(ECURVE::STEP1
 (15 8 (:REWRITE PFIELD::ADD-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (14 14 (:REWRITE PFIELD::ADD-SUBST-CONSTANT-ARG2))
 (14 14 (:REWRITE PFIELD::ADD-SUBST-CONSTANT-ARG1))
 (13 13 (:REWRITE PFIELD::ADD-OF-CONSTANTS))
 (13 8 (:REWRITE PFIELD::ADD-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (12 12 (:REWRITE PFIELD::MUL-OF--1-BECOMES-NEG-ALT))
 (7 7 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG2))
 (7 7 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG1))
 (7 7 (:REWRITE PFIELD::MUL-WHEN-CONSTANT-REDUCE-ARG1))
 (6 6 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (6 6 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (6 2 (:DEFINITION NATP))
 (5 3 (:REWRITE PFIELD::NEG-WHEN-NOT-INTEGERP-CHEAP))
 (4 4 (:REWRITE PFIELD::ADD-OF-ADD-COMBINE-CONSTANTS))
 (4 3 (:REWRITE DEFAULT-<-1))
 (4 2 (:REWRITE IFIX-WHEN-NOT-INTEGERP-UNLIMITED))
 (3 3 (:REWRITE PFIELD::NEG-WHEN-NOT-POSP-ARG2-CHEAP))
 (3 3 (:REWRITE PFIELD::NEG-WHEN-CONSTANT-ARG1))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE PFIELD::ADD-COMMUTATIVE-2-WHEN-CONSTANT))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:REWRITE PFIELD::NEG-OF-MUL-WHEN-CONSTANT))
 (2 2 (:REWRITE PFIELD::FEP-WHEN-CONSTANT))
 (2 2 (:REWRITE PFIELD::EQUAL-OF-MUL-CONSTANTS-ALT))
 (2 2 (:REWRITE PFIELD::EQUAL-OF-MUL-CONSTANTS))
 (2 2 (:REWRITE PFIELD::ADD-COMMUTATIVE-WHEN-CONSTANT))
 (2 2 (:REWRITE PFIELD::ADD-ASSOCIATIVE-WHEN-CONSTANT))
 (1 1 (:REWRITE PFIELD::SUB-WHEN-CONSTANTS))
 (1 1 (:REWRITE NOT-PRIMEP-WHEN-DIVIDES))
 )
(ECURVE::STEP2
 (6 2 (:DEFINITION NATP))
 (5 5 (:REWRITE PFIELD::ADD-SUBST-CONSTANT-ARG2))
 (5 5 (:REWRITE PFIELD::ADD-SUBST-CONSTANT-ARG1))
 (5 5 (:REWRITE PFIELD::ADD-OF-CONSTANTS))
 (5 4 (:REWRITE PFIELD::ADD-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (5 3 (:REWRITE IFIX-WHEN-NOT-INTEGERP-UNLIMITED))
 (4 4 (:REWRITE PFIELD::ADD-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:REWRITE PFIELD::NEG-WHEN-NOT-POSP-ARG2-CHEAP))
 (2 2 (:REWRITE PFIELD::NEG-WHEN-NOT-INTEGERP-CHEAP))
 (2 2 (:REWRITE PFIELD::NEG-WHEN-CONSTANT-ARG1))
 (2 2 (:REWRITE PFIELD::FEP-WHEN-CONSTANT))
 (2 2 (:REWRITE PFIELD::EQUAL-OF-ADD-COMBINE-CONSTANTS-ALT))
 (2 2 (:REWRITE PFIELD::EQUAL-OF-ADD-COMBINE-CONSTANTS))
 (2 2 (:REWRITE PFIELD::EQUAL-OF-0-AND-ADD-SAFE))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (2 1 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (1 1 (:REWRITE PFIELD::SUB-WHEN-CONSTANTS))
 (1 1 (:REWRITE NOT-PRIMEP-WHEN-DIVIDES))
 (1 1 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG2))
 (1 1 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG1))
 (1 1 (:REWRITE PFIELD::MUL-WHEN-CONSTANT-REDUCE-ARG1))
