LINEAR O-FIRST-EXPT-<=))
 (16 4 (:REWRITE <-0-+-NEGATIVE-1))
 (15 2 (:REWRITE |a(b-2)+a = a(b-1)|))
 (13 9 (:REWRITE O-FIRST-EXPT-O-P))
 (13 5 (:REWRITE O-FIRST-EXPT-0-NATP))
 (12 12 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (10 10 (:REWRITE LIMITPART-O-P))
 (10 2 (:REWRITE O-P-O^3SUM))
 (9 9 (:REWRITE O-FINP-O-RST))
 (8 8 (:REWRITE NATPART-O-FINP))
 (8 8 (:META CANCEL_PLUS-LESSP-CORRECT))
 (8 2 (:REWRITE O-P-O^2))
 (8 2 (:REWRITE NATP-POSP))
 (6 6 (:REWRITE LIMITPART-O-FINP))
 (5 5 (:REWRITE LIMITPART-LIMITP-TP))
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (4 2 (:REWRITE O<=-O-FINP-DEF))
 (4 2 (:REWRITE O-INFP-O-FINP-O<=))
 (2 2 (:REWRITE POSP-RW))
 (2 2 (:REWRITE MAKE-ORD-O-FIRST-EXPT))
 (2 1 (:REWRITE POSP-NATP))
 )
(O^3C2-L1
 (1308 28 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (1184 14 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (1048 2 (:DEFINITION O^3SUM))
 (960 16 (:REWRITE O*-O-FIRST-EXPT))
 (350 28 (:REWRITE O-FIRST-EXPT-<))
 (314 2 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (218 28 (:REWRITE O*-O-FINP))
 (216 2 (:REWRITE |a+b = 0  <=>  a=0 & b=0|))
 (194 194 (:TYPE-PRESCRIPTION OB+))
 (182 10 (:REWRITE |(a = 0) & ~(b = 0)  <=>  (a^b = 0)|))
 (162 50 (:REWRITE O-P-DEF-O-FINP-1))
 (162 6 (:REWRITE O^-O-FIRST-EXPT))
 (161 35 (:REWRITE NATP-RW))
 (146 14 (:REWRITE O+-ATOM-DEF))
 (126 28 (:REWRITE O-FINP-<))
 (126 28 (:REWRITE AC-<))
 (120 4 (:REWRITE O^3SUM-O-FIRST-EXPT))
 (114 2 (:REWRITE O*-0))
 (96 24 (:REWRITE O^-^))
 (88 60 (:TYPE-PRESCRIPTION NATPART-NATP))
 (86 10 (:REWRITE O-P-O^))
 (85 85 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (85 85 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (84 28 (:REWRITE O-FIRST-COEFF-<))
 (79 26 (:REWRITE O-FIRST-EXPT-O-INFP))
 (60 5 (:REWRITE NATP-POSP))
 (52 6 (:REWRITE |a+0 = a|))
 (48 24 (:REWRITE POSP-NATP))
 (44 36 (:REWRITE DEFAULT-+-2))
 (42 4 (:REWRITE O-P-O*))
 (37 5 (:REWRITE POSP-RW))
 (36 36 (:REWRITE DEFAULT-+-1))
 (36 2 (:REWRITE O+-O-FIRST-EXPT-2))
 (34 34 (:REWRITE LIMITPART-O-P))
 (28 28 (:REWRITE |a < b & b < c  =>  a < c|))
 (26 22 (:REWRITE LIMITPART-DEF-O-FINP))
 (26 6 (:REWRITE NOT-LIMITP-NATP))
 (24 11 (:LINEAR O-FIRST-EXPT-<=))
 (24 6 (:REWRITE <-0-+-NEGATIVE-1))
 (22 14 (:REWRITE O-FIRST-EXPT-O-P))
 (22 2 (:REWRITE O+-O-FIRST-EXPT-1))
 (22 2 (:REWRITE O*-O-FIRST-EXPT-SMASH-1A))
 (20 2 (:REWRITE LIMITP-DEF))
 (18 10 (:REWRITE NATPART-DEF-O-FINP))
 (18 6 (:REWRITE EQUAL-CONSTANT-+))
 (16 2 (:REWRITE ZP-OPEN))
 (14 11 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (12 12 (:META CANCEL_PLUS-LESSP-CORRECT))
 (12 2 (:REWRITE O-P-O^3SUM))
 (10 2 (:REWRITE O*-O-FIRST-EXPT-SMASH-2A))
 (10 2 (:REWRITE LIMITPART-O-RST))
 (8 2 (:REWRITE O-INFP-O-FINP-O<=))
 (6 6 (:REWRITE O-FINP-O-RST))
 (6 6 (:REWRITE DEFAULT-<-2))
 (6 6 (:REWRITE DEFAULT-<-1))
 (6 2 (:REWRITE O<=-O-FINP-DEF))
 (4 4 (:REWRITE NATPART-O-FINP))
 (3 1 (:REWRITE O-FIRST-EXPT-0-NATP))
 )
(POSP-DISTRIBUTIVE
 (684 264 (:TYPE-PRESCRIPTION O*-FINITE))
 (247 247 (:TYPE-PRESCRIPTION OB+))
 (195 29 (:REWRITE O-FIRST-EXPT-<))
 (169 46 (:REWRITE O-FIRST-EXPT-O-INFP))
 (141 8 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (131 26 (:REWRITE O-FIRST-COEFF-<))
 (104 9 (:REWRITE MAKE-ORD-EQUAL-4))
 (77 29 (:REWRITE O-FINP-<))
 (77 29 (:REWRITE AC-<))
 (73 29 (:REWRITE |a < b & b < c  =>  a < c|))
 (59 31 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (54 9 (:REWRITE O-INFP-O-FINP-O<=))
 (42 2 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (27 27 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (27 9 (:REWRITE O<=-O-FINP-DEF))
