(INT-REM::CLOSURE-LAWS)
(INT-REM::EQUIVALENCE-LAW)
(INT-REM::CONGRUENCE-LAWS)
(INT-REM::CLOSURE-OF-IDENTITY)
(INT-REM::EQUIVALENCE-CLASS-LAWS)
(INT-REM::COMMUTATIVITY-LAWS
 (3 3 (:REWRITE DEFAULT-+-2))
 (3 3 (:REWRITE DEFAULT-+-1))
 (3 3 (:REWRITE DEFAULT-*-2))
 (3 3 (:REWRITE DEFAULT-*-1))
 )
(INT-REM::ASSOCIATIVITY-LAWS)
(INT-REM::LEFT-DISTRIBUTIVITY-LAW
 (6 2 (:LINEAR X*Y>1-POSITIVE))
 (5 5 (:REWRITE DEFAULT-*-2))
 (5 5 (:REWRITE DEFAULT-*-1))
 (3 3 (:REWRITE DEFAULT-+-2))
 (3 3 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 )
(INT-REM::LEFT-UNICITY-LAWS)
(INT-REM::RIGHT-INVERSE-LAW
 (3 3 (:TYPE-PRESCRIPTION |x < y  =>  0 < y-x|))
 )
(INT-REM::ZERO-DIVISOR-LAW
 (1 1 (:REWRITE DEFAULT-*-2))
 (1 1 (:REWRITE DEFAULT-*-1))
 )
(INT-REM::NATP-ABS
 (14 14 (:REWRITE DEFAULT-<-2))
 (14 14 (:REWRITE DEFAULT-<-1))
 (9 9 (:REWRITE DEFAULT-UNARY-MINUS))
 (1 1 (:TYPE-PRESCRIPTION INT-REM::NATP-ABS))
 )
(INT-REM::CONGRUENCE-FOR-ABS)
(INT-REM::CLOSURE-OF-TRUNCATE-&-REM
 (1 1 (:TYPE-PRESCRIPTION TRUNCATE-TYPE . 4))
 (1 1 (:TYPE-PRESCRIPTION TRUNCATE-TYPE . 3))
 (1 1 (:TYPE-PRESCRIPTION TRUNCATE-TYPE . 2))
 (1 1 (:TYPE-PRESCRIPTION TRUNCATE-TYPE . 1))
 (1 1 (:TYPE-PRESCRIPTION REM-TYPE . 4))
 (1 1 (:TYPE-PRESCRIPTION REM-TYPE . 3))
 (1 1 (:TYPE-PRESCRIPTION REM-TYPE . 2))
 (1 1 (:TYPE-PRESCRIPTION REM-TYPE . 1))
 )
(INT-REM::CONGRUENCE-FOR-TRUNCATE-&-REM
 (16 16 (:TYPE-PRESCRIPTION TRUNCATE-TYPE . 4))
 (16 16 (:TYPE-PRESCRIPTION TRUNCATE-TYPE . 3))
 (16 16 (:TYPE-PRESCRIPTION TRUNCATE-TYPE . 2))
 (16 16 (:TYPE-PRESCRIPTION TRUNCATE-TYPE . 1))
 (16 16 (:TYPE-PRESCRIPTION REM-TYPE . 4))
 (16 16 (:TYPE-PRESCRIPTION REM-TYPE . 3))
 (16 16 (:TYPE-PRESCRIPTION REM-TYPE . 2))
 (16 16 (:TYPE-PRESCRIPTION REM-TYPE . 1))
 )
(INT-REM::DIVISION-PROPERTY
 (148 13 (:REWRITE REM-X-Y-=-X . 2))
 (92 92 (:TYPE-PRESCRIPTION REM-TYPE . 2))
 (63 53 (:REWRITE DEFAULT-<-1))
 (53 53 (:REWRITE DEFAULT-<-2))
 (27 22 (:REWRITE DEFAULT-UNARY-MINUS))
 (19 19 (:TYPE-PRESCRIPTION TRUNCATE-TYPE . 4))
 (19 19 (:TYPE-PRESCRIPTION TRUNCATE-TYPE . 3))
 (19 19 (:TYPE-PRESCRIPTION TRUNCATE-TYPE . 2))
 (19 19 (:TYPE-PRESCRIPTION TRUNCATE-TYPE . 1))
 (18 13 (:REWRITE REM-=-0 . 2))
 (13 1 (:REWRITE TRUNCATE-TYPE . 2))
 (12 8 (:REWRITE /R-WHEN-ABS-NUMERATOR=1))
 (10 5 (:REWRITE DEFAULT-*-2))
 (8 4 (:LINEAR REM-TYPE . 2))
 (8 1 (:REWRITE TRUNCATE-=-X/Y . 2))
 (6 1 (:REWRITE DEFAULT-+-2))
 (6 1 (:REWRITE DEFAULT-+-1))