 (1 1 (:REWRITE PFIELD::MUL-OF--1-BECOMES-NEG-ALT))
 (1 1 (:REWRITE PFIELD::MUL-COMMUTATIVE))
 (1 1 (:REWRITE PFIELD::EQUAL-OF-MUL-CONSTANTS-ALT))
 (1 1 (:REWRITE PFIELD::EQUAL-OF-MUL-CONSTANTS))
 (1 1 (:REWRITE PFIELD::ADD-COMMUTATIVE-WHEN-CONSTANT))
 )
(ECURVE::EQUAL-OF-SQUARE-AND-SQUARE
 (48 48 (:REWRITE PFIELD::ADD-SUBST-CONSTANT-ARG2))
 (48 48 (:REWRITE PFIELD::ADD-SUBST-CONSTANT-ARG1))
 (43 43 (:REWRITE PFIELD::ADD-OF-CONSTANTS))
 (43 25 (:REWRITE PFIELD::ADD-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (37 25 (:REWRITE PFIELD::ADD-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (36 36 (:REWRITE PFIELD::MUL-OF--1-BECOMES-NEG-ALT))
 (21 21 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG2))
 (21 21 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG1))
 (21 21 (:REWRITE PFIELD::MUL-WHEN-CONSTANT-REDUCE-ARG1))
 (19 13 (:REWRITE PFIELD::NEG-WHEN-NOT-INTEGERP-CHEAP))
 (18 18 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (18 18 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (13 13 (:REWRITE PFIELD::NEG-WHEN-NOT-POSP-ARG2-CHEAP))
 (13 13 (:REWRITE PFIELD::NEG-WHEN-CONSTANT-ARG1))
 (12 4 (:DEFINITION NATP))
 (10 10 (:REWRITE PFIELD::ADD-OF-ADD-COMBINE-CONSTANTS))
 (10 5 (:REWRITE IFIX-WHEN-NOT-INTEGERP-UNLIMITED))
 (8 8 (:REWRITE PFIELD::ADD-COMMUTATIVE-2-WHEN-CONSTANT))
 (8 6 (:REWRITE DEFAULT-<-1))
 (6 6 (:REWRITE PFIELD::NEG-OF-MUL-WHEN-CONSTANT))
 (6 6 (:REWRITE DEFAULT-<-2))
 (6 6 (:REWRITE PFIELD::ADD-ASSOCIATIVE-WHEN-CONSTANT))
 (5 5 (:REWRITE NOT-PRIMEP-WHEN-DIVIDES))
 (4 4 (:TYPE-PRESCRIPTION NATP))
 (4 4 (:REWRITE PFIELD::FEP-WHEN-CONSTANT))
 (3 3 (:REWRITE PFIELD::SUB-WHEN-CONSTANTS))
 (2 2 (:REWRITE PFIELD::EQUAL-OF-MUL-CONSTANTS-ALT))
 (2 2 (:REWRITE PFIELD::EQUAL-OF-MUL-CONSTANTS))
 (2 2 (:REWRITE PFIELD::EQUAL-OF-ADD-COMBINE-CONSTANTS-ALT))
 (2 2 (:REWRITE PFIELD::EQUAL-OF-ADD-COMBINE-CONSTANTS))
 (2 2 (:REWRITE PFIELD::EQUAL-OF-0-AND-ADD-SAFE))
 )
(ECURVE::EQUAL-OF-MUL-SAME-AND-1
 (23 23 (:REWRITE PFIELD::ADD-SUBST-CONSTANT-ARG2))
 (23 23 (:REWRITE PFIELD::ADD-SUBST-CONSTANT-ARG1))
 (12 10 (:REWRITE PFIELD::ADD-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (11 10 (:REWRITE PFIELD::ADD-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (10 10 (:REWRITE PFIELD::ADD-OF-CONSTANTS))
 (10 10 (:REWRITE PFIELD::ADD-COMMUTATIVE))
 (9 9 (:REWRITE PFIELD::MUL-OF--1-BECOMES-NEG-ALT))
 (7 7 (:REWRITE PFIELD::FEP-WHEN-CONSTANT))
 (6 6 (:REWRITE PFIELD::NEG-WHEN-NOT-POSP-ARG2-CHEAP))
 (6 6 (:REWRITE PFIELD::NEG-WHEN-NOT-INTEGERP-CHEAP))
 (6 2 (:DEFINITION NATP))
 (5 5 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG2))
 (5 5 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG1))
 (5 5 (:REWRITE PFIELD::MUL-WHEN-CONSTANT-REDUCE-ARG1))
