(POL::=-IMPLIES-=-*-MONOMIAL-1
 (2192 8 (:DEFINITION POL::NF))
 (1960 8 (:DEFINITION POL::+-MONOMIAL))
 (1463 176 (:DEFINITION TER::NATURAL-LISTP))
 (1412 42 (:DEFINITION POL::POLYNOMIAL))
 (1092 52 (:DEFINITION POL::MONOMIAL-LISTP))
 (884 10 (:DEFINITION MON::*))
 (606 303 (:TYPE-PRESCRIPTION TER::TERMP-NULLP))
 (556 10 (:DEFINITION TER::*))
 (448 448 (:TYPE-PRESCRIPTION TER::NULLP))
 (418 112 (:REWRITE O-P-O-INFP-CAR))
 (384 8 (:REWRITE TER::ANTI-SYMMETRY-OF-<))
 (352 16 (:REWRITE TER::TRICHOTOMY-OF-<))
 (352 16 (:REWRITE TER::<-HAS-FIRST))
 (323 20 (:REWRITE TER::*-IDENTITY-2))
 (313 313 (:TYPE-PRESCRIPTION TER::NATURAL-LISTP))
 (180 20 (:REWRITE TER::*-IDENTITY-1))
 (176 176 (:REWRITE DEFAULT-<-2))
 (176 176 (:REWRITE DEFAULT-<-1))
 (174 29 (:DEFINITION TER::NULLP))
 (102 102 (:REWRITE O-P-DEF-O-FINP-1))
 (93 1 (:REWRITE TER::COMMUTATIVITY-OF-*))
 (68 68 (:TYPE-PRESCRIPTION POL::MONOMIAL-LISTP))
 (68 68 (:TYPE-PRESCRIPTION POL::*-MONOMIAL))
 (50 50 (:TYPE-PRESCRIPTION TER::*))
 (48 16 (:TYPE-PRESCRIPTION POL::POLYNOMIALP-REST))
 (46 21 (:REWRITE O-INFP->NEQ-0))
 (40 40 (:REWRITE POL::POLYNOMIALP-NF))
 (39 39 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (36 18 (:REWRITE DEFAULT-+-2))
 (32 32 (:REWRITE POL::POLYNOMIALP-+-MONOMIAL))
 (28 18 (:REWRITE DEFAULT-+-1))
 (26 26 (:TYPE-PRESCRIPTION POL::POLYNOMIALP-*-MONOMIAL))
 (24 24 (:TYPE-PRESCRIPTION TER::<))
 (21 11 (:REWRITE DEFAULT-*-2))
 (18 18 (:REWRITE CDR-CONS))
 (18 18 (:REWRITE CAR-CONS))
 (16 16 (:TYPE-PRESCRIPTION POL::POLYNOMIALP-NF))
 (16 16 (:REWRITE TER::TRANSITIVITY-OF-<))
 (15 15 (:TYPE-PRESCRIPTION O-FINP))
 (15 5 (:REWRITE O-FIRST-EXPT-O-INFP))
 (12 11 (:REWRITE DEFAULT-*-1))
 (10 10 (:TYPE-PRESCRIPTION TER::TERMP-*))
 (10 5 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (8 8 (:REWRITE RATIONALP-+))
 (8 8 (:REWRITE RATIONALP-*))
 (4 1 (:REWRITE COMMUTATIVITY-OF-*))
 )
(POL::TECHNICAL-LEMMA-1
 (269 1 (:DEFINITION POL::NF))
 (245 1 (:DEFINITION POL::+-MONOMIAL))
 (108 12 (:DEFINITION TER::NATURAL-LISTP))
 (99 4 (:DEFINITION POL::POLYNOMIAL))
 (76 46 (:REWRITE DEFAULT-CDR))
 (65 1 (:REWRITE POL::COMPLETEP-NF))
 (60 3 (:DEFINITION POL::MONOMIAL-LISTP))
 (58 54 (:REWRITE DEFAULT-CAR))
 (54 13 (:REWRITE O-P-O-INFP-CAR))
 (50 25 (:TYPE-PRESCRIPTION TER::TERMP-NULLP))
 (48 1 (:REWRITE TER::ANTI-SYMMETRY-OF-<))
 (46 1 (:REWRITE POL::UNIFORMP-COMPLETEP))
 (44 2 (:REWRITE TER::TRICHOTOMY-OF-<))
 (44 2 (:REWRITE TER::<-HAS-FIRST))
 (42 1 (:DEFINITION POL::UNIFORMP))
 (30 1 (:DEFINITION MON::COMPATIBLEP))
 (26 26 (:TYPE-PRESCRIPTION O-P))
 (25 25 (:TYPE-PRESCRIPTION TER::NULLP))
 (25 25 (:TYPE-PRESCRIPTION TER::NATURAL-LISTP))
 (25 5 (:DEFINITION LEN))
 (15 13 (:REWRITE O-P-DEF-O-FINP-1))
 (12 12 (:REWRITE DEFAULT-<-2))
 (12 12 (:REWRITE DEFAULT-<-1))
 (12 6 (:REWRITE DEFAULT-+-2))
 (6 6 (:REWRITE DEFAULT-+-1))
 (6 2 (:TYPE-PRESCRIPTION POL::POLYNOMIALP-REST))
 (5 5 (:TYPE-PRESCRIPTION POL::UNIFORMP))
 (5 5 (:TYPE-PRESCRIPTION POL::MONOMIAL-LISTP))
 (5 5 (:REWRITE POL::POLYNOMIALP-NF))
