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(EQUIVALENCE-LAW)
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(CLOSURE-OF-C_=_E)
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 (8 4 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
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(==_E-REFINES-ASSOCIATES-PP)
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 (42 3 (:REWRITE DEFAULT-<-1))
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(ASSOCIATES-PP-IMPLIES-EQUAL-SIZE-LEMMA-1
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(ASSOCIATES-PP-IMPLIES-EQUAL-SIZE-LEMMA-2
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 (42 6 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
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(ASSOCIATES-PP-IMPLIES-EQUAL-SIZE
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(UNIT-P)
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(UNIT-P-=-UNIT-PP)
(==_E-IMPLIES-EQUAL-UNIT-PP)
(ASSOCIATES-PP-IMPLIES-EQUAL-UNIT-PP)
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 (2 1 (:REWRITE DIVIDES-P-IMPLIES-RR_E=0))
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 (1 1 (:REWRITE |1_E-0_E|))
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 (30 5 (:REWRITE DIVIDES-PP-IMPLIES-WITNESS=QQ_E))
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(SIZE-IMPLIES-IRREDUCIBLE-P
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 (378 378 (:REWRITE CLOSURE-LAWS))
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(EDP-LISTP)
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(EDP-LISTP-IRREDUCIBLE-FACTORS-1)
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(*_E-LST)
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(*_E-LST-=-**_E-LST
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(*_E-LST-APPEND
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(RIGHT-UNICITY-LAW-FOR-*_E)
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(*_E-LST-IRREDUCIBLE-FACTORS
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(GCD-P)
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(==_E-IMPLIES-==_E-GCD-PP-WITNESS-1)
(==_E-IMPLIES-==_E-GCD-PP-WITNESS-2)
(==_E-IMPLIES-==_E-GCD-PP-WITNESS-3)
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(GCD-P-NECC-1
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(INTEGERP-FIND-SMALLEST-N)
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(NATP-FIND-SMALLEST-N-0)
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(EQUATION-0)
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 (63 18 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
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(ASSOCIATES-PP-REFINES-UNIT-ASSOCIATES-PP-LEMMA-3
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 (138 42 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (121 18 (:REWRITE IRREDUCIBLE-PP-IMPLIES-UNIT-PP-FACTOR))
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(ASSOCIATES-PP-REFINES-UNIT-ASSOCIATES-PP
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(UNIT-ASSOCIATES-PP-REFINES-ASSOCIATES-PP-LEMMA-1
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(UNIT-ASSOCIATES-PP-REFINES-ASSOCIATES-PP
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(UNIT-ASSOCIATES-PP-IMPLIES-REDUCIBLE-PP-LEMMA-1
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(UNIT-ASSOCIATES-PP-IMPLIES-REDUCIBLE-PP-LEMMA-2
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(UNIT-ASSOCIATES-PP-IMPLIES-REDUCIBLE-PP-LEMMA-5
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(MEMBER-UNIT-ASSOCIATE)
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(DELETE-ONE-UNIT-ASSOCIATE)
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(BAG-EQUAL-UNIT-ASSOCIATES)
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(MULTIPLICITY-UNIT-ASSOCIATE)
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 (5 5 (:REWRITE EQUAL-CONSTANT-+))
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(MULTIPLICITY-UNIT-ASSOCIATE-PP-DELETE-ONE-UNIT-ASSOCIATE-PP-2
 (38 38 (:REWRITE DEFAULT-CDR))
 (32 32 (:REWRITE DEFAULT-CAR))
 (31 31 (:REWRITE UNIT-ASSOCIATES-PP-SUFF))
 (26 13 (:REWRITE DEFAULT-+-2))
 (13 13 (:REWRITE DEFAULT-+-1))
 )
(BAG-EQUAL-UNIT-ASSOCIATES-PP->EQUAL-MULTIPLICITY-UNIT-ASSOCIATE-PP
 (123 123 (:REWRITE DEFAULT-CDR))
 (114 114 (:REWRITE DEFAULT-CAR))
 (114 19 (:DEFINITION DELETE-ONE-UNIT-ASSOCIATE-PP))
 (79 79 (:REWRITE UNIT-ASSOCIATES-PP-SUFF))
 (66 33 (:REWRITE DEFAULT-+-2))