 (4 4 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (4 4 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (3 3 (:REWRITE NOT-PRIMEP-WHEN-DIVIDES))
 (3 2 (:REWRITE IFIX-WHEN-NOT-INTEGERP-UNLIMITED))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE PFIELD::EQUAL-OF-MUL-CONSTANTS-ALT))
 (1 1 (:REWRITE PFIELD::EQUAL-OF-MUL-CONSTANTS))
 (1 1 (:REWRITE PFIELD::ADD-COMMUTATIVE-2-WHEN-CONSTANT))
 )
(ECURVE::EQUAL-OF-DIV-AND-0
 (6 2 (:DEFINITION NATP))
 (3 3 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG2))
 (3 3 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG1))
 (3 3 (:REWRITE PFIELD::MUL-WHEN-CONSTANT-REDUCE-ARG1))
 (3 3 (:REWRITE PFIELD::MUL-OF--1-BECOMES-NEG-ALT))
 (3 2 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (3 2 (:REWRITE IFIX-WHEN-NOT-INTEGERP-UNLIMITED))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (2 2 (:REWRITE PFIELD::FEP-WHEN-CONSTANT))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE NOT-PRIMEP-WHEN-DIVIDES))
 (1 1 (:REWRITE PFIELD::EQUAL-OF-MUL-CONSTANTS-ALT))
 (1 1 (:REWRITE PFIELD::EQUAL-OF-MUL-CONSTANTS))
 )
(ECURVE::MUL-OF-DIV-SAME-ARG1-ARG2
 (10 2 (:REWRITE PFIELD::FEP-HOLDS))
 (6 2 (:DEFINITION NATP))
 (5 5 (:REWRITE PFIELD::MUL-OF--1-BECOMES-NEG-ALT))
 (4 4 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG2))
 (4 4 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG1))
 (4 4 (:REWRITE PFIELD::MUL-WHEN-CONSTANT-REDUCE-ARG1))
 (3 2 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (2 2 (:REWRITE PFIELD::FEP-WHEN-CONSTANT))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (1 1 (:TYPE-PRESCRIPTION PFIELD::NATP-OF-INV))
 (1 1 (:REWRITE NOT-PRIMEP-WHEN-DIVIDES))
 (1 1 (:REWRITE PFIELD::MUL-OF-MUL-COMBINE-CONSTANTS))
 (1 1 (:REWRITE IFIX-WHEN-NOT-INTEGERP-UNLIMITED))
 )
(ECURVE::EQUAL-OF-DIV-AND-DIV-SAME-ARG2
 (8 4 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (4 4 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (4 4 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG2))
 (4 4 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG1))
 (4 4 (:REWRITE PFIELD::MUL-WHEN-CONSTANT-REDUCE-ARG1))
 (4 4 (:REWRITE PFIELD::MUL-OF--1-BECOMES-NEG-ALT))
 (4 4 (:REWRITE PFIELD::MUL-COMMUTATIVE))
 (3 3 (:REWRITE NOT-PRIMEP-WHEN-DIVIDES))
 (3 3 (:REWRITE PFIELD::FEP-WHEN-CONSTANT))
 (3 3 (:REWRITE PFIELD::EQUAL-OF-MUL-CONSTANTS-ALT))
 (3 3 (:REWRITE PFIELD::EQUAL-OF-MUL-CONSTANTS))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (3 1 (:DEFINITION NATP))
 (1 1 (:TYPE-PRESCRIPTION NATP))
 )
(ECURVE::LEMMA1
 (10 2 (:REWRITE PFIELD::FEP-HOLDS))
 (7 7 (:REWRITE PFIELD::MUL-OF--1-BECOMES-NEG-ALT))
 (6 6 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG2))