 (4 4 (:REWRITE POL::POLYNOMIALP-+-MONOMIAL))
 (3 3 (:TYPE-PRESCRIPTION TER::<))
 (2 2 (:TYPE-PRESCRIPTION POL::POLYNOMIALP-NF))
 (2 2 (:TYPE-PRESCRIPTION O-FINP))
 (2 2 (:REWRITE TER::TRANSITIVITY-OF-<))
 (2 2 (:REWRITE O-INFP->NEQ-0))
 (2 2 (:REWRITE POL::COMPLETEP-UNIFORMP))
 (1 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1 1 (:REWRITE RATIONALP-+))
 (1 1 (:REWRITE CDR-CONS))
 (1 1 (:REWRITE CAR-CONS))
 )
(POL::TECHNICAL-LEMMA-2
 (804 3 (:DEFINITION POL::NF))
 (735 3 (:DEFINITION POL::+-MONOMIAL))
 (330 37 (:DEFINITION TER::NATURAL-LISTP))
 (297 12 (:DEFINITION POL::POLYNOMIAL))
 (200 10 (:DEFINITION POL::MONOMIAL-LISTP))
 (171 159 (:REWRITE DEFAULT-CAR))
 (155 113 (:REWRITE DEFAULT-CDR))
 (152 76 (:TYPE-PRESCRIPTION TER::TERMP-NULLP))
 (144 3 (:REWRITE TER::ANTI-SYMMETRY-OF-<))
 (132 6 (:REWRITE TER::TRICHOTOMY-OF-<))
 (132 6 (:REWRITE TER::<-HAS-FIRST))
 (118 29 (:REWRITE O-P-O-INFP-CAR))
 (76 76 (:TYPE-PRESCRIPTION TER::NULLP))
 (76 76 (:TYPE-PRESCRIPTION TER::NATURAL-LISTP))
 (58 58 (:TYPE-PRESCRIPTION O-P))
 (37 37 (:REWRITE DEFAULT-<-2))
 (37 37 (:REWRITE DEFAULT-<-1))
 (32 1 (:DEFINITION POL::UNIFORMP))
 (31 29 (:REWRITE O-P-DEF-O-FINP-1))
 (25 5 (:DEFINITION LEN))
 (23 1 (:DEFINITION MON::COMPATIBLEP))
 (18 6 (:TYPE-PRESCRIPTION POL::POLYNOMIALP-REST))
 (16 8 (:REWRITE DEFAULT-+-2))
 (15 15 (:REWRITE POL::POLYNOMIALP-NF))
 (12 12 (:REWRITE POL::POLYNOMIALP-+-MONOMIAL))
 (9 9 (:TYPE-PRESCRIPTION TER::<))
 (8 8 (:REWRITE DEFAULT-+-1))
 (6 6 (:TYPE-PRESCRIPTION POL::POLYNOMIALP-NF))
 (6 6 (:REWRITE TER::TRANSITIVITY-OF-<))
 (6 6 (:REWRITE O-INFP->NEQ-0))
 (3 3 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (3 3 (:REWRITE RATIONALP-+))
 (3 3 (:REWRITE CDR-CONS))
 (3 3 (:REWRITE CAR-CONS))
 (2 2 (:TYPE-PRESCRIPTION O-FINP))
 (2 2 (:REWRITE POL::COMPLETEP-UNIFORMP))
 )
(POL::INDUCTION-SCHEME)
(POL::NF-*-MONOMIAL
 (1844 922 (:TYPE-PRESCRIPTION TER::TERMP-NULLP))
 (1327 25 (:DEFINITION TER::*))
 (1257 1257 (:TYPE-PRESCRIPTION TER::NULLP))
 (1230 1029 (:REWRITE DEFAULT-CDR))
 (743 50 (:REWRITE TER::*-IDENTITY-2))
 (617 160 (:REWRITE O-P-O-INFP-CAR))
 (588 12 (:REWRITE TER::ANTI-SYMMETRY-OF-<))
 (540 24 (:REWRITE TER::TRICHOTOMY-OF-<))
 (540 24 (:REWRITE TER::<-HAS-FIRST))
 (418 50 (:REWRITE TER::*-IDENTITY-1))
 (402 67 (:DEFINITION TER::NULLP))
 (327 327 (:REWRITE DEFAULT-<-2))
 (327 327 (:REWRITE DEFAULT-<-1))
 (209 209 (:TYPE-PRESCRIPTION TER::*))
 (155 151 (:REWRITE O-P-DEF-O-FINP-1))
 (144 72 (:REWRITE DEFAULT-+-2))
 (97 72 (:REWRITE DEFAULT-+-1))
 (71 71 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (58 45 (:REWRITE O-INFP->NEQ-0))
 (48 48 (:REWRITE POL::POLYNOMIALP-+-MONOMIAL))
 (40 31 (:REWRITE DEFAULT-*-2))
 (36 36 (:TYPE-PRESCRIPTION TER::<))
 (33 33 (:REWRITE POL::POLYNOMIALP-NF))
 (31 31 (:REWRITE DEFAULT-*-1))
 (24 24 (:REWRITE TER::TRANSITIVITY-OF-<))
 (18 18 (:TYPE-PRESCRIPTION POL::POLYNOMIALP-NF))
 (12 12 (:REWRITE RATIONALP-+))
 (11 11 (:REWRITE POL::COMPLETEP-UNIFORMP))
 (10 10 (:TYPE-PRESCRIPTION O-FINP))
 (9 9 (:REWRITE RATIONALP-*))