 (5 5 (:REWRITE DEFAULT-*-1))
 (4 4 (:REWRITE NUMERATOR-WHEN-INTEGERP))
 (4 4 (:REWRITE DEFAULT-UNARY-/))
 )
(INT-REM::ABS-*
 (84 76 (:REWRITE DEFAULT-<-2))
 (80 76 (:REWRITE DEFAULT-<-1))
 (43 8 (:LINEAR X*Y>1-POSITIVE))
 (37 36 (:REWRITE DEFAULT-*-2))
 (37 36 (:REWRITE DEFAULT-*-1))
 (20 20 (:REWRITE DEFAULT-UNARY-MINUS))
 (3 1 (:REWRITE ZERO-IS-ONLY-ZERO-DIVISOR))
 )
(INT-REM::DIVIDES-P)
(INT-REM::DIVIDES-P-SUFF)
(INT-REM::UNIT-P)
(INT-REM::ABS-UNIT-P=1
 (42 42 (:TYPE-PRESCRIPTION REM-TYPE . 4))
 (42 42 (:TYPE-PRESCRIPTION REM-TYPE . 3))
 (42 42 (:TYPE-PRESCRIPTION REM-TYPE . 2))
 (42 42 (:TYPE-PRESCRIPTION REM-TYPE . 1))
 (38 4 (:REWRITE REM-X-Y-=-X . 2))
 (35 35 (:TYPE-PRESCRIPTION TRUNCATE-TYPE . 4))
 (35 35 (:TYPE-PRESCRIPTION TRUNCATE-TYPE . 3))
 (35 35 (:TYPE-PRESCRIPTION TRUNCATE-TYPE . 2))
 (35 35 (:TYPE-PRESCRIPTION TRUNCATE-TYPE . 1))
 (30 22 (:REWRITE DEFAULT-*-2))
 (23 22 (:REWRITE DEFAULT-*-1))
 (18 14 (:REWRITE DEFAULT-<-1))
 (18 1 (:REWRITE TRUNCATE-TYPE . 2))
 (17 14 (:REWRITE DEFAULT-<-2))
 (12 8 (:REWRITE /R-WHEN-ABS-NUMERATOR=1))
 (12 7 (:REWRITE DEFAULT-+-2))
 (12 7 (:REWRITE DEFAULT-+-1))
 (10 3 (:LINEAR X*Y>1-POSITIVE))
 (9 4 (:REWRITE REM-=-0 . 2))
 (8 1 (:REWRITE TRUNCATE-=-X/Y . 2))
 (6 2 (:LINEAR REM-BOUNDS))
 (4 4 (:REWRITE NUMERATOR-WHEN-INTEGERP))
 (4 4 (:REWRITE DEFAULT-UNARY-/))
 (3 1 (:LINEAR REM-TYPE . 4))
 (3 1 (:LINEAR REM-TYPE . 3))
 (3 1 (:LINEAR REM-TYPE . 2))
 (3 1 (:LINEAR REM-TYPE . 1))
 (1 1 (:TYPE-PRESCRIPTION |x < y  =>  0 < y-x|))
 )
(INT-REM::ABS=1-IMPLIES-UNIT-P)
(INT-REM::UNIT-P=_+1_OR_-1
 (14 14 (:REWRITE INT-REM::DIVIDES-P-SUFF))
 (6 6 (:REWRITE DEFAULT-*-2))
 (6 6 (:REWRITE DEFAULT-*-1))
 (5 4 (:REWRITE DEFAULT-<-1))
 (4 4 (:REWRITE DEFAULT-UNARY-MINUS))
 (4 4 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1 1 (:LINEAR X*Y>1-POSITIVE))
 )
(INT-REM::ABS-<-ABS-*
 (12 12 (:REWRITE DEFAULT-<-2))
 (12 12 (:REWRITE DEFAULT-<-1))
 (9 9 (:REWRITE DEFAULT-UNARY-MINUS))
 (5 5 (:REWRITE DEFAULT-*-2))
 (5 5 (:REWRITE DEFAULT-*-1))
 (3 1 (:LINEAR X*Y>1-POSITIVE))
 )
(INT-REM::REDUCIBLE-P)
(INT-REM::REDUCIBLE-P-SUFF
 (4 4 (:DEFINITION MV-NTH))
 )
(INT-REM::IRREDUCIBLE-P)
(INT-REM::IRREDUCIBLE-P-IMPLIES-PRIME-PROPERTY
 (139 8 (:REWRITE INT-REM::DIVIDES-P-SUFF))
 (103 3 (:REWRITE INT-REM::REDUCIBLE-P-SUFF))
 (72 24 (:LINEAR X*Y>1-POSITIVE))
 (58 58 (:TYPE-PRESCRIPTION NONNEGATIVE-PRODUCT))
 (24 24 (:REWRITE DEFAULT-<-2))