 (6 6 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG1))
 (6 6 (:REWRITE PFIELD::MUL-WHEN-CONSTANT-REDUCE-ARG1))
 (6 2 (:DEFINITION NATP))
 (4 3 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (3 3 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:REWRITE IFIX-WHEN-NOT-INTEGERP-UNLIMITED))
 (2 2 (:REWRITE PFIELD::FEP-WHEN-CONSTANT))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (1 1 (:TYPE-PRESCRIPTION PFIELD::NATP-OF-INV))
 (1 1 (:REWRITE NOT-PRIMEP-WHEN-DIVIDES))
 (1 1 (:REWRITE PFIELD::MUL-OF-MUL-COMBINE-CONSTANTS))
 )
(ECURVE::LEMMA2)
(ECURVE::EQUAL-OF-1-AND-DIV
 (6 2 (:DEFINITION NATP))
 (4 2 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (3 3 (:REWRITE NOT-PRIMEP-WHEN-DIVIDES))
 (3 3 (:REWRITE PFIELD::MUL-OF--1-BECOMES-NEG-ALT))
 (3 3 (:REWRITE PFIELD::FEP-WHEN-CONSTANT))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (2 2 (:TYPE-PRESCRIPTION PFIELD::NATP-OF-INV))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (2 2 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG2))
 (2 2 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG1))
 (2 2 (:REWRITE PFIELD::MUL-WHEN-CONSTANT-REDUCE-ARG1))
 (2 2 (:REWRITE PFIELD::MUL-COMMUTATIVE))
 (1 1 (:REWRITE PFIELD::EQUAL-OF-MUL-CONSTANTS-ALT))
 (1 1 (:REWRITE PFIELD::EQUAL-OF-MUL-CONSTANTS))
 )
(ECURVE::EQUAL-OF-X-AND-NEG-X
 (6 2 (:DEFINITION NATP))
 (5 5 (:REWRITE DEFAULT-<-2))
 (5 5 (:REWRITE DEFAULT-<-1))
 (3 3 (:REWRITE NOT-PRIMEP-WHEN-DIVIDES))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:REWRITE PFIELD::FEP-WHEN-CONSTANT))
 (2 2 (:REWRITE PFIELD::ADD-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (2 2 (:REWRITE PFIELD::ADD-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (2 2 (:REWRITE PFIELD::ADD-SUBST-CONSTANT-ARG2))
 (2 2 (:REWRITE PFIELD::ADD-SUBST-CONSTANT-ARG1))
 (2 2 (:REWRITE PFIELD::ADD-OF-CONSTANTS))
 (2 2 (:REWRITE PFIELD::ADD-COMMUTATIVE))
 (1 1 (:REWRITE PFIELD::NEG-WHEN-NOT-POSP-ARG2-CHEAP))
 (1 1 (:REWRITE PFIELD::NEG-WHEN-NOT-INTEGERP-CHEAP))
 (1 1 (:REWRITE PFIELD::NEG-WHEN-CONSTANT-ARG1))
 (1 1 (:REWRITE PFIELD::EQUAL-OF-ADD-COMBINE-CONSTANTS-ALT))
 (1 1 (:REWRITE PFIELD::EQUAL-OF-ADD-COMBINE-CONSTANTS))
 (1 1 (:REWRITE PFIELD::EQUAL-OF-0-AND-ADD-SAFE))
 )
(ECURVE::EQUAL-OF-MUL-CONSTANTS-MOD
 (46 6 (:REWRITE PFIELD::MOD-WHEN-FEP))
 (31 9 (:DEFINITION NATP))
 (10 10 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG2))
 (10 10 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG1))
 (10 10 (:REWRITE PFIELD::MUL-WHEN-CONSTANT-REDUCE-ARG1))
 (10 10 (:REWRITE PFIELD::MUL-OF--1-BECOMES-NEG-ALT))
 (10 10 (:REWRITE DEFAULT-<-2))
 (10 10 (:REWRITE DEFAULT-<-1))
 (9 9 (:TYPE-PRESCRIPTION NATP))
 (9 9 (:REWRITE PFIELD::FEP-WHEN-CONSTANT))