 (6 2 (:REWRITE O-FIRST-EXPT-O-INFP))
 (4 2 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (2 2 (:REWRITE POL::*-MONOMIAL-CANCELLATIVE-EQUAL))
 )
(POL::=-IMPLIES-=-*-MONOMIAL-2
 (980 4 (:DEFINITION POL::+-MONOMIAL))
 (698 4 (:DEFINITION POL::*-MONOMIAL))
 (692 84 (:DEFINITION TER::NATURAL-LISTP))
 (664 20 (:DEFINITION POL::POLYNOMIAL))
 (432 216 (:TYPE-PRESCRIPTION TER::TERMP-NULLP))
 (419 383 (:REWRITE DEFAULT-CAR))
 (406 286 (:REWRITE DEFAULT-CDR))
 (344 4 (:DEFINITION MON::*))
 (284 70 (:REWRITE O-P-O-INFP-CAR))
 (276 276 (:TYPE-PRESCRIPTION TER::NULLP))
 (220 4 (:DEFINITION TER::*))
 (192 4 (:REWRITE TER::ANTI-SYMMETRY-OF-<))
 (176 8 (:REWRITE TER::TRICHOTOMY-OF-<))
 (176 8 (:REWRITE TER::<-HAS-FIRST))
 (128 4 (:DEFINITION POL::UNIFORMP))
 (124 8 (:REWRITE TER::*-IDENTITY-2))
 (84 84 (:REWRITE DEFAULT-<-2))
 (84 84 (:REWRITE DEFAULT-<-1))
 (82 66 (:REWRITE O-P-DEF-O-FINP-1))
 (72 12 (:DEFINITION TER::NULLP))
 (72 8 (:REWRITE TER::*-IDENTITY-1))
 (56 28 (:REWRITE DEFAULT-+-2))
 (32 28 (:REWRITE DEFAULT-+-1))
 (24 8 (:TYPE-PRESCRIPTION POL::POLYNOMIALP-REST))
 (22 22 (:REWRITE POL::POLYNOMIALP-NF))
 (20 20 (:TYPE-PRESCRIPTION TER::*))
 (19 19 (:TYPE-PRESCRIPTION O-FINP))
 (16 16 (:TYPE-PRESCRIPTION POL::*-MONOMIAL))
 (16 16 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (16 16 (:REWRITE POL::POLYNOMIALP-+-MONOMIAL))
 (15 10 (:REWRITE O-INFP->NEQ-0))
 (12 12 (:TYPE-PRESCRIPTION TER::<))
 (8 8 (:TYPE-PRESCRIPTION POL::POLYNOMIALP-NF))
 (8 8 (:TYPE-PRESCRIPTION POL::POLYNOMIALP-*-MONOMIAL))
 (8 8 (:REWRITE TER::TRANSITIVITY-OF-<))
 (8 8 (:REWRITE POL::COMPLETEP-UNIFORMP))
 (8 8 (:REWRITE CDR-CONS))
 (8 8 (:REWRITE CAR-CONS))
 (8 4 (:REWRITE DEFAULT-*-2))
 (4 4 (:TYPE-PRESCRIPTION TER::TERMP-*))
 (4 4 (:REWRITE RATIONALP-+))
 (4 4 (:REWRITE RATIONALP-*))
 (4 4 (:REWRITE DEFAULT-*-1))
 (3 1 (:REWRITE O-FIRST-EXPT-O-INFP))
 (2 1 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 )
(POL::ORDEREDP-*-MONOMIAL-ORDEREDP
 (10072 5038 (:TYPE-PRESCRIPTION TER::TERMP-NULLP))
 (6680 6680 (:TYPE-PRESCRIPTION TER::NULLP))
 (5714 107 (:DEFINITION TER::*))
 (5212 4766 (:REWRITE DEFAULT-CAR))
 (4829 91 (:REWRITE TER::ANTI-SYMMETRY-OF-<))
 (4420 206 (:REWRITE TER::<-HAS-FIRST))
 (3826 206 (:REWRITE TER::TRICHOTOMY-OF-<))
 (3317 214 (:REWRITE TER::*-IDENTITY-2))
 (2140 567 (:REWRITE O-P-O-INFP-CAR))
 (1980 329 (:DEFINITION TER::NULLP))
 (1910 214 (:REWRITE TER::*-IDENTITY-1))
 (1161 1161 (:REWRITE DEFAULT-<-2))
 (1161 1161 (:REWRITE DEFAULT-<-1))
 (811 206 (:REWRITE TER::TRANSITIVITY-OF-<))
 (694 347 (:TYPE-PRESCRIPTION POL::POLYNOMIALP-REST))
 (576 288 (:REWRITE DEFAULT-+-2))
 (539 517 (:REWRITE O-P-DEF-O-FINP-1))
 (422 422 (:TYPE-PRESCRIPTION TER::*))
 (395 288 (:REWRITE DEFAULT-+-1))
 (302 123 (:REWRITE O-INFP->NEQ-0))
 (264 264 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (135 85 (:REWRITE DEFAULT-*-2))
 (121 121 (:TYPE-PRESCRIPTION O-FINP))
 (99 33 (:REWRITE O-FIRST-EXPT-O-INFP))
 (85 85 (:REWRITE DEFAULT-*-1))