 (64 16 (:DEFINITION MEMBER-UNIT-ASSOCIATE-PP))
 (33 33 (:REWRITE DEFAULT-+-1))
 (20 5 (:REWRITE MEMBER-UNIT-ASSOCIATE-PP-DELETE-ONE-UNIT-ASSOCIATE-PP))
 (5 5 (:REWRITE EQUAL-CONSTANT-+))
 )
(BAG-EQUAL-UNIT-ASSOCIATES->EQUAL-MULTIPLICITY-UNIT-ASSOCIATE)
(DIVIDES-PP-MEMBER-UNIT-ASSOCIATE-PP-**_E-LST
 (685 123 (:REWRITE UNIT-P-IMPLIES-EDP))
 (598 19 (:DEFINITION UNIT-P))
 (514 19 (:DEFINITION DIVIDES-P))
 (452 218 (:REWRITE EQUIVALENCE-LAW))
 (123 123 (:TYPE-PRESCRIPTION UNIT-P))
 (108 12 (:REWRITE ZERO-DIVISOR-LAW))
 (65 19 (:REWRITE DIVIDES-P-SUFF))
 (51 7 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (49 19 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (27 27 (:REWRITE DEFAULT-CAR))
 (8 8 (:REWRITE UNIT-ASSOCIATES-PP-SUFF))
 (6 6 (:REWRITE DEFAULT-CDR))
 (5 5 (:REWRITE TRANSITIVITY-DIVIDES-PP))
 (1 1 (:REWRITE NULLITY-LAWS))
 )
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 (602 99 (:REWRITE UNIT-P-IMPLIES-EDP))
 (513 19 (:DEFINITION UNIT-P))
 (423 19 (:DEFINITION DIVIDES-P))
 (346 186 (:REWRITE EQUIVALENCE-LAW))
 (104 104 (:REWRITE CLOSURE-LAWS))
 (99 99 (:TYPE-PRESCRIPTION UNIT-P))
 (80 20 (:REWRITE IRREDUCIBLE-PP-IMPLIES-UNIT-PP-FACTOR))
 (72 8 (:REWRITE ZERO-DIVISOR-LAW))
 (71 19 (:REWRITE DIVIDES-P-SUFF))
 (61 7 (:REWRITE DIVIDES-PP-SUFF))
 (52 10 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-PP))
 (47 19 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (39 7 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (31 7 (:REWRITE UNIT-ASSOCIATES-PP-REFINES-ASSOCIATES-PP-LEMMA-1))
 (16 3 (:REWRITE DIVIDES-PP-IMPLIES-WITNESS=QQ_E))
 (8 3 (:REWRITE ASSOCIATES-PP-REFINES-UNIT-ASSOCIATES-PP-LEMMA-2))
 (7 7 (:REWRITE TRANSITIVITY-DIVIDES-PP))
 (6 2 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
 (5 5 (:REWRITE UNIT-PP-NOT-REDUCIBLE-PP))
 (2 2 (:REWRITE UNIT-ASSOCIATES-PP-SUFF))
 (2 2 (:REWRITE RIGHT-UNICITY-LAWS))
 (2 2 (:REWRITE NULLITY-LAWS))
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(GCD-PP-OF-IRREDUCIBLE-PP
 (61 2 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
 (45 3 (:REWRITE DIVIDES-PP-SUFF))
 (38 10 (:REWRITE UNIT-P-IMPLIES-EDP))
 (30 25 (:TYPE-PRESCRIPTION NATP-SIZE-==_E))
 (27 3 (:DEFINITION UNIT-P))
 (21 4 (:LINEAR SIZE->=-SIZE-1_E))
 (21 3 (:DEFINITION DIVIDES-P))
 (19 3 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (18 18 (:TYPE-PRESCRIPTION NATP-SIZE))
 (18 3 (:REWRITE UNIT-ASSOCIATES-PP-REFINES-ASSOCIATES-PP-LEMMA-1))
 (10 10 (:TYPE-PRESCRIPTION UNIT-P))
 (6 6 (:REWRITE EQUIVALENCE-LAW))
 (5 5 (:REWRITE CLOSURE-LAWS))
 (3 3 (:REWRITE TRANSITIVITY-DIVIDES-PP))
 (3 3 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (3 3 (:REWRITE DIVIDES-P-SUFF))
 (3 1 (:REWRITE PROJECTION-LAWS))
 (2 2 (:REWRITE UNIT-ASSOCIATES-PP-SUFF))
 (2 2 (:REWRITE RIGHT-UNICITY-LAWS))
 (2 2 (:REWRITE NULLITY-LAWS))
 (1 1 (:REWRITE GCD-PP-NECC))
 (1 1 (:REWRITE |1_E-0_E|))
 )
(GCD-PP-OF-IRREDUCIBLE-PP-DIVIDES-PP
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 (783 87 (:DEFINITION UNIT-P))
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 (478 51 (:REWRITE UNIT-ASSOCIATES-PP-REFINES-ASSOCIATES-PP-LEMMA-1))
 (477 51 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (427 42 (:REWRITE DIVIDES-PP-SUFF))
 (304 304 (:TYPE-PRESCRIPTION UNIT-P))
 (196 7 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
 (174 174 (:REWRITE EQUIVALENCE-LAW))
 (100 70 (:TYPE-PRESCRIPTION NATP-SIZE-==_E))
 (87 87 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (87 87 (:REWRITE DIVIDES-P-SUFF))
 (63 63 (:TYPE-PRESCRIPTION NATP-SIZE))
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 (12 4 (:REWRITE PROJECTION-LAWS))
 (11 11 (:REWRITE CLOSURE-LAWS))
 (7 7 (:REWRITE UNIT-ASSOCIATES-PP-SUFF))
 (7 7 (:REWRITE GCD-PP-NECC))
 (5 5 (:REWRITE RIGHT-UNICITY-LAWS))
 (5 5 (:REWRITE NULLITY-LAWS))
 (3 3 (:REWRITE COMMUTATIVITY-LAWS-FOR-++_E-&-**_E))
 (2 1 (:REWRITE DIVIDES-PP-IMPLIES-RR_E=0-LEMMA-1))
 (2 1 (:REWRITE DIVIDES-P-IMPLIES-RR_E=0))
 (1 1 (:REWRITE |1_E-0_E|))
 )
(UNIT-PP-BEZOUT)
(ASSOCIATE-PP-UNIT-PP
 (190 28 (:REWRITE UNIT-P-IMPLIES-EDP))
 (158 8 (:DEFINITION UNIT-P))
 (118 8 (:DEFINITION DIVIDES-P))
 (106 72 (:REWRITE EQUIVALENCE-LAW))
 (42 6 (:REWRITE UNIT-ASSOCIATES-PP-REFINES-ASSOCIATES-PP-LEMMA-1))
 (40 6 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (32 8 (:REWRITE DIVIDES-P-SUFF))
 (28 28 (:TYPE-PRESCRIPTION UNIT-P))
 (28 28 (:REWRITE CLOSURE-LAWS))
 (26 2 (:REWRITE DIVIDES-PP-SUFF))
 (18 2 (:REWRITE ZERO-DIVISOR-LAW))