 (24 24 (:REWRITE DEFAULT-<-1))
 (18 18 (:REWRITE DEFAULT-*-2))
 (18 18 (:REWRITE DEFAULT-*-1))
 (2 2 (:REWRITE EQUAL-*-X-Y-Y))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE DEFAULT-CAR))
 )
(INT-REM::IRREDUCIBLE-FACTORS
 (218 14 (:REWRITE INT-REM::REDUCIBLE-P-SUFF))
 (38 8 (:REWRITE DEFAULT-<-2))
 (38 8 (:REWRITE DEFAULT-<-1))
 (34 10 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (12 9 (:REWRITE DEFAULT-*-2))
 (12 9 (:REWRITE DEFAULT-*-1))
 (6 2 (:LINEAR X*Y>1-POSITIVE))
 (6 2 (:LINEAR INT-REM::ABS-<-ABS-*))
 (4 4 (:TYPE-PRESCRIPTION NONNEGATIVE-PRODUCT))
 (3 1 (:REWRITE INT-REM::ABS-<-ABS-*))
 (2 2 (:REWRITE INT-REM::ABS-*))
 (2 2 (:LINEAR INT-REM::ABS-*))
 (1 1 (:TYPE-PRESCRIPTION TRUE-LISTP))
 )
(INT-REM::INTEGERP-LISTP)
(INT-REM::IRREDUCIBLE-LISTP)
(INT-REM::*-LST)
(INT-REM::IRREDUCIBLE-FACTORIZATION-EXISTENCE
 (252 12 (:REWRITE INT-REM::REDUCIBLE-P-SUFF))
 (120 120 (:TYPE-PRESCRIPTION INT-REM::UNIT-P))
 (120 120 (:REWRITE INT-REM::UNIT-P=_+1_OR_-1))
 (55 11 (:DEFINITION BINARY-APPEND))
 (31 31 (:REWRITE DEFAULT-CAR))
 (26 26 (:REWRITE DEFAULT-CDR))
 (10 5 (:REWRITE DEFAULT-*-2))
 (5 5 (:REWRITE DEFAULT-*-1))
 )
(INT-REM::UNIT-ASSOCIATES-P)
(INT-REM::UNIT-ASSOCIATES-P-SUFF)
(INT-REM::IRREDUCIBLE-P-UNIT-ASSOCIATES
 (6 6 (:REWRITE DEFAULT-*-2))
 (6 6 (:REWRITE DEFAULT-*-1))
 (2 2 (:REWRITE INT-REM::DIVIDES-P-SUFF))
 (1 1 (:REWRITE INT-REM::UNIT-ASSOCIATES-P-SUFF))
 )
(INT-REM::MEMBER-UNIT-ASSOCIATE)
(INT-REM::DELETE-ONE-UNIT-ASSOCIATE)
(INT-REM::BAG-EQUAL-UNIT-ASSOCIATES)
(INT-REM::BAG-EQUAL-UNIT-ASSOCIATES->EQUAL-LEN
 (58 38 (:REWRITE DEFAULT-*-2))
 (56 38 (:REWRITE DEFAULT-*-1))
 (50 50 (:REWRITE DEFAULT-CAR))
 (38 38 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (35 35 (:REWRITE DEFAULT-CDR))
 (18 18 (:REWRITE INT-REM::UNIT-ASSOCIATES-P-SUFF))
 )
(INT-REM::BAG-EQUAL-UNIT-ASSOCIATES->IFF-MEMBER-UNIT-ASSOCIATE)
(INT-REM::MULTIPLICITY-UNIT-ASSOCIATE)
(INT-REM::BAG-EQUAL-UNIT-ASSOCIATES->EQUAL-MULTIPLICITY-UNIT-ASSOCIATE
 (20 13 (:REWRITE DEFAULT-*-2))
 (19 13 (:REWRITE DEFAULT-*-1))
 (14 14 (:REWRITE DEFAULT-CDR))
 (14 7 (:REWRITE DEFAULT-+-2))
 (13 13 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (12 12 (:REWRITE DEFAULT-CAR))
 (7 7 (:REWRITE DEFAULT-+-1))
 (6 6 (:REWRITE INT-REM::UNIT-ASSOCIATES-P-SUFF))
 )
(INT-REM::IRREDUCIBLE-FACTORIZATION-UNIQUENESS-GENERAL)
(INT-REM::IRREDUCIBLE-FACTORIZATION-UNIQUENESS)