 (66 33 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (59 59 (:REWRITE POL::COMPLETEP-UNIFORMP))
 (50 50 (:REWRITE RATIONALP-*))
 )
(POL::NF-*-MONOMIAL-ORDEREDP
 (185 1 (:DEFINITION POL::*-MONOMIAL))
 (144 1 (:DEFINITION POL::ORDEREDP))
 (131 14 (:DEFINITION TER::NATURAL-LISTP))
 (120 60 (:TYPE-PRESCRIPTION TER::TERMP-NULLP))
 (86 1 (:DEFINITION MON::*))
 (84 54 (:REWRITE DEFAULT-CDR))
 (84 4 (:DEFINITION POL::MONOMIAL-LISTP))
 (75 75 (:TYPE-PRESCRIPTION TER::NULLP))
 (73 64 (:REWRITE DEFAULT-CAR))
 (67 1 (:DEFINITION POL::POLYNOMIAL))
 (55 1 (:DEFINITION TER::*))
 (53 13 (:REWRITE O-P-O-INFP-CAR))
 (48 1 (:REWRITE TER::ANTI-SYMMETRY-OF-<))
 (44 2 (:REWRITE TER::TRICHOTOMY-OF-<))
 (44 2 (:REWRITE TER::<-HAS-FIRST))
 (32 1 (:DEFINITION POL::UNIFORMP))
 (31 2 (:REWRITE TER::*-IDENTITY-2))
 (18 3 (:DEFINITION TER::NULLP))
 (18 2 (:REWRITE TER::*-IDENTITY-1))
 (16 12 (:REWRITE O-P-DEF-O-FINP-1))
 (14 14 (:REWRITE DEFAULT-<-2))
 (14 14 (:REWRITE DEFAULT-<-1))
 (14 7 (:REWRITE DEFAULT-+-2))
 (8 7 (:REWRITE DEFAULT-+-1))
 (7 7 (:TYPE-PRESCRIPTION O-FINP))
 (7 2 (:REWRITE O-INFP->NEQ-0))
 (5 5 (:TYPE-PRESCRIPTION TER::*))
 (4 4 (:TYPE-PRESCRIPTION POL::MONOMIAL-LISTP))
 (3 3 (:TYPE-PRESCRIPTION TER::<))
 (3 3 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (3 1 (:REWRITE O-FIRST-EXPT-O-INFP))
 (2 2 (:TYPE-PRESCRIPTION POL::POLYNOMIALP-*-MONOMIAL))
 (2 2 (:REWRITE TER::TRANSITIVITY-OF-<))
 (2 2 (:REWRITE POL::COMPLETEP-UNIFORMP))
 (2 1 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (2 1 (:REWRITE DEFAULT-*-2))
 (1 1 (:TYPE-PRESCRIPTION TER::TERMP-*))
 (1 1 (:REWRITE RATIONALP-*))
 (1 1 (:REWRITE DEFAULT-*-1))
 (1 1 (:REWRITE CDR-CONS))
 (1 1 (:REWRITE CAR-CONS))
 )
(POL::TECHNICAL-LEMMA-1
 (269 1 (:DEFINITION POL::NF))
 (245 1 (:DEFINITION POL::+-MONOMIAL))
 (108 12 (:DEFINITION TER::NATURAL-LISTP))
 (99 4 (:DEFINITION POL::POLYNOMIAL))
 (76 46 (:REWRITE DEFAULT-CDR))
 (65 1 (:REWRITE POL::COMPLETEP-NF))
 (60 3 (:DEFINITION POL::MONOMIAL-LISTP))
 (58 54 (:REWRITE DEFAULT-CAR))
 (54 13 (:REWRITE O-P-O-INFP-CAR))
 (50 25 (:TYPE-PRESCRIPTION TER::TERMP-NULLP))
 (48 1 (:REWRITE TER::ANTI-SYMMETRY-OF-<))
 (46 1 (:REWRITE POL::UNIFORMP-COMPLETEP))
 (44 2 (:REWRITE TER::TRICHOTOMY-OF-<))
 (44 2 (:REWRITE TER::<-HAS-FIRST))
 (42 1 (:DEFINITION POL::UNIFORMP))
 (30 1 (:DEFINITION MON::COMPATIBLEP))
 (26 26 (:TYPE-PRESCRIPTION O-P))
 (25 25 (:TYPE-PRESCRIPTION TER::NULLP))
 (25 25 (:TYPE-PRESCRIPTION TER::NATURAL-LISTP))
 (25 5 (:DEFINITION LEN))
 (15 13 (:REWRITE O-P-DEF-O-FINP-1))
 (12 12 (:REWRITE DEFAULT-<-2))
 (12 12 (:REWRITE DEFAULT-<-1))
 (12 6 (:REWRITE DEFAULT-+-2))
 (6 6 (:REWRITE DEFAULT-+-1))
 (6 2 (:TYPE-PRESCRIPTION POL::POLYNOMIALP-REST))
 (5 5 (:TYPE-PRESCRIPTION POL::UNIFORMP))
 (5 5 (:TYPE-PRESCRIPTION POL::MONOMIAL-LISTP))
 (5 5 (:REWRITE POL::POLYNOMIALP-NF))
 (4 4 (:REWRITE POL::POLYNOMIALP-+-MONOMIAL))
 (3 3 (:TYPE-PRESCRIPTION TER::<))
 (2 2 (:TYPE-PRESCRIPTION POL::POLYNOMIALP-NF))
 (2 2 (:TYPE-PRESCRIPTION O-FINP))
 (2 2 (:REWRITE TER::TRANSITIVITY-OF-<))
 (2 2 (:REWRITE O-INFP->NEQ-0))