 (9 6 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (6 6 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (3 3 (:TYPE-PRESCRIPTION PFIELD::NATP-OF-INV))
 (3 3 (:REWRITE NOT-PRIMEP-WHEN-DIVIDES))
 (2 2 (:REWRITE PFIELD::EQUAL-OF-MUL-CONSTANTS-ALT))
 (2 2 (:REWRITE PFIELD::EQUAL-OF-MUL-CONSTANTS))
 )
(ECURVE::MUL-OF-MINUS1-BECOMES-NEG-2
 (4 1 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (2 2 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG2))
 (2 2 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG1))
 (2 2 (:REWRITE PFIELD::MUL-WHEN-CONSTANT-REDUCE-ARG1))
 (2 2 (:REWRITE PFIELD::MUL-OF--1-BECOMES-NEG-ALT))
 (2 1 (:REWRITE PFIELD::NEG-WHEN-NOT-POSP-ARG2-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION POSP))
 (1 1 (:TYPE-PRESCRIPTION PFIELD::MINUS1))
 (1 1 (:TYPE-PRESCRIPTION PFIELD::INTEGERP-OF-MINUS1-TYPE))
 (1 1 (:TYPE-PRESCRIPTION PFIELD::<-OF-0--AND-MINUS1-TYPE))
 (1 1 (:REWRITE PFIELD::NEG-WHEN-NOT-INTEGERP-CHEAP))
 (1 1 (:REWRITE PFIELD::NEG-WHEN-CONSTANT-ARG1))
 (1 1 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 )
(ECURVE::LEMMA1
 (10 2 (:REWRITE PFIELD::FEP-HOLDS))
 (6 2 (:DEFINITION NATP))
 (5 5 (:REWRITE PFIELD::MUL-OF--1-BECOMES-NEG-ALT))
 (4 4 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG2))
 (4 4 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG1))
 (4 4 (:REWRITE PFIELD::MUL-WHEN-CONSTANT-REDUCE-ARG1))
 (3 2 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (2 2 (:REWRITE PFIELD::FEP-WHEN-CONSTANT))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (1 1 (:TYPE-PRESCRIPTION PFIELD::NATP-OF-INV))
 (1 1 (:REWRITE NOT-PRIMEP-WHEN-DIVIDES))
 (1 1 (:REWRITE PFIELD::NEG-WHEN-NOT-POSP-ARG2-CHEAP))
 (1 1 (:REWRITE PFIELD::NEG-WHEN-NOT-INTEGERP-CHEAP))
 (1 1 (:REWRITE PFIELD::NEG-WHEN-CONSTANT-ARG1))
 (1 1 (:REWRITE PFIELD::MUL-OF-MUL-COMBINE-CONSTANTS))
 (1 1 (:REWRITE IFIX-WHEN-NOT-INTEGERP-UNLIMITED))
 )
(ECURVE::LEMMA2
 (3 3 (:REWRITE PFIELD::NEG-WHEN-NOT-POSP-ARG2-CHEAP))
 (3 3 (:REWRITE PFIELD::NEG-WHEN-NOT-INTEGERP-CHEAP))
 (3 3 (:REWRITE PFIELD::NEG-WHEN-CONSTANT-ARG1))
 (2 1 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION PFIELD::NATP-OF-INV))
 (1 1 (:REWRITE NOT-PRIMEP-WHEN-DIVIDES))
 (1 1 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (1 1 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG2))
 (1 1 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG1))
 (1 1 (:REWRITE PFIELD::MUL-WHEN-CONSTANT-REDUCE-ARG1))
 (1 1 (:REWRITE PFIELD::MUL-OF--1-BECOMES-NEG-ALT))
 (1 1 (:REWRITE PFIELD::MUL-COMMUTATIVE))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(ECURVE::LEMMA3
 (6 2 (:DEFINITION NATP))