 (25 25 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (25 3 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (23 1 (:REWRITE O-INFP-O+-2))
 (22 10 (:REWRITE O-P-DEF-O-FINP-1))
 (20 4 (:REWRITE COMMUTATIVITY-OF-+))
 (18 4 (:REWRITE O-INFP->NEQ-0))
 (17 4 (:REWRITE O-FIRST-EXPT-0-NATP))
 (16 8 (:REWRITE DEFAULT-+-2))
 (16 8 (:REWRITE DEFAULT-+-1))
 (16 4 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (16 3 (:LINEAR O-FIRST-EXPT-<=))
 (15 10 (:REWRITE O-FINP-O-RST))
 (10 2 (:REWRITE O*-O-FINP))
 (9 8 (:REWRITE O+-ATOM-DEF))
 (8 5 (:REWRITE DEFAULT-*-2))
 (8 2 (:REWRITE NATP-RW))
 (7 5 (:REWRITE DEFAULT-*-1))
 (6 1 (:REWRITE O-INFP-O+-3))
 (4 4 (:TYPE-PRESCRIPTION NATP))
 (4 4 (:REWRITE O-FIRST-COEFF-0))
 (4 4 (:DEFINITION FIX))
 (4 1 (:REWRITE NATP-POSP))
 (3 3 (:REWRITE |~(a < a)|))
 (2 2 (:REWRITE EQUAL-CONSTANT-+))
 (1 1 (:REWRITE POSP-RW))
 (1 1 (:REWRITE O+-O-RST-2))
 (1 1 (:REWRITE O+-O-FIRST-COEFF-3))
 )
(O^3C2-L2-L1
 (4052 72 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (3209 18 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (2654 10 (:DEFINITION O^3SUM))
 (2337 107 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (1407 167 (:REWRITE O-FIRST-EXPT-<))
 (978 149 (:REWRITE O-FIRST-EXPT-O-INFP))
 (808 149 (:REWRITE O-FIRST-COEFF-<))
 (713 8 (:REWRITE |a+b = 0  <=>  a=0 & b=0|))
 (624 72 (:REWRITE O+-ATOM-DEF))
 (532 4 (:REWRITE O+-O-FIRST-EXPT-2))
 (518 107 (:REWRITE O*-O-FINP))
 (423 168 (:REWRITE AC-<))
 (362 362 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (362 362 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (314 8 (:REWRITE O-INFP-O-FINP-O<=))
 (312 44 (:REWRITE |a+0 = a|))
 (300 6 (:REWRITE O-P-O+))
 (237 4 (:REWRITE O+-O-FIRST-EXPT-1))
 (228 168 (:REWRITE |a < b & b < c  =>  a < c|))
 (188 30 (:REWRITE O-FIRST-EXPT-O-P))
 (169 43 (:REWRITE NATP-RW))
 (158 30 (:REWRITE O-FIRST-EXPT-0-NATP))
 (126 8 (:REWRITE O-INFP-O*))
 (110 88 (:REWRITE DEFAULT-+-2))
 (109 30 (:LINEAR O-FIRST-EXPT-<=))
 (92 68 (:REWRITE NATPART-DEF-O-FINP))
 (88 88 (:REWRITE DEFAULT-+-1))
 (87 30 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (67 28 (:REWRITE MAKE-ORD-EQUAL-4))
 (67 2 (:REWRITE |(a < b) & ~(c = 0)  <=>  ca < cb|))
 (50 5 (:REWRITE LIMITP-DEF))
 (48 5 (:REWRITE O*-O-FIRST-EXPT-SMASH-1A))
 (47 34 (:REWRITE LIMITPART-DEF-O-FINP))
 (35 1 (:REWRITE O-INFP-O+-3))
 (25 1 (:REWRITE O-INFP-O+))
 (24 18 (:REWRITE O-FINP-O-RST))
 (23 4 (:REWRITE LIMITPART-O-RST))
 (23 1 (:REWRITE O-INFP-O+-2))
 (21 8 (:REWRITE O<=-O-FINP-DEF))
 (16 8 (:REWRITE O-INFP-O*-2))
 (16 2 (:REWRITE ZP-OPEN))
 (13 13 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (10 5 (:REWRITE O*-O-FIRST-EXPT-SMASH-2A))
 (8 8 (:REWRITE NATPART-O-FINP))
 (8 2 (:REWRITE <-0-+-NEGATIVE-1))
 (6 6 (:REWRITE |a < b  <=>  c+a < c+b :l1|))
 (6 6 (:REWRITE POSP-RW))
 (5 5 (:META CANCEL_PLUS-LESSP-CORRECT))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 )
(O^3C2-L2-L2
 (961 14 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (747 14 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (549 9 (:REWRITE O*-O-FIRST-EXPT))
 (400 29 (:REWRITE O-FIRST-EXPT-<))
 (279 3 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (188 26 (:REWRITE O-INFP->NEQ-0))
 (160 8 (:REWRITE O-FIRST-EXPT-O^2))
 (156 78 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (150 5 (:REWRITE O^3SUM-O-FIRST-EXPT))
 (129 29 (:REWRITE O-FINP-<))
 (129 29 (:REWRITE AC-<))
 (105 105 (:TYPE-PRESCRIPTION OB+))