 (16 8 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (8 8 (:TYPE-PRESCRIPTION UNIT-ASSOCIATES-PP))
 (8 8 (:EQUIVALENCE ==_E-EQUIVALENCE-LAW))
 (4 4 (:REWRITE UNIT-ASSOCIATES-PP-SUFF))
 (2 2 (:REWRITE |1_E-0_E|))
 (1 1 (:REWRITE GCD-PP-ASSOCIATES-PP))
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(IRREDUCIBLE-PP-GCD=1_E
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 (1128 1128 (:REWRITE CLOSURE-LAWS))
 (976 976 (:TYPE-PRESCRIPTION UNIT-P))
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 (681 44 (:REWRITE DIVIDES-PP-SUFF))
 (455 91 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-PP))
 (417 182 (:REWRITE IRREDUCIBLE-PP-IMPLIES-UNIT-PP-FACTOR))
 (417 123 (:REWRITE DIVIDES-P-SUFF))
 (345 123 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (279 279 (:TYPE-PRESCRIPTION BEZOUT))
 (262 76 (:REWRITE DEFAULT-CAR))
 (180 20 (:REWRITE ASSOCIATE-PP-UNIT-PP))
 (138 45 (:REWRITE DEFAULT-CDR))
 (132 44 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (132 44 (:REWRITE PROJECTION-LAWS))
 (112 5 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
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 (44 44 (:REWRITE RIGHT-UNICITY-LAWS))
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 (40 32 (:REWRITE CLOSURE-LAWS-FOR-++_E-&-**_E))
 (38 38 (:TYPE-PRESCRIPTION NATP-SIZE))
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 (20 20 (:REWRITE GCD-PP-ASSOCIATES-PP))
 (12 8 (:REWRITE REDUCIBLE-PP-SUFF))
 (10 4 (:LINEAR SIZE->=-SIZE-1_E))
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 (6 6 (:TYPE-PRESCRIPTION BOOLEANP-DIVIDES-P))
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(EDP-LINEAR-COMBINATION
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 (80 3 (:REWRITE LINEAR-COMBINATION-DIVIDES-PP-GCD))
 (63 36 (:REWRITE EQUIVALENCE-LAW))
 (36 18 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (36 18 (:REWRITE DIVIDES-P-SUFF))
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 (6256 1432 (:REWRITE UNIT-P-IMPLIES-EDP))
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 (1594 1114 (:REWRITE EQUIVALENCE-LAW))
 (1432 1432 (:TYPE-PRESCRIPTION UNIT-P))
 (759 199 (:DEFINITION UNIT-PP))
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 (608 1 (:REWRITE IRREDUCIBLE-PP-GCD=1_E))
 (575 1 (:DEFINITION IRREDUCIBLE-PP))
 (479 384 (:REWRITE DIVIDES-P-SUFF))
 (420 384 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (398 398 (:REWRITE IRREDUCIBLE-PP-IMPLIES-UNIT-PP-FACTOR))
 (325 313 (:REWRITE CLOSURE-LAWS))
 (315 17 (:REWRITE ZERO-DIVISOR-LAW))
 (277 1 (:DEFINITION REDUCIBLE-PP))
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(IRREDUCIBLE-PP-IMPLIES-PRIME-PROPERTY
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 (184 16 (:REWRITE DIVIDES-P-SUFF))
 (181 10 (:REWRITE DIVIDES-PP-**_E))
 (179 18 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
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 (9 3 (:REWRITE ZERO-DIVISOR-LAW-FOR-**_E))
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 (1 1 (:REWRITE |1_E-0_E|))
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(IRREDUCIBLE-P-IMPLIES-PRIME-PROPERTY
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 (92 3 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
 (83 19 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
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 (1 1 (:REWRITE |1_E-0_E|))
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(IRREDUCIBLE-PP-UNIT-ASSOCIATES
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 (225 13 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
 (171 44 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (100 10 (:REWRITE DIVIDES-PP-SUFF))
 (84 60 (:TYPE-PRESCRIPTION NATP-SIZE-==_E))
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 (8 8 (:REWRITE IRREDUCIBLE-PP-IMPLIES-UNIT-PP-FACTOR))
 (4 4 (:REWRITE RIGHT-UNICITY-LAWS))
 (4 4 (:REWRITE NULLITY-LAWS))
 (1 1 (:REWRITE UNIT-ASSOCIATES-PP-SUFF))
 (1 1 (:REWRITE |1_E-0_E|))
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(IRREDUCIBLE-P-UNIT-ASSOCIATES)
(EDP-IRREDUCIBLE-PP)
(DIVIDES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-LEMMA
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 (1987 60 (:DEFINITION UNIT-P))
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 (640 498 (:TYPE-PRESCRIPTION NATP-SIZE-==_E))
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 (380 380 (:TYPE-PRESCRIPTION NATP-SIZE))