 (2 2 (:REWRITE POL::COMPLETEP-UNIFORMP))
 (1 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1 1 (:REWRITE RATIONALP-+))
 (1 1 (:REWRITE CDR-CONS))
 (1 1 (:REWRITE CAR-CONS))
 )
(POL::TECHNICAL-LEMMA-2
 (804 3 (:DEFINITION POL::NF))
 (735 3 (:DEFINITION POL::+-MONOMIAL))
 (330 37 (:DEFINITION TER::NATURAL-LISTP))
 (297 12 (:DEFINITION POL::POLYNOMIAL))
 (200 10 (:DEFINITION POL::MONOMIAL-LISTP))
 (171 159 (:REWRITE DEFAULT-CAR))
 (155 113 (:REWRITE DEFAULT-CDR))
 (152 76 (:TYPE-PRESCRIPTION TER::TERMP-NULLP))
 (144 3 (:REWRITE TER::ANTI-SYMMETRY-OF-<))
 (132 6 (:REWRITE TER::TRICHOTOMY-OF-<))
 (132 6 (:REWRITE TER::<-HAS-FIRST))
 (118 29 (:REWRITE O-P-O-INFP-CAR))
 (76 76 (:TYPE-PRESCRIPTION TER::NULLP))
 (76 76 (:TYPE-PRESCRIPTION TER::NATURAL-LISTP))
 (58 58 (:TYPE-PRESCRIPTION O-P))
 (37 37 (:REWRITE DEFAULT-<-2))
 (37 37 (:REWRITE DEFAULT-<-1))
 (32 1 (:DEFINITION POL::UNIFORMP))
 (31 29 (:REWRITE O-P-DEF-O-FINP-1))
 (25 5 (:DEFINITION LEN))
 (23 1 (:DEFINITION MON::COMPATIBLEP))
 (18 6 (:TYPE-PRESCRIPTION POL::POLYNOMIALP-REST))
 (16 8 (:REWRITE DEFAULT-+-2))
 (15 15 (:REWRITE POL::POLYNOMIALP-NF))
 (12 12 (:REWRITE POL::POLYNOMIALP-+-MONOMIAL))
 (9 9 (:TYPE-PRESCRIPTION TER::<))
 (8 8 (:REWRITE DEFAULT-+-1))
 (6 6 (:TYPE-PRESCRIPTION POL::POLYNOMIALP-NF))
 (6 6 (:REWRITE TER::TRANSITIVITY-OF-<))
 (6 6 (:REWRITE O-INFP->NEQ-0))
 (3 3 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (3 3 (:REWRITE RATIONALP-+))
 (3 3 (:REWRITE CDR-CONS))
 (3 3 (:REWRITE CAR-CONS))
 (2 2 (:TYPE-PRESCRIPTION O-FINP))
 (2 2 (:REWRITE POL::COMPLETEP-UNIFORMP))
 )
(POL::TECHNICAL-LEMMA-3
 (8838 4419 (:TYPE-PRESCRIPTION TER::TERMP-NULLP))
 (8391 11 (:REWRITE POL::ORDEREDP-+-MONOMIAL-POLYNOMIAL-ORDERED))
 (8078 16 (:REWRITE POL::ORDEREDP-*-MONOMIAL-ORDEREDP))
 (5219 5219 (:TYPE-PRESCRIPTION TER::NULLP))
 (4949 26 (:REWRITE POL::TECHNICAL-LEMMA-1))
 (4776 98 (:REWRITE TER::ANTI-SYMMETRY-OF-<))
 (4725 211 (:REWRITE TER::TRICHOTOMY-OF-<))
 (4725 211 (:REWRITE TER::<-HAS-FIRST))
 (4217 1043 (:REWRITE O-P-O-INFP-CAR))
 (2993 56 (:DEFINITION TER::*))
 (2111 19 (:REWRITE POL::NF-*-MONOMIAL-ORDEREDP))
 (1704 112 (:REWRITE TER::*-IDENTITY-2))
 (1530 1530 (:REWRITE DEFAULT-<-2))
 (1530 1530 (:REWRITE DEFAULT-<-1))
 (1142 1016 (:REWRITE O-P-DEF-O-FINP-1))
 (1026 1026 (:TYPE-PRESCRIPTION TER::*))
 (976 112 (:REWRITE TER::*-IDENTITY-1))
 (960 160 (:DEFINITION TER::NULLP))
 (770 385 (:REWRITE DEFAULT-+-2))
 (765 37 (:DEFINITION POL::COMPLETEP))
 (441 385 (:REWRITE DEFAULT-+-1))
 (415 241 (:REWRITE O-INFP->NEQ-0))
 (343 343 (:REWRITE POL::POLYNOMIALP-+-MONOMIAL))
 (338 20 (:REWRITE POL::COMPLETEP-NF))
 (330 330 (:REWRITE POL::POLYNOMIALP-NF))
 (324 324 (:TYPE-PRESCRIPTION TER::<))
 (234 234 (:TYPE-PRESCRIPTION POL::COMPLETEP))
 (225 225 (:TYPE-PRESCRIPTION O-FINP))
 (221 221 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (211 211 (:REWRITE TER::TRANSITIVITY-OF-<))
 (168 56 (:TYPE-PRESCRIPTION POL::COMPLETEP-NF))
 (143 143 (:TYPE-PRESCRIPTION POL::POLYNOMIALP-NF))