 (105 3 (:REWRITE |a+b = 0  <=>  a=0 & b=0|))
 (99 14 (:REWRITE O*-O-FINP))
 (92 14 (:REWRITE O+-ATOM-DEF))
 (82 9 (:REWRITE |a+0 = a|))
 (80 35 (:REWRITE O-P-DEF-O-FINP-1))
 (75 12 (:REWRITE NATP-RW))
 (74 23 (:REWRITE O-FIRST-EXPT-O-INFP))
 (70 29 (:REWRITE O-FIRST-COEFF-<))
 (64 8 (:REWRITE O^2-O-INFP))
 (40 23 (:REWRITE O-FIRST-EXPT-O-P))
 (33 33 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (33 33 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (32 7 (:REWRITE NOT-LIMITP-NATP))
 (29 29 (:REWRITE |a < b & b < c  =>  a < c|))
 (28 13 (:LINEAR O-FIRST-EXPT-<=))
 (27 27 (:TYPE-PRESCRIPTION NATP))
 (24 14 (:REWRITE NATPART-DEF-O-FINP))
 (20 5 (:REWRITE O-P-O^2))
 (18 3 (:REWRITE O-P-O^3SUM))
 (16 16 (:REWRITE LIMITPART-O-P))
 (16 13 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (16 13 (:REWRITE DEFAULT-+-2))
 (16 8 (:REWRITE LIMITPART-O-FIRST-EXPT))
 (16 2 (:REWRITE ZP-OPEN))
 (16 2 (:REWRITE O-P-O*))
 (13 13 (:REWRITE LIMITPART-LIMITP-TP))
 (13 13 (:REWRITE DEFAULT-+-1))
 (10 1 (:REWRITE LIMITP-DEF))
 (8 8 (:REWRITE LIMITPART-O-FINP))
 (8 2 (:REWRITE <-0-+-NEGATIVE-1))
 (6 6 (:REWRITE LIMITPART-DEF-O-FINP))
 (6 3 (:REWRITE POSP-NATP))
 (5 5 (:REWRITE O-FINP-O-RST))
 (5 5 (:REWRITE NATPART-O-FINP))
 (4 4 (:META CANCEL_PLUS-LESSP-CORRECT))
 (4 1 (:REWRITE NATP-POSP))
 (3 1 (:REWRITE O-FIRST-EXPT-0-NATP))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE POSP-RW))
 )
(O^3C2-L2
 (2744 4 (:DEFINITION O^3SUM))
 (2340 32 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (1116 12 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (988 67 (:REWRITE O-INFP->NEQ-0))
 (902 16 (:REWRITE O*-O-FIRST-EXPT))
 (472 8 (:DEFINITION OB^))
 (402 90 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (363 34 (:REWRITE O-FIRST-EXPT-O-INFP))
 (350 22 (:REWRITE O-FIRST-EXPT-<))
 (344 32 (:REWRITE O*-O-FINP))
 (340 2 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (290 62 (:REWRITE O-P-DEF-O-FINP-1))
 (242 16 (:REWRITE O^3C2-L1))
 (242 10 (:REWRITE O*-0))
 (215 45 (:REWRITE NATP-RW))
 (210 2 (:REWRITE |a+b = 0  <=>  a=0 & b=0|))
 (204 12 (:REWRITE O+-ATOM-DEF))
 (200 20 (:REWRITE |(a = 0) & ~(b = 0)  <=>  (a^b = 0)|))
 (196 4 (:REWRITE O-INFP-O*))
 (168 12 (:REWRITE O^-O-FIRST-EXPT))
 (164 6 (:REWRITE O^3SUM-O-FIRST-EXPT))
 (142 16 (:REWRITE O^-^))
 (138 138 (:TYPE-PRESCRIPTION OB+))
 (120 4 (:REWRITE O-INFP-O*-2))
 (116 16 (:REWRITE O-P-O^))
 (106 106 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (106 106 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (106 21 (:REWRITE NATP-POSP))
 (84 22 (:REWRITE O-FINP-<))
 (84 22 (:REWRITE AC-<))
 (72 8 (:REWRITE O-INFP-O^-1))
 (69 21 (:REWRITE POSP-RW))
 (68 22 (:REWRITE O-FIRST-COEFF-<))
 (66 54 (:REWRITE DEFAULT-+-2))
 (54 54 (:REWRITE DEFAULT-+-1))
 (48 24 (:REWRITE POSP-NATP))
 (48 16 (:REWRITE EQUAL-CONSTANT-+))
 (40 10 (:REWRITE <-0-+-NEGATIVE-1))
 (36 4 (:REWRITE |a+0 = a|))
 (36 4 (:REWRITE |a(b-2)+a = a(b-1)|))
 (32 20 (:REWRITE NATPART-DEF-O-FINP))
 (32 16 (:REWRITE LIMITPART-O-FIRST-EXPT))
 (32 6 (:REWRITE NOT-LIMITP-NATP))
 (32 4 (:REWRITE ZP-OPEN))
 (28 28 (:META CANCEL_PLUS-LESSP-CORRECT))
 (26 2 (:REWRITE O-P-O*))
 (24 16 (:REWRITE O-FIRST-EXPT-O-P))
 (22 22 (:REWRITE |a < b & b < c  =>  a < c|))
 (20 4 (:REWRITE |(ab)c = a(bc)|))
 (20 2 (:REWRITE LIMITP-DEF))
 (16 8 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (16 7 (:LINEAR O-FIRST-EXPT-<=))
 (16 4 (:REWRITE <-+-NEGATIVE-0-1))
 (14 14 (:REWRITE DEFAULT-<-2))
 (14 14 (:REWRITE DEFAULT-<-1))
 (12 2 (:REWRITE O-P-O^3SUM))