 (364 364 (:TYPE-PRESCRIPTION UNIT-P))
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 (222 58 (:LINEAR SIZE->=-SIZE-1_E))
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 (184 16 (:REWRITE DIVIDES-PP-MEMBER-UNIT-ASSOCIATE-PP-**_E-LST))
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 (87 87 (:REWRITE PRIME-PROPERTY-LEMMA))
 (63 63 (:REWRITE NULLITY-LAWS))
 (54 2 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-PP))
 (43 43 (:REWRITE DEFAULT-CAR))
 (28 28 (:TYPE-PRESCRIPTION BOOLEANP-DIVIDES-P))
 (24 7 (:REWRITE CLOSURE-LAWS-FOR-++_E-&-**_E))
 (16 16 (:REWRITE COMMUTATIVITY-LAWS-FOR-++_E-&-**_E))
 (15 15 (:REWRITE DEFAULT-CDR))
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 (4 4 (:REWRITE IRREDUCIBLE-PP-IMPLIES-UNIT-PP-FACTOR))
 (2 2 (:REWRITE CANCELLATION-LAWS-FOR-**_E))
 (2 2 (:REWRITE |1_E-0_E|))
 (1 1 (:REWRITE PROJECTION-LAWS-1))
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(IRREDUCIBLE-PP-NOT-UNIT-PP)
(DIVIDES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP
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 (1151 72 (:DEFINITION UNIT-P))
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 (712 422 (:REWRITE EQUIVALENCE-LAW))
 (653 182 (:REWRITE UNIT-P-IMPLIES-EDP))
 (543 2 (:REWRITE REDUCIBLE-P-SUFF))
 (535 3 (:REWRITE DIVIDES-PP-MEMBER-UNIT-ASSOCIATE-PP-**_E-LST))
 (442 2 (:DEFINITION REDUCIBLE-P))
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 (225 225 (:TYPE-PRESCRIPTION UNIT-P))
 (224 1 (:DEFINITION **_E-LST))
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 (6 2 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-P))
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 (198 2 (:REWRITE IRREDUCIBLE-PP-IMPLIES-PRIME-PROPERTY))
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 (38 21 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
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 (3 3 (:REWRITE COMMUTATIVITY-LAWS-FOR-++_E-&-**_E))
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 (2 2 (:REWRITE REDUCIBLE-PP-SUFF))
 (2 2 (:REWRITE DEFAULT-CDR))
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 (1 1 (:REWRITE TRANSITIVITY-DIVIDES-PP))
 (1 1 (:REWRITE RIGHT-UNICITY-LAWS))
 (1 1 (:REWRITE PRIME-PROPERTY-LEMMA))
 (1 1 (:REWRITE NULLITY-LAWS))
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(==_E-**_E-UNIT-ASSOCIATES-PP-WITNESS
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 (347 46 (:REWRITE IRREDUCIBLE-PP-IMPLIES-UNIT-PP-FACTOR))
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 (271 23 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-PP))
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 (48 31 (:TYPE-PRESCRIPTION NATP-SIZE-==_E))
 (43 5 (:REWRITE REDUCIBLE-PP-SUFF))
 (32 4 (:REWRITE DIVIDES-PP-SUFF))
 (31 31 (:TYPE-PRESCRIPTION NATP-SIZE))
 (26 26 (:TYPE-PRESCRIPTION BOOLEANP-DIVIDES-P))
 (20 10 (:DEFINITION MV-NTH))
 (15 15 (:TYPE-PRESCRIPTION IRREDUCIBLE-PP))
 (12 12 (:TYPE-PRESCRIPTION DIVIDES-PP))
 (9 4 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (8 8 (:REWRITE UNIT-ASSOCIATES-PP-SUFF))
 (7 3 (:LINEAR SIZE->=-SIZE-1_E))
 (5 5 (:REWRITE UNIT-PP-NOT-REDUCIBLE-PP))
 (5 5 (:REWRITE DEFAULT-CDR))
 (5 5 (:REWRITE DEFAULT-CAR))
 (4 4 (:REWRITE TRANSITIVITY-DIVIDES-PP))
 (4 4 (:REWRITE PRIME-PROPERTY-LEMMA))
 (1 1 (:REWRITE RIGHT-UNICITY-LAWS))
 (1 1 (:REWRITE NULLITY-LAWS))
 )
(==_E-**_E-UNIT-ASSOCIATES-PP-WITNESS-1
 (2164 347 (:REWRITE UNIT-P-IMPLIES-EDP))
 (2020 56 (:DEFINITION UNIT-P))
 (1874 40 (:DEFINITION DIVIDES-P))
 (1720 659 (:REWRITE EQUIVALENCE-LAW))
 (1568 7 (:DEFINITION **_E-LST))
 (705 29 (:REWRITE ZERO-DIVISOR-LAW))
 (588 582 (:REWRITE CLOSURE-LAWS))
 (581 1 (:REWRITE IRREDUCIBLE-PP-UNIT-ASSOCIATES))
 (388 388 (:TYPE-PRESCRIPTION UNIT-P))
 (306 1 (:REWRITE DIVIDES-PP-MEMBER-UNIT-ASSOCIATE-PP-**_E-LST))
 (249 6 (:REWRITE INVERSE-CANCELLATION-LAWS-**_E))
 (220 4 (:DEFINITION IRREDUCIBLE-PP))
 (200 2 (:REWRITE IRREDUCIBLE-PP-IMPLIES-PRIME-PROPERTY))
 (187 2 (:REWRITE IRREDUCIBLE-LISTP-IMPLIES-EDP-LISTP))
 (181 2 (:DEFINITION IRREDUCIBLE-LISTP))
 (167 2 (:DEFINITION IRREDUCIBLE-P))
 (166 1 (:DEFINITION EDP-LISTP))
 (134 4 (:DEFINITION REDUCIBLE-PP))
 (120 56 (:REWRITE DIVIDES-P-SUFF))
 (98 56 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (98 2 (:REWRITE IRREDUCIBLE-LISTP-1-IMPLIES-EDP-LISTP))
 (92 2 (:DEFINITION IRREDUCIBLE-LISTP-1))
 (70 2 (:DEFINITION REDUCIBLE-P))
 (65 2 (:REWRITE REDUCIBLE-P-SUFF))
 (53 13 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-PP))