 (4 2 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION PFIELD::NATP-OF-INV))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:REWRITE NOT-PRIMEP-WHEN-DIVIDES))
 (2 2 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (2 2 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG2))
 (2 2 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG1))
 (2 2 (:REWRITE PFIELD::MUL-WHEN-CONSTANT-REDUCE-ARG1))
 (2 2 (:REWRITE PFIELD::MUL-OF--1-BECOMES-NEG-ALT))
 (2 2 (:REWRITE PFIELD::MUL-COMMUTATIVE))
 (2 2 (:REWRITE PFIELD::FEP-WHEN-CONSTANT))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE PFIELD::NEG-WHEN-NOT-POSP-ARG2-CHEAP))
 (1 1 (:REWRITE PFIELD::NEG-WHEN-NOT-INTEGERP-CHEAP))
 (1 1 (:REWRITE PFIELD::NEG-WHEN-CONSTANT-ARG1))
 (1 1 (:REWRITE PFIELD::EQUAL-OF-MUL-CONSTANTS-ALT))
 (1 1 (:REWRITE PFIELD::EQUAL-OF-MUL-CONSTANTS))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(ECURVE::LEMMA4
 (33 2 (:REWRITE PFIELD::FEP-HOLDS))
 (16 2 (:REWRITE CANCEL-MOD-+))
 (14 1 (:DEFINITION NATP))
 (5 5 (:META META-INTEGERP-CORRECT))
 (3 3 (:REWRITE REDUCE-INTEGERP-+))
 (3 3 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (3 3 (:REWRITE PFIELD::NEG-WHEN-NOT-POSP-ARG2-CHEAP))
 (3 3 (:REWRITE PFIELD::NEG-WHEN-NOT-INTEGERP-CHEAP))
 (3 3 (:REWRITE DEFAULT-UNARY-/))
 (3 2 (:REWRITE SIMPLIFY-SUMS-<))
 (3 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (3 2 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (3 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (2 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (2 2 (:REWRITE SIMPLIFY-MOD-+-MOD-WEAK))
 (2 2 (:REWRITE SIMPLIFY-MOD-+-MINUS-MOD))
 (2 2 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2 2 (:REWRITE NORMALIZE-ADDENDS))
 (2 2 (:REWRITE PFIELD::MUL-OF--1-BECOMES-NEG-ALT))
 (2 2 (:REWRITE MOD-MINUS-2))
 (2 2 (:REWRITE MOD-CANCEL-*))
 (2 2 (:REWRITE DEFAULT-UNARY-MINUS))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE |(equal (- x) (- y))|))
 (2 2 (:REWRITE |(< (- x) (- y))|))
 (2 2 (:REWRITE |(* (- x) y)|))
 (1 1 (:TYPE-PRESCRIPTION NATP))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-=-0))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-<-0))
 (1 1 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (1 1 (:REWRITE NOT-PRIMEP-WHEN-DIVIDES))
 (1 1 (:REWRITE MOD-X-Y-=-X . 4))
 (1 1 (:REWRITE PFIELD::FEP-WHEN-CONSTANT))
 (1 1 (:REWRITE |(equal (- x) 0)|))
 (1 1 (:REWRITE |(< (- x) 0)|))
 (1 1 (:REWRITE |(* 1 x)|))
 )
(ECURVE::EQUAL-OF-MINUS1-AND-DIV
 (6 6 (:REWRITE PFIELD::ADD-SUBST-CONSTANT-ARG2))
 (6 6 (:REWRITE PFIELD::ADD-SUBST-CONSTANT-ARG1))
 (6 6 (:REWRITE PFIELD::ADD-OF-CONSTANTS))
 (6 2 (:DEFINITION NATP))
 (3 3 (:REWRITE NOT-PRIMEP-WHEN-DIVIDES))
 (3 3 (:REWRITE PFIELD::NEG-WHEN-NOT-POSP-ARG2-CHEAP))