 (10 7 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (8 8 (:REWRITE LIMITPART-DEF-O-FINP))
 (6 6 (:REWRITE O-FINP-O-RST))
 (4 4 (:REWRITE NATPART-O-FINP))
 (3 1 (:REWRITE O-FIRST-EXPT-0-NATP))
 )
(O^3C2-L4
 (4708 53 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (4631 49 (:REWRITE O*-O-FIRST-EXPT))
 (2704 7 (:DEFINITION O^3SUM))
 (1881 13 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (1510 58 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (1358 109 (:REWRITE O-FIRST-EXPT-<))
 (1076 1 (:REWRITE |a <= b & c < d  =>  a+c < b+d|))
 (1074 1 (:REWRITE O-FIRST-EXPT-<-O+))
 (883 10 (:REWRITE O+-O-FIRST-EXPT-2))
 (868 12 (:REWRITE |a+b = 0  <=>  a=0 & b=0|))
 (710 319 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (702 131 (:REWRITE O-INFP->NEQ-0))
 (622 79 (:REWRITE O-FIRST-EXPT-O-INFP))
 (456 8 (:REWRITE O*-0))
 (455 53 (:REWRITE O+-ATOM-DEF))
 (438 105 (:REWRITE O-FIRST-COEFF-<))
 (418 22 (:REWRITE |(a = 0) & ~(b = 0)  <=>  (a^b = 0)|))
 (414 9 (:REWRITE O-INFP-O-FINP-O<=))
 (413 7 (:DEFINITION OB^))
 (381 109 (:REWRITE O-FINP-<))
 (381 109 (:REWRITE AC-<))
 (336 168 (:TYPE-PRESCRIPTION O^2))
 (325 10 (:REWRITE O+-O-FIRST-EXPT-1))
 (322 33 (:REWRITE |a+0 = a|))
 (282 19 (:REWRITE O^3SUM-O-FIRST-EXPT))
 (266 58 (:REWRITE O*-O-FINP))
 (255 101 (:REWRITE O-FIRST-EXPT-O-P))
 (252 12 (:REWRITE O^-O-FIRST-EXPT))
 (236 3 (:REWRITE O-FIRST-EXPT-O+-<))
 (206 41 (:REWRITE NATP-RW))
 (182 7 (:REWRITE O-FIRST-EXPT-O^2))
 (167 167 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (167 167 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (112 14 (:REWRITE O^2-O-INFP))
 (109 109 (:REWRITE |a < b & b < c  =>  a < c|))
 (102 12 (:REWRITE |a(b-2)+a = a(b-1)|))
 (100 43 (:LINEAR O-FIRST-EXPT-<=))
 (95 14 (:REWRITE O^-^))
 (88 14 (:REWRITE O^3C2-L1))
 (82 68 (:REWRITE DEFAULT-+-2))
 (82 41 (:REWRITE LIMITPART-O-FIRST-EXPT))
 (68 68 (:REWRITE DEFAULT-+-1))
 (61 20 (:REWRITE NOT-LIMITP-NATP))
 (56 7 (:REWRITE ZP-OPEN))
 (55 1 (:REWRITE |a < b  <=>  c+a < c+b|))
 (52 30 (:REWRITE NATPART-DEF-O-FINP))
 (50 43 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (41 12 (:REWRITE NATP-POSP))
 (37 4 (:REWRITE O-INFP-O*))
 (36 9 (:REWRITE <-0-+-NEGATIVE-1))
 (35 9 (:REWRITE O<=-O-FINP-DEF))
 (32 4 (:REWRITE O-INFP-O*-2))
 (28 12 (:REWRITE POSP-RW))
 (28 7 (:REWRITE O-P-O^2))
 (23 5 (:REWRITE O-FIRST-EXPT-0-NATP))
 (18 18 (:REWRITE LIMITPART-DEF-O-FINP))
 (18 18 (:META CANCEL_PLUS-LESSP-CORRECT))
 (14 14 (:REWRITE LIMITPART-LIMITP-TP))
 (14 7 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (12 4 (:REWRITE EQUAL-CONSTANT-+))
 (11 11 (:REWRITE O-FINP-O-RST))
 (10 1 (:REWRITE LIMITP-DEF))
 (9 9 (:REWRITE DEFAULT-<-2))
 (9 9 (:REWRITE DEFAULT-<-1))
 (8 4 (:REWRITE O-INFP-O+-3))
 (8 4 (:REWRITE O-INFP-O+-2))
 (8 4 (:REWRITE O-INFP-O+))
 (4 4 (:REWRITE |~(a < a)|))
 (4 4 (:REWRITE NATPART-O-FINP))
 )
(NEW-IND-2)
(O^3C2-L6
 (474 3 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (373 5 (:REWRITE O*-O-FIRST-EXPT))
 (160 16 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (76 4 (:DEFINITION OB^))
 (75 3 (:REWRITE O*-0))
 (58 1 (:REWRITE |(a <= b) & (c < d)  =>  ac < bd|))
 (49 16 (:REWRITE O*-O-FINP))
 (45 3 (:REWRITE O+-ATOM-DEF))
 (42 27 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (42 6 (:REWRITE |(a = 0) & ~(b = 0)  <=>  (a^b = 0)|))
 (41 1 (:REWRITE |(a < b) & ~(c = 0)  <=>  ca < cb|))
 (36 2 (:REWRITE O^-O-FIRST-EXPT))
 (35 8 (:REWRITE O-FIRST-EXPT-<))
 (32 4 (:REWRITE O^-ALT-DEF))
 (31 4 (:REWRITE NATP-RW))
 (26 4 (:REWRITE O-FIRST-EXPT-O-INFP))