 (50 4 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
 (47 8 (:REWRITE COMMUTATIVITY-LAWS-FOR-++_E-&-**_E))
 (44 44 (:TYPE-PRESCRIPTION UNIT-PP))
 (36 36 (:TYPE-PRESCRIPTION BOOLEANP-DIVIDES-P))
 (33 1 (:REWRITE DIVIDES-PP-SUFF))
 (26 26 (:REWRITE IRREDUCIBLE-PP-IMPLIES-UNIT-PP-FACTOR))
 (25 25 (:REWRITE DEFAULT-CAR))
 (24 12 (:DEFINITION MV-NTH))
 (18 18 (:TYPE-PRESCRIPTION NATP-SIZE-==_E))
 (18 18 (:TYPE-PRESCRIPTION NATP-SIZE))
 (18 18 (:REWRITE DEFAULT-CDR))
 (17 1 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (10 10 (:TYPE-PRESCRIPTION IRREDUCIBLE-LISTP-1))
 (10 10 (:TYPE-PRESCRIPTION IRREDUCIBLE-LISTP))
 (6 1 (:REWRITE PROJECTION-LAWS))
 (5 5 (:TYPE-PRESCRIPTION EDP-LISTP))
 (4 4 (:REWRITE UNIT-PP-NOT-REDUCIBLE-PP))
 (4 4 (:REWRITE REDUCIBLE-PP-SUFF))
 (4 2 (:LINEAR SIZE->=-SIZE-1_E))
 (4 1 (:REWRITE RIGHT-UNICITY-LAWS))
 (2 2 (:TYPE-PRESCRIPTION IRREDUCIBLE-PP))
 (2 2 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-P))
 (2 2 (:REWRITE REDUCIBLE-P-SUFF-2))
 (1 1 (:TYPE-PRESCRIPTION DIVIDES-PP))
 (1 1 (:REWRITE UNIT-ASSOCIATES-PP-SUFF))
 (1 1 (:REWRITE TRANSITIVITY-DIVIDES-PP))
 (1 1 (:REWRITE PRIME-PROPERTY-LEMMA))
 )
(**_E-IRREDUCIBLE-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP-LEMMA
 (3497 119 (:DEFINITION UNIT-P))
 (3134 527 (:REWRITE UNIT-P-IMPLIES-EDP))
 (3095 85 (:DEFINITION DIVIDES-P))
 (2831 1242 (:REWRITE EQUIVALENCE-LAW))
 (2016 9 (:DEFINITION **_E-LST))
 (1405 1 (:REWRITE DIVIDES-PP-MEMBER-UNIT-ASSOCIATE-PP-**_E-LST))
 (1179 2 (:REWRITE IRREDUCIBLE-LISTP-IMPLIES-EDP-LISTP))
 (1173 2 (:DEFINITION IRREDUCIBLE-LISTP))
 (1155 2 (:DEFINITION IRREDUCIBLE-P))
 (1039 53 (:REWRITE ZERO-DIVISOR-LAW))
 (961 955 (:REWRITE CLOSURE-LAWS))
 (793 1 (:DEFINITION EDP-LISTP))
 (570 570 (:TYPE-PRESCRIPTION UNIT-P))
 (543 2 (:REWRITE REDUCIBLE-P-SUFF))
 (448 4 (:DEFINITION IRREDUCIBLE-PP))
 (442 2 (:DEFINITION REDUCIBLE-P))
 (368 2 (:REWRITE IRREDUCIBLE-PP-IMPLIES-PRIME-PROPERTY))
 (361 119 (:REWRITE DIVIDES-P-SUFF))
 (264 4 (:DEFINITION REDUCIBLE-PP))
 (197 119 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (168 2 (:REWRITE IRREDUCIBLE-LISTP-1-IMPLIES-EDP-LISTP))
 (162 2 (:DEFINITION IRREDUCIBLE-LISTP-1))
 (72 72 (:TYPE-PRESCRIPTION BOOLEANP-DIVIDES-P))
 (60 4 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
 (54 54 (:EQUIVALENCE ==_E-EQUIVALENCE-LAW))
 (42 42 (:TYPE-PRESCRIPTION UNIT-PP))
 (36 12 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-PP))
 (29 29 (:REWRITE DEFAULT-CAR))
 (28 18 (:TYPE-PRESCRIPTION NATP-SIZE-==_E))
 (24 24 (:REWRITE IRREDUCIBLE-PP-IMPLIES-UNIT-PP-FACTOR))
 (24 12 (:DEFINITION MV-NTH))
 (20 20 (:REWRITE DEFAULT-CDR))
 (18 18 (:TYPE-PRESCRIPTION NATP-SIZE))
 (11 1 (:REWRITE DIVIDES-PP-SUFF))
 (10 10 (:TYPE-PRESCRIPTION IRREDUCIBLE-LISTP-1))
 (10 10 (:TYPE-PRESCRIPTION IRREDUCIBLE-LISTP))
 (6 2 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-P))
 (6 2 (:LINEAR SIZE->=-SIZE-1_E))
 (5 5 (:TYPE-PRESCRIPTION EDP-LISTP))
 (4 4 (:REWRITE UNIT-PP-NOT-REDUCIBLE-PP))
 (4 4 (:REWRITE REDUCIBLE-PP-SUFF))
 (3 1 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (2 2 (:TYPE-PRESCRIPTION IRREDUCIBLE-PP))
 (2 2 (:REWRITE REDUCIBLE-P-SUFF-2))
 (1 1 (:REWRITE TRANSITIVITY-DIVIDES-PP))
 (1 1 (:REWRITE RIGHT-UNICITY-LAWS))
 (1 1 (:REWRITE PRIME-PROPERTY-LEMMA))
 (1 1 (:REWRITE NULLITY-LAWS))
 )
(**_E-IRREDUCIBLE-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP
 (1092 176 (:REWRITE UNIT-P-IMPLIES-EDP))
 (1002 22 (:DEFINITION UNIT-P))
 (950 14 (:DEFINITION DIVIDES-P))
 (888 350 (:REWRITE EQUIVALENCE-LAW))
 (501 3 (:DEFINITION **_E-LST))
 (382 2 (:REWRITE IRREDUCIBLE-PP-UNIT-ASSOCIATES))
 (373 17 (:REWRITE ZERO-DIVISOR-LAW))
 (313 313 (:REWRITE CLOSURE-LAWS))
 (251 1 (:DEFINITION IRREDUCIBLE-LISTP-1))
 (192 192 (:TYPE-PRESCRIPTION UNIT-P))
 (174 1 (:REWRITE DIVIDES-PP-MEMBER-UNIT-ASSOCIATE-PP-**_E-LST))
 (103 1 (:REWRITE DIVIDES-PP-SUFF))
 (88 1 (:REWRITE IRREDUCIBLE-LISTP-IMPLIES-EDP-LISTP))
 (85 1 (:DEFINITION IRREDUCIBLE-LISTP))
 (78 1 (:DEFINITION IRREDUCIBLE-P))
 (74 2 (:REWRITE IRREDUCIBLE-PP-IMPLIES-PRIME-PROPERTY))
 (69 3 (:REWRITE ASSOCIATIVITY-LAWS-FOR-++_E-&-**_E))
 (55 8 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
 (46 22 (:REWRITE DIVIDES-P-SUFF))
 (45 1 (:DEFINITION MEMBER-UNIT-ASSOCIATE-PP))
 (38 6 (:REWRITE INVERSE-CANCELLATION-LAWS-**_E))
 (36 22 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (36 2 (:REWRITE DIVIDES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-LEMMA))