 (99 33 (:REWRITE O-FIRST-EXPT-O-INFP))
 (92 65 (:REWRITE DEFAULT-*-2))
 (82 82 (:REWRITE RATIONALP-+))
 (66 33 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (65 65 (:REWRITE DEFAULT-*-1))
 (53 53 (:REWRITE POL::COMPLETEP-UNIFORMP))
 (27 27 (:REWRITE RATIONALP-*))
 (16 16 (:REWRITE POL::*-MONOMIAL-CANCELLATIVE-EQUAL))
 (6 2 (:REWRITE POL::UNIFORMP-COMPLETEP))
 (3 3 (:TYPE-PRESCRIPTION POL::POLYNOMIALP-+-MONOMIAL))
 (3 1 (:REWRITE POL::UNIFORMP-NF))
 )
(POL::NF-*-MONOMIAL-NF
 (1888 7 (:DEFINITION POL::NF))
 (1715 7 (:DEFINITION POL::+-MONOMIAL))
 (1105 127 (:DEFINITION TER::NATURAL-LISTP))
 (978 33 (:DEFINITION POL::POLYNOMIAL))
 (813 5 (:DEFINITION POL::*-MONOMIAL))
 (735 34 (:DEFINITION POL::MONOMIAL-LISTP))
 (609 552 (:REWRITE DEFAULT-CAR))
 (600 300 (:TYPE-PRESCRIPTION TER::TERMP-NULLP))
 (526 398 (:REWRITE DEFAULT-CDR))
 (430 5 (:DEFINITION MON::*))
 (375 375 (:TYPE-PRESCRIPTION TER::NULLP))
 (367 93 (:REWRITE O-P-O-INFP-CAR))
 (339 3 (:REWRITE POL::TECHNICAL-LEMMA-1))
 (336 7 (:REWRITE TER::ANTI-SYMMETRY-OF-<))
 (330 15 (:REWRITE TER::TRICHOTOMY-OF-<))
 (330 15 (:REWRITE TER::<-HAS-FIRST))
 (286 4 (:REWRITE POL::TECHNICAL-LEMMA-2))
 (275 5 (:DEFINITION TER::*))
 (179 4 (:REWRITE POL::NF-*-MONOMIAL-ORDEREDP))
 (155 10 (:REWRITE TER::*-IDENTITY-2))
 (139 1 (:DEFINITION POL::ORDEREDP))
 (127 127 (:REWRITE DEFAULT-<-2))
 (127 127 (:REWRITE DEFAULT-<-1))
 (98 88 (:REWRITE O-P-DEF-O-FINP-1))
 (90 15 (:DEFINITION TER::NULLP))
 (90 10 (:REWRITE TER::*-IDENTITY-1))
 (64 2 (:DEFINITION POL::UNIFORMP))
 (62 31 (:REWRITE DEFAULT-+-2))
 (44 2 (:DEFINITION POL::COMPLETEP))
 (43 15 (:TYPE-PRESCRIPTION POL::POLYNOMIALP-REST))
 (38 38 (:REWRITE POL::POLYNOMIALP-NF))
 (36 31 (:REWRITE DEFAULT-+-1))
 (34 4 (:REWRITE POL::NF-*-MONOMIAL))
 (28 28 (:REWRITE POL::POLYNOMIALP-+-MONOMIAL))
 (27 17 (:REWRITE O-INFP->NEQ-0))
 (25 25 (:TYPE-PRESCRIPTION TER::*))
 (24 24 (:TYPE-PRESCRIPTION POL::*-MONOMIAL))
 (23 23 (:TYPE-PRESCRIPTION TER::<))
 (22 22 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (19 1 (:REWRITE POL::COMPLETEP-NF))
 (16 16 (:TYPE-PRESCRIPTION POL::POLYNOMIALP-NF))
 (16 16 (:TYPE-PRESCRIPTION O-FINP))
 (15 15 (:REWRITE TER::TRANSITIVITY-OF-<))
 (13 13 (:TYPE-PRESCRIPTION POL::COMPLETEP))
 (12 12 (:REWRITE CDR-CONS))
 (12 12 (:REWRITE CAR-CONS))
 (10 10 (:TYPE-PRESCRIPTION POL::POLYNOMIALP-*-MONOMIAL))
 (10 5 (:REWRITE DEFAULT-*-2))
 (9 9 (:TYPE-PRESCRIPTION POL::ORDEREDP))
 (9 3 (:TYPE-PRESCRIPTION POL::COMPLETEP-NF))
 (7 7 (:REWRITE RATIONALP-+))
 (6 2 (:REWRITE O-FIRST-EXPT-O-INFP))
 (5 5 (:TYPE-PRESCRIPTION TER::TERMP-*))
 (5 5 (:REWRITE DEFAULT-*-1))
 (4 4 (:REWRITE POL::COMPLETEP-UNIFORMP))
 (4 2 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (3 3 (:REWRITE RATIONALP-*))
 (2 2 (:TYPE-PRESCRIPTION POL::UNIFORMP-NF))
 (2 2 (:TYPE-PRESCRIPTION POL::ORDEREDP-NF))
 (1 1 (:DEFINITION ENDP))
 )
(POL::INDUCTION-SCHEME
 (6 6 (:REWRITE DEFAULT-CAR))
 (6 1 (:DEFINITION TER::NATURAL-LISTP))
 (4 1 (:REWRITE O-P-O-INFP-CAR))
 (3 3 (:REWRITE DEFAULT-CDR))
 (2 2 (:TYPE-PRESCRIPTION O-P))