 (23 1 (:REWRITE O-INFP-O-FINP-O<=))
 (21 6 (:REWRITE O-INFP->NEQ-0))
 (20 8 (:REWRITE O-FINP-<))
 (19 8 (:REWRITE AC-<))
 (19 2 (:REWRITE |a+0 = a|))
 (18 5 (:REWRITE NATP-POSP))
 (18 2 (:REWRITE |a(b-2)+a = a(b-1)|))
 (14 14 (:REWRITE DEFAULT-+-2))
 (14 14 (:REWRITE DEFAULT-+-1))
 (13 5 (:REWRITE POSP-RW))
 (12 12 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (12 12 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (12 4 (:REWRITE FOLD-CONSTS-IN-+))
 (12 4 (:LINEAR O-FIRST-EXPT-<=))
 (11 9 (:REWRITE O-FIRST-EXPT-O-P))
 (10 7 (:REWRITE O-FIRST-COEFF-<))
 (8 8 (:REWRITE |a < b & b < c  =>  a < c|))
 (8 8 (:REWRITE O^-^))
 (8 4 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (6 5 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (6 1 (:REWRITE |a(b-1)+a = ab|))
 (6 1 (:REWRITE O-FIRST-EXPT-0-NATP))
 (4 1 (:REWRITE <-0-+-NEGATIVE-1))
 (3 3 (:REWRITE NATPART-DEF-O-FINP))
 (3 3 (:REWRITE LIMITPART-DEF-O-FINP))
 (3 3 (:META CANCEL_PLUS-LESSP-CORRECT))
 (3 1 (:REWRITE O<=-O-FINP-DEF))
 (3 1 (:REWRITE EQUAL-CONSTANT-+))
 (2 2 (:TYPE-PRESCRIPTION POSP))
 (2 1 (:REWRITE LIMITPART-O-FIRST-EXPT))
 (1 1 (:REWRITE |~(a < a)|))
 (1 1 (:REWRITE NOT-LIMITP-NATP))
 (1 1 (:REWRITE LIMITPART-O-FINP))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 )
(O^3C2
 (881 8 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (811 3 (:DEFINITION O^3SUM))
 (554 9 (:REWRITE O*-O-FIRST-EXPT))
 (251 79 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (234 6 (:DEFINITION OB^))
 (221 35 (:REWRITE O-INFP->NEQ-0))
 (212 16 (:REWRITE O-FIRST-EXPT-<))
 (208 1 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (191 35 (:REWRITE O*-O-FINP))
 (142 5 (:REWRITE O^3SUM-O-FIRST-EXPT))
 (137 8 (:REWRITE O+-ATOM-DEF))
 (132 3 (:DEFINITION O^2))
 (124 36 (:REWRITE O-P-DEF-O-FINP-1))
 (123 9 (:REWRITE |(a = 0) & ~(b = 0)  <=>  (a^b = 0)|))
 (120 31 (:REWRITE O-FIRST-EXPT-O-INFP))
 (104 20 (:REWRITE NATP-RW))
 (102 69 (:TYPE-PRESCRIPTION NATPART-NATP))
 (100 100 (:TYPE-PRESCRIPTION OB+))
 (93 4 (:REWRITE O^-O-FIRST-EXPT))
 (78 78 (:TYPE-PRESCRIPTION MAKE-ORD))
 (73 16 (:REWRITE O-FINP-<))
 (70 16 (:REWRITE AC-<))
 (68 14 (:REWRITE O^-^))
 (63 51 (:REWRITE DEFAULT-+-2))
 (58 58 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (58 58 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (54 13 (:REWRITE O-FIRST-COEFF-<))
 (51 51 (:REWRITE DEFAULT-+-1))
 (44 1 (:REWRITE |(a <= b) & (c < d)  =>  ac < bd|))
 (41 5 (:REWRITE O-P-O^))
 (40 20 (:REWRITE POSP-NATP))
 (40 11 (:REWRITE NATP-POSP))
 (36 4 (:REWRITE |a(b-2)+a = a(b-1)|))
 (30 3 (:REWRITE LIMITP-DEF))
 (28 5 (:REWRITE NOT-LIMITP-NATP))
 (27 11 (:REWRITE POSP-RW))
 (26 16 (:REWRITE NATPART-DEF-O-FINP))
 (25 1 (:REWRITE O*-0))
 (25 1 (:REWRITE |(a < b) & ~(c = 0)  <=>  ca < cb|))
 (24 12 (:REWRITE LIMITPART-O-FIRST-EXPT))
 (24 10 (:LINEAR O-FIRST-EXPT-<=))
 (24 3 (:REWRITE ZP-OPEN))
 (21 7 (:REWRITE EQUAL-CONSTANT-+))
 (20 5 (:REWRITE <-0-+-NEGATIVE-1))
 (18 2 (:REWRITE |a+0 = a|))
 (16 16 (:REWRITE |a < b & b < c  =>  a < c|))
 (16 10 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (15 11 (:REWRITE O-FIRST-EXPT-O-P))
 (15 9 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (15 3 (:DEFINITION OMEGA-TERM))
 (12 3 (:REWRITE MAKE-ORD-EQUAL-4))
 (11 11 (:META CANCEL_PLUS-LESSP-CORRECT))
 (9 9 (:REWRITE LIMITPART-DEF-O-FINP))
 (6 2 (:REWRITE O-FIRST-EXPT-0-NATP))
 (6 1 (:REWRITE O-INFP-O-FINP-O<=))
 (5 5 (:REWRITE O-FINP-O-RST))
 (5 5 (:REWRITE DEFAULT-<-2))
 (5 5 (:REWRITE DEFAULT-<-1))
 (4 4 (:REWRITE NATPART-O-FINP))