 (35 1 (:DEFINITION REDUCIBLE-P))
 (30 18 (:REWRITE CLOSURE-LAWS-FOR-++_E-&-**_E))
 (27 1 (:REWRITE REDUCIBLE-P-SUFF))
 (25 9 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-PP))
 (25 1 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (18 18 (:REWRITE IRREDUCIBLE-PP-IMPLIES-UNIT-PP-FACTOR))
 (17 17 (:REWRITE EDP-**_E-LST))
 (16 16 (:TYPE-PRESCRIPTION BOOLEANP-DIVIDES-P))
 (14 9 (:TYPE-PRESCRIPTION NATP-SIZE-==_E))
 (10 10 (:REWRITE DEFAULT-CAR))
 (9 9 (:TYPE-PRESCRIPTION NATP-SIZE))
 (9 9 (:REWRITE UNIT-PP-NOT-REDUCIBLE-PP))
 (9 9 (:REWRITE REDUCIBLE-PP-SUFF))
 (9 3 (:REWRITE NULLITY-LAWS))
 (8 2 (:REWRITE RIGHT-UNICITY-LAWS))
 (7 7 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE UNIT-PP-CLOSURE-**_E))
 (6 3 (:REWRITE COMMUTATIVITY-LAWS-FOR-++_E-&-**_E))
 (6 1 (:REWRITE ZERO-DIVISOR-LAW-FOR-**_E))
 (5 5 (:TYPE-PRESCRIPTION IRREDUCIBLE-LISTP))
 (4 2 (:DEFINITION MV-NTH))
 (3 1 (:LINEAR SIZE->=-SIZE-1_E))
 (2 2 (:REWRITE UNIT-ASSOCIATES-PP-SUFF))
 (1 1 (:TYPE-PRESCRIPTION EDP-LISTP))
 (1 1 (:REWRITE TRANSITIVITY-DIVIDES-PP))
 (1 1 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-P))
 (1 1 (:REWRITE REDUCIBLE-P-SUFF-2))
 (1 1 (:REWRITE PRIME-PROPERTY-LEMMA))
 (1 1 (:REWRITE IRREDUCIBLE-LISTP-1-IMPLIES-EDP-LISTP))
 )
(**_E-LST-OF-IRREDUCIBLE-LISTP-1-NOT-UNIT-ASSOCIATE-PP-1_E
 (4688 246 (:REWRITE IRREDUCIBLE-PP-IMPLIES-PRIME-PROPERTY))
 (2849 28 (:REWRITE IRREDUCIBLE-PP-UNIT-ASSOCIATES))
 (2308 59 (:REWRITE UNIT-PP-NOT-REDUCIBLE-PP))
 (1951 149 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
 (1539 15 (:REWRITE DIVIDES-PP-MEMBER-UNIT-ASSOCIATE-PP-**_E-LST))
 (1162 367 (:REWRITE UNIT-P-IMPLIES-EDP))
 (922 593 (:TYPE-PRESCRIPTION NATP-SIZE-==_E))
 (775 775 (:TYPE-PRESCRIPTION UNIT-P))
 (655 16 (:REWRITE IRREDUCIBLE-LISTP-IMPLIES-EDP-LISTP))
 (635 172 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-PP))
 (613 10 (:DEFINITION IRREDUCIBLE-LISTP))
 (593 593 (:TYPE-PRESCRIPTION NATP-SIZE))
 (513 10 (:DEFINITION IRREDUCIBLE-P))
 (478 123 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (442 14 (:DEFINITION MEMBER-UNIT-ASSOCIATE-PP))
 (387 183 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (356 356 (:TYPE-PRESCRIPTION IRREDUCIBLE-PP))
 (344 344 (:REWRITE IRREDUCIBLE-PP-IMPLIES-UNIT-PP-FACTOR))
 (298 27 (:REWRITE DIVIDES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (298 27 (:REWRITE DIVIDES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-LEMMA))
 (253 10 (:REWRITE REDUCIBLE-P-SUFF))
 (170 10 (:DEFINITION REDUCIBLE-P))
 (163 65 (:LINEAR SIZE->=-SIZE-1_E))
 (157 86 (:REWRITE EQUIVALENCE-LAW))
 (129 1 (:DEFINITION EDP-LISTP))
 (123 123 (:REWRITE PRIME-PROPERTY-LEMMA))
 (116 116 (:REWRITE TRANSITIVITY-DIVIDES-PP))
 (93 93 (:REWRITE DEFAULT-CAR))
 (88 82 (:REWRITE NULLITY-LAWS))
 (81 81 (:TYPE-PRESCRIPTION UNIT-PP))
 (80 80 (:REWRITE UNIT-PP-1_E))
 (69 3 (:REWRITE ASSOCIATIVITY-LAWS-FOR-++_E-&-**_E))
 (66 66 (:TYPE-PRESCRIPTION MEMBER-UNIT-ASSOCIATE-PP))
 (65 65 (:REWRITE DEFAULT-CDR))
 (65 65 (:REWRITE |1_E-0_E|))
 (60 16 (:REWRITE IRREDUCIBLE-LISTP-1-IMPLIES-EDP-LISTP))
 (59 59 (:REWRITE REDUCIBLE-PP-SUFF))
 (56 56 (:TYPE-PRESCRIPTION IRREDUCIBLE-LISTP))
 (56 8 (:REWRITE UNIT-PP-CLOSURE-**_E))
 (40 20 (:DEFINITION MV-NTH))
 (38 6 (:REWRITE INVERSE-CANCELLATION-LAWS-**_E))
 (30 18 (:REWRITE CLOSURE-LAWS-FOR-++_E-&-**_E))
 (28 28 (:REWRITE UNIT-ASSOCIATES-PP-SUFF))
 (27 27 (:REWRITE **_E-IRREDUCIBLE-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (20 17 (:REWRITE COMMUTATIVITY-LAWS-FOR-++_E-&-**_E))
 (19 19 (:TYPE-PRESCRIPTION EDP-LISTP))
 (15 15 (:REWRITE **_E-IRREDUCIBLE-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP-LEMMA))
 (10 10 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-P))
 (10 10 (:REWRITE REDUCIBLE-P-SUFF-2))
 (6 1 (:REWRITE ZERO-DIVISOR-LAW-FOR-**_E))
 )
(IRREDUCIBLE-LISTP-1-DELETE-ONE-UNIT-ASSOCIATE-PP
 (4107 745 (:REWRITE UNIT-P-IMPLIES-EDP))
 (3650 134 (:DEFINITION UNIT-P))
 (3305 116 (:DEFINITION DIVIDES-P))
 (2815 1126 (:REWRITE EQUIVALENCE-LAW))
 (1033 54 (:REWRITE ZERO-DIVISOR-LAW))
 (858 28 (:REWRITE IRREDUCIBLE-PP-IMPLIES-PRIME-PROPERTY))
 (745 745 (:TYPE-PRESCRIPTION UNIT-P))
 (666 9 (:REWRITE DIVIDES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (666 9 (:REWRITE DIVIDES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-LEMMA))
 (578 58 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
 (255 134 (:REWRITE DIVIDES-P-SUFF))