 (2 1 (:TYPE-PRESCRIPTION TER::TERMP-NULLP))
 (1 1 (:TYPE-PRESCRIPTION TER::NULLP))
 (1 1 (:TYPE-PRESCRIPTION TER::NATURAL-LISTP))
 (1 1 (:REWRITE O-P-DEF-O-FINP-1))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 )
(POL::NF-*-1
 (11748 48 (:DEFINITION POL::+-MONOMIAL))
 (7499 233 (:DEFINITION POL::POLYNOMIAL))
 (7264 41 (:DEFINITION POL::*-MONOMIAL))
 (4813 4453 (:REWRITE DEFAULT-CAR))
 (3664 1832 (:TYPE-PRESCRIPTION TER::TERMP-NULLP))
 (3570 41 (:DEFINITION MON::*))
 (3556 2951 (:REWRITE DEFAULT-CDR))
 (2516 683 (:REWRITE O-P-O-INFP-CAR))
 (2427 2427 (:TYPE-PRESCRIPTION TER::NULLP))
 (2304 48 (:REWRITE TER::ANTI-SYMMETRY-OF-<))
 (2279 41 (:DEFINITION TER::*))
 (2244 102 (:REWRITE TER::TRICHOTOMY-OF-<))
 (2244 102 (:REWRITE TER::<-HAS-FIRST))
 (1323 82 (:REWRITE TER::*-IDENTITY-2))
 (989 989 (:REWRITE DEFAULT-<-2))
 (989 989 (:REWRITE DEFAULT-<-1))
 (769 11 (:REWRITE POL::NF-*-MONOMIAL-ORDEREDP))
 (741 6 (:DEFINITION POL::ORDEREDP))
 (738 82 (:REWRITE TER::*-IDENTITY-1))
 (714 119 (:DEFINITION TER::NULLP))
 (611 611 (:REWRITE O-P-DEF-O-FINP-1))
 (372 4 (:REWRITE TER::COMMUTATIVITY-OF-*))
 (312 312 (:TYPE-PRESCRIPTION POL::*-MONOMIAL))
 (270 135 (:REWRITE DEFAULT-+-2))
 (205 205 (:TYPE-PRESCRIPTION TER::*))
 (192 192 (:REWRITE POL::POLYNOMIALP-+-MONOMIAL))
 (176 135 (:REWRITE DEFAULT-+-1))
 (175 175 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (156 156 (:TYPE-PRESCRIPTION TER::<))
 (134 28 (:DEFINITION BINARY-APPEND))
 (107 107 (:REWRITE O-INFP->NEQ-0))
 (102 102 (:REWRITE TER::TRANSITIVITY-OF-<))
 (89 89 (:REWRITE CDR-CONS))
 (89 89 (:REWRITE CAR-CONS))
 (86 45 (:REWRITE DEFAULT-*-2))
 (68 8 (:REWRITE POL::COMMUTATIVITY-OF-APPEND-TECHNICAL-LEMMA))
 (54 16 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (49 45 (:REWRITE DEFAULT-*-1))
 (48 48 (:REWRITE RATIONALP-+))
 (43 43 (:TYPE-PRESCRIPTION POL::ORDEREDP))
 (41 41 (:TYPE-PRESCRIPTION TER::TERMP-*))
 (41 41 (:REWRITE RATIONALP-*))
 (26 11 (:REWRITE POL::NF-*-MONOMIAL))
 (22 22 (:REWRITE POL::COMPLETEP-UNIFORMP))
 (20 11 (:REWRITE POL::*-MONOMIAL-CANCELLATIVE-EQUAL))
 (16 16 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (16 16 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (16 4 (:REWRITE COMMUTATIVITY-OF-*))
 (1 1 (:TYPE-PRESCRIPTION POL::UNIFORMP-NF))
 (1 1 (:TYPE-PRESCRIPTION POL::ORDEREDP-NF))
 )
(POL::=-IMPLIES-=-*-2
 (3430 14 (:DEFINITION POL::+-MONOMIAL))
 (2052 247 (:DEFINITION TER::NATURAL-LISTP))
 (1788 62 (:DEFINITION POL::POLYNOMIAL))
 (1231 1145 (:REWRITE DEFAULT-CAR))
 (1089 6 (:DEFINITION POL::*-MONOMIAL))
 (1062 796 (:REWRITE DEFAULT-CDR))
 (882 441 (:TYPE-PRESCRIPTION TER::TERMP-NULLP))
 (840 212 (:REWRITE O-P-O-INFP-CAR))
 (672 14 (:REWRITE TER::ANTI-SYMMETRY-OF-<))
 (616 28 (:REWRITE TER::TRICHOTOMY-OF-<))
 (616 28 (:REWRITE TER::<-HAS-FIRST))
 (531 531 (:TYPE-PRESCRIPTION TER::NULLP))
 (516 6 (:DEFINITION MON::*))
 (330 6 (:DEFINITION TER::*))
 (324 6 (:DEFINITION POL::+))
 (247 247 (:REWRITE DEFAULT-<-2))
 (247 247 (:REWRITE DEFAULT-<-1))
 (216 206 (:REWRITE O-P-DEF-O-FINP-1))