 (3 3 (:REWRITE |~(a < a)|))
 (3 1 (:REWRITE O<=-O-FINP-DEF))
 (2 2 (:REWRITE |a < b  <=>  c+a < c+b :l1|))
 )
(O^3C
 (2791 38 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (1685 24 (:REWRITE O*-O-FIRST-EXPT))
 (772 63 (:REWRITE O-FIRST-EXPT-<))
 (376 80 (:REWRITE O*-O-FINP))
 (323 19 (:REWRITE |(a = 0) & ~(b = 0)  <=>  (a^b = 0)|))
 (312 12 (:REWRITE O^3SUM-O-FIRST-EXPT))
 (309 11 (:REWRITE O^-O-FIRST-EXPT))
 (301 133 (:REWRITE O-P-DEF-O-FINP-1))
 (289 3 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (287 62 (:REWRITE NATP-RW))
 (265 76 (:REWRITE O-FIRST-EXPT-O-INFP))
 (251 63 (:REWRITE O-FINP-<))
 (251 63 (:REWRITE AC-<))
 (226 73 (:REWRITE O^-^))
 (184 63 (:REWRITE O-FIRST-COEFF-<))
 (179 179 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (179 179 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (130 102 (:REWRITE DEFAULT-+-2))
 (124 14 (:REWRITE LIMITP-DEF))
 (102 102 (:REWRITE DEFAULT-+-1))
 (96 32 (:REWRITE FOLD-CONSTS-IN-+))
 (96 2 (:REWRITE |a+b = 0  <=>  a=0 & b=0|))
 (84 52 (:REWRITE O-FIRST-EXPT-O-P))
 (82 16 (:REWRITE NATP-POSP))
 (76 52 (:REWRITE NATPART-DEF-O-FINP))
 (76 31 (:LINEAR O-FIRST-EXPT-<=))
 (76 16 (:REWRITE POSP-RW))
 (64 8 (:REWRITE ZP-OPEN))
 (63 63 (:REWRITE |a < b & b < c  =>  a < c|))
 (63 9 (:REWRITE O-P-O^))
 (56 14 (:REWRITE <-0-+-NEGATIVE-1))
 (52 31 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (48 16 (:REWRITE EQUAL-CONSTANT-+))
 (48 6 (:REWRITE O-P-O*))
 (32 32 (:META CANCEL_PLUS-LESSP-CORRECT))
 (27 27 (:REWRITE LIMITPART-DEF-O-FINP))
 (21 7 (:REWRITE O-FIRST-EXPT-0-NATP))
 (18 18 (:REWRITE DEFAULT-<-2))
 (18 18 (:REWRITE DEFAULT-<-1))
 (12 12 (:REWRITE O-FINP-O-RST))
 (12 2 (:REWRITE O-P-O^3SUM))
 (8 1 (:REWRITE O*-1))
 (6 6 (:REWRITE NATPART-O-FINP))
 (4 2 (:REWRITE POSP-NATP))
 )
(O^4
 (84 16 (:REWRITE O-FIRST-EXPT-O-INFP))
 (39 1 (:DEFINITION OB^))
 (28 11 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (16 4 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (16 4 (:LINEAR O-FIRST-EXPT-<=))
 (15 1 (:REWRITE NATP-POSP))
 (12 4 (:REWRITE O-FIRST-EXPT-0-NATP))
 (11 11 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (11 11 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (10 1 (:REWRITE POSP-RW))
 (7 1 (:REWRITE MAKE-ORD-EQUAL-4))
 (5 2 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (4 3 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (4 2 (:REWRITE O*-O-FINP))
 (4 1 (:REWRITE NOT-LIMITP-NATP))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:REWRITE O^-^))
 (2 1 (:REWRITE LIMITP-DEF))
 (2 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:TYPE-PRESCRIPTION MAKE-ORD))
 (1 1 (:TYPE-PRESCRIPTION LIMITP))
 (1 1 (:REWRITE NATPART-DEF-O-FINP))
 (1 1 (:REWRITE NATP-RW))
 (1 1 (:REWRITE LIMITPART-DEF-O-FINP))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 (1 1 (:META CANCEL_PLUS-LESSP-CORRECT))
 )
(O^-O-FIRST-COEFF-1
 (1444 266 (:REWRITE O-FIRST-EXPT-O-INFP))
 (1119 26 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (793 19 (:REWRITE |(o-first-expt a) < a|))
 (735 22 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (683 16 (:REWRITE O*-O-FIRST-EXPT))
 (636 141 (:REWRITE O-INFP->NEQ-0))
 (611 5 (:REWRITE O-FIRST-EXPT-<-O+))
 (336 336 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (336 336 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (335 60 (:REWRITE O-FIRST-EXPT-<))
 (285 60 (:REWRITE O-FIRST-COEFF-<))
 (246 123 (:TYPE-PRESCRIPTION O+-O-FINP))
 (205 25 (:REWRITE LIMITP-DEF))
 (193 61 (:REWRITE AC-<))
 (149 60 (:REWRITE O-FINP-<))