 (203 134 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (174 58 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-PP))
 (172 14 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (116 116 (:REWRITE IRREDUCIBLE-PP-IMPLIES-UNIT-PP-FACTOR))
 (58 58 (:REWRITE UNIT-PP-NOT-REDUCIBLE-PP))
 (58 58 (:REWRITE REDUCIBLE-PP-SUFF))
 (56 36 (:TYPE-PRESCRIPTION NATP-SIZE-==_E))
 (36 36 (:TYPE-PRESCRIPTION NATP-SIZE))
 (36 36 (:TYPE-PRESCRIPTION BOOLEANP-DIVIDES-P))
 (28 28 (:REWRITE DEFAULT-CAR))
 (14 14 (:REWRITE TRANSITIVITY-DIVIDES-PP))
 (14 14 (:REWRITE PRIME-PROPERTY-LEMMA))
 (14 14 (:REWRITE DEFAULT-CDR))
 (13 13 (:REWRITE UNIT-ASSOCIATES-PP-SUFF))
 (10 4 (:LINEAR SIZE->=-SIZE-1_E))
 (9 9 (:REWRITE **_E-IRREDUCIBLE-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 )
(UNIT-ASSOCIATES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP
 (1329 226 (:REWRITE UNIT-P-IMPLIES-EDP))
 (1231 31 (:DEFINITION UNIT-P))
 (1139 19 (:DEFINITION DIVIDES-P))
 (1088 375 (:REWRITE EQUIVALENCE-LAW))
 (799 5 (:DEFINITION **_E-LST))
 (437 17 (:REWRITE ZERO-DIVISOR-LAW))
 (236 2 (:DEFINITION IRREDUCIBLE-LISTP-1))
 (235 235 (:TYPE-PRESCRIPTION UNIT-P))
 (208 1 (:REWRITE DIVIDES-PP-MEMBER-UNIT-ASSOCIATE-PP-**_E-LST))
 (110 4 (:REWRITE IRREDUCIBLE-PP-IMPLIES-PRIME-PROPERTY))
 (105 9 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
 (89 1 (:DEFINITION MEMBER-UNIT-ASSOCIATE-PP))
 (85 31 (:REWRITE DIVIDES-P-SUFF))
 (85 4 (:REWRITE IRREDUCIBLE-LISTP-IMPLIES-EDP-LISTP))
 (76 1 (:DEFINITION IRREDUCIBLE-LISTP))
 (74 31 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (69 1 (:DEFINITION IRREDUCIBLE-P))
 (58 10 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-PP))
 (51 2 (:REWRITE DIVIDES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-LEMMA))
 (35 1 (:DEFINITION REDUCIBLE-P))
 (27 27 (:TYPE-PRESCRIPTION NATP-SIZE-==_E))
 (27 27 (:TYPE-PRESCRIPTION NATP-SIZE))
 (24 24 (:TYPE-PRESCRIPTION BOOLEANP-DIVIDES-P))
 (20 20 (:REWRITE IRREDUCIBLE-PP-IMPLIES-UNIT-PP-FACTOR))
 (18 2 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (18 1 (:REWRITE REDUCIBLE-P-SUFF))
 (16 16 (:REWRITE DEFAULT-CAR))
 (12 1 (:DEFINITION EDP-LISTP))
 (11 11 (:REWRITE DEFAULT-CDR))
 (11 1 (:REWRITE IRREDUCIBLE-PP-UNIT-ASSOCIATES))
 (10 10 (:REWRITE UNIT-PP-NOT-REDUCIBLE-PP))
 (10 10 (:REWRITE REDUCIBLE-PP-SUFF))
 (8 8 (:TYPE-PRESCRIPTION IRREDUCIBLE-LISTP))
 (7 7 (:TYPE-PRESCRIPTION EDP-LISTP))
 (7 3 (:LINEAR SIZE->=-SIZE-1_E))
 (6 4 (:REWRITE IRREDUCIBLE-LISTP-1-IMPLIES-EDP-LISTP))
 (4 2 (:DEFINITION MV-NTH))
 (3 3 (:REWRITE **_E-IRREDUCIBLE-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (2 2 (:REWRITE TRANSITIVITY-DIVIDES-PP))
 (2 2 (:REWRITE PRIME-PROPERTY-LEMMA))
 (1 1 (:REWRITE UNIT-ASSOCIATES-PP-SUFF))
 (1 1 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-P))
 (1 1 (:REWRITE REDUCIBLE-P-SUFF-2))
 (1 1 (:REWRITE **_E-IRREDUCIBLE-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP-LEMMA))
 )
(REDUCIBLE-PP-**_E
 (948 248 (:REWRITE UNIT-P-IMPLIES-EDP))
 (658 74 (:DEFINITION UNIT-P))
 (492 74 (:DEFINITION DIVIDES-P))
 (248 248 (:TYPE-PRESCRIPTION UNIT-P))
 (245 152 (:REWRITE IRREDUCIBLE-PP-IMPLIES-UNIT-PP-FACTOR))
 (230 30 (:REWRITE UNIT-PP-NOT-REDUCIBLE-PP))
 (184 76 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-PP))
 (132 132 (:REWRITE EQUIVALENCE-LAW))
 (96 4 (:DEFINITION IRREDUCIBLE-PP))
 (92 74 (:REWRITE DIVIDES-P-SUFF))
 (74 74 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (73 18 (:REWRITE UNIT-PP-CLOSURE-**_E))
 (57 5 (:DEFINITION UNIT-PP))
 (36 12 (:REWRITE CANCELLATION-LAWS-FOR-**_E))
 (20 20 (:REWRITE CLOSURE-LAWS))
 (20 10 (:REWRITE IRREDUCIBLE-PP-IMPLIES-PRIME-PROPERTY))
 (19 19 (:TYPE-PRESCRIPTION IRREDUCIBLE-PP))
 (16 6 (:REWRITE ZERO-DIVISOR-LAW-FOR-**_E))
 (11 5 (:REWRITE DIVIDES-PP-SUFF))
 (6 5 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (5 5 (:TYPE-PRESCRIPTION DIVIDES-PP))
 (5 5 (:REWRITE TRANSITIVITY-DIVIDES-PP))
 (5 5 (:REWRITE REDUCIBLE-PP-SUFF))
 (5 5 (:REWRITE PRIME-PROPERTY-LEMMA))
 (4 4 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
 )
(REDUCIBLE-PP-**_E-1)
(REDUCIBLE-PP-**_E-LST
 (400 107 (:REWRITE UNIT-P-IMPLIES-EDP))
 (271 29 (:DEFINITION UNIT-P))
 (199 29 (:DEFINITION DIVIDES-P))
 (107 107 (:TYPE-PRESCRIPTION UNIT-P))
 (100 11 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
 (65 31 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-PP))
 (65 24 (:REWRITE UNIT-PP-NOT-REDUCIBLE-PP))
 (62 62 (:REWRITE IRREDUCIBLE-PP-IMPLIES-UNIT-PP-FACTOR))
 (56 56 (:REWRITE EQUIVALENCE-LAW))