 (3 3 (:REWRITE PFIELD::NEG-WHEN-NOT-INTEGERP-CHEAP))
 (3 3 (:REWRITE PFIELD::NEG-WHEN-CONSTANT-ARG1))
 (3 3 (:REWRITE PFIELD::ADD-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (3 3 (:REWRITE PFIELD::ADD-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (3 3 (:REWRITE PFIELD::ADD-COMMUTATIVE-WHEN-CONSTANT))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:REWRITE PFIELD::FEP-WHEN-CONSTANT))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE PFIELD::EQUAL-OF-ADD-COMBINE-CONSTANTS-ALT))
 (1 1 (:REWRITE PFIELD::EQUAL-OF-ADD-COMBINE-CONSTANTS))
 (1 1 (:REWRITE PFIELD::EQUAL-OF-0-AND-ADD-SAFE))
 )
(ECURVE::DIV-OF-NEG-AND-NEG
 (8 5 (:REWRITE PFIELD::NEG-WHEN-NOT-INTEGERP-CHEAP))
 (6 2 (:DEFINITION NATP))
 (5 5 (:REWRITE PFIELD::NEG-WHEN-NOT-POSP-ARG2-CHEAP))
 (4 4 (:REWRITE PFIELD::NEG-WHEN-CONSTANT-ARG1))
 (4 4 (:REWRITE PFIELD::MUL-OF--1-BECOMES-NEG-ALT))
 (4 2 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (3 3 (:TYPE-PRESCRIPTION PFIELD::NATP-OF-INV))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (2 2 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG2))
 (2 2 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG1))
 (2 2 (:REWRITE PFIELD::MUL-WHEN-CONSTANT-REDUCE-ARG1))
 (2 2 (:REWRITE PFIELD::MUL-COMMUTATIVE))
 (2 2 (:REWRITE PFIELD::FEP-WHEN-CONSTANT))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 1 (:REWRITE IFIX-WHEN-NOT-INTEGERP-UNLIMITED))
 (1 1 (:TYPE-PRESCRIPTION PFIELD::NATP-OF-NEG))
 (1 1 (:REWRITE NOT-PRIMEP-WHEN-DIVIDES))
 (1 1 (:REWRITE PFIELD::NEG-OF-MUL-WHEN-CONSTANT))
 )
(ECURVE::EXTEND-FRACTION-TO-SUM
 (20 4 (:REWRITE PFIELD::FEP-HOLDS))
 (15 15 (:REWRITE PFIELD::MUL-OF--1-BECOMES-NEG-ALT))
 (13 13 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG2))
 (13 13 (:REWRITE PFIELD::MUL-WHEN-EQUAL-OF-MOD-SUBST-ARG1))
 (13 13 (:REWRITE PFIELD::MUL-WHEN-CONSTANT-REDUCE-ARG1))
 (12 4 (:DEFINITION NATP))
 (11 8 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (11 8 (:REWRITE PFIELD::MUL-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (6 6 (:TYPE-PRESCRIPTION PFIELD::NATP-OF-MUL))
 (6 3 (:REWRITE PFIELD::ADD-WHEN-NOT-INTEGERP-ARG2-CHEAP))
 (5 5 (:REWRITE PFIELD::ADD-SUBST-CONSTANT-ARG2))
 (5 5 (:REWRITE PFIELD::ADD-SUBST-CONSTANT-ARG1))
 (5 5 (:REWRITE PFIELD::ADD-OF-CONSTANTS))
 (4 4 (:TYPE-PRESCRIPTION PFIELD::NATP-OF-INV))
 (4 4 (:TYPE-PRESCRIPTION NATP))
 (4 4 (:REWRITE PFIELD::FEP-WHEN-CONSTANT))
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (4 3 (:REWRITE PFIELD::ADD-WHEN-NOT-INTEGERP-ARG1-CHEAP))
 (2 2 (:REWRITE PFIELD::MUL-OF-MUL-COMBINE-CONSTANTS))
 (2 2 (:REWRITE PFIELD::MUL-COMMUTATIVE-2))
 (2 2 (:REWRITE PFIELD::ADD-COMMUTATIVE-WHEN-CONSTANT))
 (1 1 (:REWRITE NOT-PRIMEP-WHEN-DIVIDES))
 )