 (186 12 (:REWRITE TER::*-IDENTITY-2))
 (108 18 (:DEFINITION TER::NULLP))
 (108 12 (:REWRITE TER::*-IDENTITY-1))
 (106 53 (:REWRITE DEFAULT-+-2))
 (84 28 (:TYPE-PRESCRIPTION POL::POLYNOMIALP-REST))
 (73 73 (:REWRITE POL::POLYNOMIALP-NF))
 (59 53 (:REWRITE DEFAULT-+-1))
 (56 56 (:REWRITE POL::POLYNOMIALP-+-MONOMIAL))
 (48 48 (:TYPE-PRESCRIPTION POL::*-MONOMIAL))
 (48 38 (:REWRITE O-INFP->NEQ-0))
 (42 42 (:TYPE-PRESCRIPTION TER::<))
 (32 32 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (30 30 (:TYPE-PRESCRIPTION TER::*))
 (30 6 (:DEFINITION BINARY-APPEND))
 (28 28 (:TYPE-PRESCRIPTION POL::POLYNOMIALP-NF))
 (28 28 (:REWRITE TER::TRANSITIVITY-OF-<))
 (22 22 (:REWRITE POL::COMPLETEP-UNIFORMP))
 (20 20 (:REWRITE CDR-CONS))
 (20 20 (:REWRITE CAR-CONS))
 (18 18 (:TYPE-PRESCRIPTION POL::POLYNOMIALP-*-MONOMIAL))
 (14 14 (:REWRITE RATIONALP-+))
 (12 6 (:REWRITE DEFAULT-*-2))
 (10 10 (:TYPE-PRESCRIPTION O-FINP))
 (6 6 (:TYPE-PRESCRIPTION TER::TERMP-*))
 (6 6 (:REWRITE RATIONALP-*))
 (6 6 (:REWRITE DEFAULT-*-1))
 )
(POL::=-IMPLIES-=-*-1
 (1120 4 (:DEFINITION POL::*))
 (1096 4 (:DEFINITION POL::NF))
 (980 4 (:DEFINITION POL::+-MONOMIAL))
 (812 4 (:DEFINITION POL::*-MONOMIAL))
 (782 96 (:DEFINITION TER::NATURAL-LISTP))
 (760 36 (:DEFINITION POL::MONOMIAL-LISTP))
 (664 20 (:DEFINITION POL::POLYNOMIAL))
 (472 436 (:REWRITE DEFAULT-CAR))
 (392 4 (:DEFINITION MON::*))
 (326 274 (:REWRITE DEFAULT-CDR))
 (324 162 (:TYPE-PRESCRIPTION TER::TERMP-NULLP))
 (272 70 (:REWRITE O-P-O-INFP-CAR))
 (232 4 (:DEFINITION TER::*))
 (216 4 (:DEFINITION POL::+))
 (212 212 (:TYPE-PRESCRIPTION TER::NULLP))
 (192 4 (:REWRITE TER::ANTI-SYMMETRY-OF-<))
 (186 2 (:REWRITE TER::COMMUTATIVITY-OF-*))
 (176 8 (:REWRITE TER::TRICHOTOMY-OF-<))
 (176 8 (:REWRITE TER::<-HAS-FIRST))
 (166 166 (:TYPE-PRESCRIPTION TER::NATURAL-LISTP))
 (150 8 (:REWRITE TER::*-IDENTITY-2))
 (96 96 (:REWRITE DEFAULT-<-2))
 (96 96 (:REWRITE DEFAULT-<-1))
 (72 8 (:REWRITE TER::*-IDENTITY-1))
 (70 66 (:REWRITE O-P-DEF-O-FINP-1))
 (60 10 (:DEFINITION TER::NULLP))
 (32 32 (:TYPE-PRESCRIPTION POL::*-MONOMIAL))
 (24 24 (:TYPE-PRESCRIPTION POL::*))
 (24 8 (:TYPE-PRESCRIPTION POL::POLYNOMIALP-REST))
 (20 20 (:TYPE-PRESCRIPTION TER::*))
 (20 20 (:REWRITE POL::POLYNOMIALP-NF))
 (20 10 (:REWRITE DEFAULT-+-2))
 (20 4 (:DEFINITION BINARY-APPEND))
 (18 18 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (16 16 (:REWRITE POL::POLYNOMIALP-+-MONOMIAL))
 (14 10 (:REWRITE DEFAULT-+-1))
 (12 12 (:TYPE-PRESCRIPTION POL::POLYNOMIALP-*-MONOMIAL))
 (12 12 (:TYPE-PRESCRIPTION TER::<))
 (10 6 (:REWRITE DEFAULT-*-2))
 (8 8 (:TYPE-PRESCRIPTION POL::POLYNOMIALP-NF))
 (8 8 (:TYPE-PRESCRIPTION POL::POLYNOMIALP-*))
 (8 8 (:REWRITE TER::TRANSITIVITY-OF-<))
 (8 8 (:REWRITE O-INFP->NEQ-0))
 (8 8 (:REWRITE CDR-CONS))
 (8 8 (:REWRITE CAR-CONS))
 (8 6 (:REWRITE DEFAULT-*-1))
 (8 2 (:REWRITE COMMUTATIVITY-OF-*))
 (4 4 (:TYPE-PRESCRIPTION TER::TERMP-*))
 (4 4 (:TYPE-PRESCRIPTION O-FINP))
 (4 4 (:REWRITE RATIONALP-+))
 (4 4 (:REWRITE RATIONALP-*))
 )