 (143 8 (:REWRITE O+-O-FIRST-EXPT-2))
 (139 34 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (128 8 (:REWRITE O--0))
 (123 123 (:TYPE-PRESCRIPTION OB+))
 (95 36 (:REWRITE O*-O-FINP))
 (90 8 (:REWRITE O+-O-FIRST-EXPT-1))
 (83 61 (:REWRITE |a < b & b < c  =>  a < c|))
 (77 12 (:REWRITE DEFAULT-*-2))
 (68 68 (:REWRITE NATP-RW))
 (48 3 (:REWRITE O-INFP-O-FINP-O<=))
 (43 43 (:REWRITE O-FINP-O-RST))
 (41 11 (:REWRITE NATP-POSP))
 (32 6 (:REWRITE ZIP-OPEN))
 (32 2 (:REWRITE O-INFP-O+-2))
 (30 2 (:REWRITE O-INFP-O+))
 (28 9 (:REWRITE O^-LIMITP-O-FIRST-COEFF))
 (26 6 (:REWRITE COMMUTATIVITY-OF-+))
 (24 24 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (22 22 (:REWRITE O+-ATOM-DEF))
 (22 4 (:REWRITE O^-O-FIRST-EXPT))
 (21 5 (:REWRITE O-INFP-O^-1))
 (20 18 (:REWRITE DEFAULT-+-2))
 (20 18 (:REWRITE DEFAULT-+-1))
 (16 4 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (16 4 (:LINEAR EXPT->-1))
 (12 12 (:REWRITE DEFAULT-*-1))
 (12 12 (:META CANCEL_PLUS-LESSP-CORRECT))
 (11 11 (:REWRITE POSP-RW))
 (10 10 (:REWRITE DEFAULT-<-2))
 (10 10 (:REWRITE DEFAULT-<-1))
 (9 1 (:REWRITE O*-O-RST))
 (8 8 (:LINEAR EXPT-IS-INCREASING-FOR-BASE>1))
 (8 3 (:REWRITE O<=-O-FINP-DEF))
 (8 2 (:REWRITE O-INFP-O+-3))
 (8 2 (:REWRITE <-0-+-NEGATIVE-1))
 (6 6 (:REWRITE POSP-O-FIRST-COEFF))
 (6 6 (:REWRITE O-FIRST-COEFF-0))
 (6 2 (:REWRITE FOLD-CONSTS-IN-+))
 (6 2 (:REWRITE EQUAL-CONSTANT-+))
 (5 1 (:REWRITE |(a^b = 1)  <=>  (a = 1) V (b = 0)|))
 (2 2 (:REWRITE EXPONENTS-ADD-FOR-NONNEG-EXPONENTS))
 (2 2 (:REWRITE EXPONENTS-ADD))
 (2 2 (:REWRITE |0+a = a|))
 )
(O^4C-L1
 (464 1 (:DEFINITION OB^))
 (402 201 (:TYPE-PRESCRIPTION O*-FINITE))
 (227 1 (:REWRITE O*-O-INFP-DEF))
 (171 4 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (131 4 (:REWRITE O*-O-FIRST-EXPT))
 (112 5 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (108 23 (:REWRITE O-FIRST-EXPT-O-INFP))
 (102 4 (:REWRITE |(o-first-expt a) < a|))
 (96 53 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (85 1 (:REWRITE O-FIRST-EXPT-<-O+))
 (73 57 (:TYPE-PRESCRIPTION O^-O-FINP))
 (53 7 (:REWRITE O-FIRST-EXPT-<))
 (49 7 (:REWRITE O-FIRST-COEFF-<))
 (42 21 (:TYPE-PRESCRIPTION O+-O-FINP))
 (38 9 (:REWRITE O-FIRST-EXPT-0-NATP))
 (34 9 (:REWRITE O-INFP->NEQ-0))
 (28 28 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (28 28 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (28 9 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (23 5 (:LINEAR O-FIRST-EXPT-<=))
 (21 21 (:TYPE-PRESCRIPTION OB+))
 (18 10 (:REWRITE O-P-DEF-O-FINP-1))
 (17 1 (:REWRITE O+-O-FIRST-EXPT-1))
 (16 1 (:REWRITE O+-O-FIRST-EXPT-2))
 (15 7 (:REWRITE O-FINP-<))
 (15 7 (:REWRITE AC-<))
 (14 14 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (11 6 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (9 6 (:REWRITE O*-O-FINP))
 (7 7 (:REWRITE |a < b & b < c  =>  a < c|))
 (7 7 (:REWRITE O-FIRST-EXPT-O-P))
 (6 1 (:REWRITE LIMITP-DEF))
 (5 5 (:REWRITE O-FINP-O-RST))
 (5 5 (:REWRITE O+-ATOM-DEF))
 (4 4 (:TYPE-PRESCRIPTION NATP))
 (4 1 (:REWRITE O^-LIMITP-O-RST-2))
 (4 1 (:REWRITE O*-O-RST))
 (3 3 (:REWRITE NATP-RW))
 (3 2 (:REWRITE DEFAULT-CDR))
 (3 2 (:REWRITE DEFAULT-CAR))
 (3 1 (:REWRITE O*-0))
 (2 2 (:REWRITE O^-^))
 (1 1 (:REWRITE |a0 = 0|))
 (1 1 (:REWRITE O^-O-RST))
 )
(O^4C
 (696 6 (:DEFINITION OB^))
 (354 4 (:REWRITE O*-O-INFP-DEF))
 (338 12 (:REWRITE MAKE-ORD-EQUAL-4))
 (192 8 (:DEFINITION OMEGA-TERM))
 (154 13 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (115 67 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (96 4 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (74 2 (:REWRITE |o-first-expt(b) < o-first-expt(c)  =>  (a^b)*(a^c) = a^c|))
 (66 18 (:REWRITE O^-O-FIRST-COEFF-1))
 (66 16 (:REWRITE O-FIRST-EXPT-O-INFP))
 (63 63 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (63 63 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (53 13 (:REWRITE O*-O-FINP))
 (48 12 (:REWRITE O-FIRST-EXPT-<))
 (46 44 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (44 6 (:REWRITE LIMITP-DEF))
 (44 4 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (40 12 (:REWRITE O-INFP->NEQ-0))
 (32 12 (:REWRITE O-FIRST-COEFF-<))
 (30 18 (:REWRITE O^-LIMITP-O-FIRST-COEFF))
 (30 6 (:REWRITE NATP-RW))
 (30 2 (:REWRITE NATP-POSP))
 (28 12 (:REWRITE O-FINP-<))
 (28 12 (:REWRITE AC-<))
 (24 10 (:LINEAR O-FIRST-EXPT-<=))
 (20 2 (:REWRITE POSP-RW))
 (16 10 (:REWRITE O-P-O-FIRST-EXPT-NEQ-0))
 (12 12 (:TYPE-PRESCRIPTION NATP))
 (12 12 (:TYPE-PRESCRIPTION MAKE-ORD))
 (12 12 (:REWRITE |a < b & b < c  =>  a < c|))
 (12 12 (:REWRITE O^-^))
 (12 12 (:REWRITE O-FINP-O-RST))
 (12 6 (:REWRITE LIMITPART-O-FIRST-EXPT))
 (10 6 (:REWRITE LIMITPART-DEF-O-FINP))
 (10 2 (:REWRITE LIMITPART-O-RST))
 (8 8 (:REWRITE NATPART-DEF-O-FINP))
 (8 4 (:REWRITE LIMITPART-O-FIRST-COEFF))
 (8 2 (:REWRITE NOT-LIMITP-NATP))
 (6 6 (:REWRITE O-P-O^))
 (6 2 (:REWRITE O-FIRST-EXPT-0-NATP))
 (6 2 (:REWRITE |(a = 0) & ~(b = 0)  <=>  (a^b = 0)|))
 (4 4 (:REWRITE |a0 = 0|))
 (4 4 (:REWRITE O+-ATOM-DEF))
 (4 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE LIMITPART-O-FINP))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:META CANCEL_PLUS-LESSP-CORRECT))
 )
(OB^
 (888 49 (:REWRITE MAKE-ORD-EQUAL-4))
 (287 11 (:REWRITE O+-O-FIRST-EXPT-SMASH))
 (237 1 (:DEFINITION O^1))
 (233 233 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (226 8 (:REWRITE O+-O-FIRST-EXPT-SMASH-2))
 (177 177 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (177 177 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (166 5 (:REWRITE |(o-first-expt a) < a|))
 (155 3 (:REWRITE O*-O-FIRST-EXPT))
 (148 40 (:REWRITE O*-O-FIRST-EXPT-SMASH-2))
 (121 31 (:REWRITE O-FIRST-EXPT-0-NATP))
 (118 21 (:REWRITE DEFAULT-*-2))
 (117 9 (:REWRITE O--0))
 (89 25 (:REWRITE O-FIRST-EXPT-<))
 (85 1 (:REWRITE O-FIRST-EXPT-<-O+))
 (80 25 (:REWRITE O-FIRST-COEFF-<))
 (78 15 (:REWRITE NATP-POSP))
 (72 36 (:TYPE-PRESCRIPTION O+-O-FINP))
 (63 25 (:REWRITE O-FINP-<))
 (63 25 (:REWRITE AC-<))
 (59 53 (:REWRITE DEFAULT-+-2))
 (59 53 (:REWRITE DEFAULT-+-1))
 (55 9 (:REWRITE ZIP-OPEN))
 (47 25 (:REWRITE |a < b & b < c  =>  a < c|))
 (46 46 (:REWRITE NATP-RW))
 (39 15 (:REWRITE POSP-RW))
 (36 36 (:TYPE-PRESCRIPTION OB+))
 (36 9 (:REWRITE <-0-+-NEGATIVE-1))
 (34 32 (:REWRITE O-FINP-O-RST))
 (34 17 (:REWRITE O*-O-FIRST-COEFF))
 (30 6 (:REWRITE /R-WHEN-ABS-NUMERATOR=1))
 (28 28 (:META CANCEL_PLUS-LESSP-CORRECT))
 (27 9 (:REWRITE FOLD-CONSTS-IN-+))
 (27 9 (:REWRITE EQUAL-CONSTANT-+))
 (26 21 (:REWRITE DEFAULT-*-1))
 (25 19 (:REWRITE DEFAULT-<-2))
 (20 20 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (20 4 (:LINEAR EXPT-IS-INCREASING-FOR-BASE>1))
 (19 19 (:REWRITE DEFAULT-<-1))
 (17 1 (:REWRITE O+-O-FIRST-EXPT-1))
 (16 1 (:REWRITE O+-O-FIRST-EXPT-2))
 (12 3 (:REWRITE DEFAULT-UNARY-/))
 (11 11 (:REWRITE O+-ATOM-DEF))
 (10 2 (:LINEAR EXPT->-1))
 (8 8 (:REWRITE O-FIRST-EXPT-O-P))
 (6 6 (:REWRITE NUMERATOR-WHEN-INTEGERP))
 (6 6 (:REWRITE EXPONENTS-ADD-FOR-NONNEG-EXPONENTS))
 (6 6 (:REWRITE EXPONENTS-ADD))
 (6 6 (:REWRITE DEFAULT-NUMERATOR))
 (4 1 (:REWRITE O^3RW))
 )