 (52 52 (:EQUIVALENCE ==_E-EQUIVALENCE-LAW))
 (51 51 (:REWRITE DEFAULT-CAR))
 (43 29 (:REWRITE DIVIDES-P-SUFF))
 (42 27 (:TYPE-PRESCRIPTION NATP-SIZE-==_E))
 (41 41 (:REWRITE DEFAULT-CDR))
 (30 30 (:REWRITE REDUCIBLE-PP-SUFF))
 (29 29 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (27 27 (:TYPE-PRESCRIPTION NATP-SIZE))
 (14 14 (:REWRITE EDP-**_E-LST))
 (14 14 (:REWRITE CLOSURE-LAWS))
 (6 6 (:REWRITE UNIT-PP-CLOSURE-**_E))
 (6 3 (:LINEAR SIZE->=-SIZE-1_E))
 )
(NOT-IRREDUCIBLE-PP-1_E)
(IRREDUCIBLE-LISTP-1-IRREDUCIBLE-PP-MEMBER-UNIT-ASSOCIATE-PP
 (63 7 (:REWRITE IRREDUCIBLE-PP-UNIT-ASSOCIATES))
 (59 12 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
 (22 11 (:REWRITE UNIT-P-IMPLIES-EDP))
 (16 16 (:REWRITE DEFAULT-CAR))
 (14 14 (:TYPE-PRESCRIPTION NATP-SIZE-==_E))
 (14 14 (:TYPE-PRESCRIPTION DIVIDES-PP))
 (14 14 (:REWRITE IRREDUCIBLE-PP-IMPLIES-PRIME-PROPERTY))
 (11 11 (:TYPE-PRESCRIPTION UNIT-P))
 (10 3 (:LINEAR SIZE->=-SIZE-1_E))
 (8 8 (:REWRITE UNIT-ASSOCIATES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (8 8 (:REWRITE DIVIDES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (8 8 (:REWRITE DIVIDES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-LEMMA))
 (8 8 (:REWRITE **_E-IRREDUCIBLE-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (7 7 (:TYPE-PRESCRIPTION NATP-SIZE))
 (7 7 (:REWRITE UNIT-ASSOCIATES-PP-SUFF))
 (7 7 (:REWRITE TRANSITIVITY-DIVIDES-PP))
 (7 7 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (7 7 (:REWRITE PRIME-PROPERTY-LEMMA))
 (7 7 (:REWRITE DIVIDES-PP-SUFF))
 (4 4 (:REWRITE DEFAULT-CDR))
 )
(UNIT-ASSOCIATES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP-1
 (3358 10 (:DEFINITION IRREDUCIBLE-PP))
 (2324 370 (:REWRITE UNIT-P-IMPLIES-EDP))
 (2176 54 (:DEFINITION UNIT-P))
 (2088 10 (:DEFINITION REDUCIBLE-PP))
 (2080 2 (:DEFINITION IRREDUCIBLE-LISTP-1))
 (2045 38 (:DEFINITION DIVIDES-P))
 (1870 730 (:REWRITE EQUIVALENCE-LAW))
 (1289 38 (:DEFINITION UNIT-PP))
 (992 82 (:REWRITE IRREDUCIBLE-PP-IMPLIES-PRIME-PROPERTY))
 (817 2 (:REWRITE IRREDUCIBLE-PP-UNIT-ASSOCIATES))
 (766 38 (:REWRITE ZERO-DIVISOR-LAW))
 (704 704 (:REWRITE CLOSURE-LAWS))
 (550 26 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
 (480 480 (:EQUIVALENCE ==_E-EQUIVALENCE-LAW))
 (446 3 (:REWRITE UNIT-ASSOCIATES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (438 39 (:REWRITE DIVIDES-PP-SUFF))
 (388 388 (:TYPE-PRESCRIPTION UNIT-P))
 (352 2 (:REWRITE DIVIDES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-LEMMA))
 (297 10 (:REWRITE UNIT-PP-NOT-REDUCIBLE-PP))
 (242 162 (:TYPE-PRESCRIPTION NATP-SIZE-==_E))
 (162 162 (:TYPE-PRESCRIPTION NATP-SIZE))
 (160 3 (:REWRITE IRREDUCIBLE-LISTP-IMPLIES-EDP-LISTP))
 (152 2 (:DEFINITION IRREDUCIBLE-LISTP))
 (138 2 (:DEFINITION IRREDUCIBLE-P))
 (121 39 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (104 54 (:REWRITE DIVIDES-P-SUFF))
 (104 38 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-PP))
 (92 54 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (76 76 (:REWRITE IRREDUCIBLE-PP-IMPLIES-UNIT-PP-FACTOR))
 (70 2 (:DEFINITION REDUCIBLE-P))
 (48 24 (:DEFINITION MV-NTH))
 (48 18 (:LINEAR SIZE->=-SIZE-1_E))
 (43 43 (:TYPE-PRESCRIPTION UNIT-PP))
 (42 42 (:TYPE-PRESCRIPTION BOOLEANP-DIVIDES-P))
 (41 41 (:REWRITE PRIME-PROPERTY-LEMMA))
 (39 39 (:REWRITE TRANSITIVITY-DIVIDES-PP))
 (36 2 (:REWRITE REDUCIBLE-P-SUFF))
 (31 31 (:REWRITE COMMUTATIVITY-LAWS-FOR-++_E-&-**_E))
 (30 27 (:REWRITE RIGHT-UNICITY-LAWS))
 (30 27 (:REWRITE NULLITY-LAWS))
 (24 24 (:REWRITE DEFAULT-CAR))
 (21 21 (:REWRITE EDP-**_E-LST))
 (20 20 (:REWRITE DEFAULT-CDR))
 (11 11 (:TYPE-PRESCRIPTION IRREDUCIBLE-LISTP))
 (10 10 (:REWRITE REDUCIBLE-PP-SUFF))
 (5 5 (:REWRITE REDUCIBLE-PP-**_E-LST))
 (3 3 (:REWRITE **_E-IRREDUCIBLE-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP-LEMMA))
 (3 3 (:REWRITE **_E-IRREDUCIBLE-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (2 2 (:REWRITE UNIT-ASSOCIATES-PP-SUFF))
 (2 2 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-P))
 (2 2 (:REWRITE REDUCIBLE-P-SUFF-2))
 (2 2 (:REWRITE PROJECTION-LAWS))
 )
(MEMBER-UNIT-ASSOCIATE-PP-EDP-LISTP-IMPLIES-EDP
 (15445 9 (:REWRITE IRREDUCIBLE-LISTP-IMPLIES-EDP-LISTP))
 (15423 10 (:DEFINITION IRREDUCIBLE-LISTP))
 (15329 6576 (:REWRITE EQUIVALENCE-LAW))
 (15074 409 (:DEFINITION UNIT-P))
 (14088 10 (:DEFINITION IRREDUCIBLE-P))
 (11243 325 (:DEFINITION DIVIDES-P))
 (9646 2608 (:REWRITE UNIT-P-IMPLIES-EDP))
 (7995 6 (:DEFINITION REDUCIBLE-P))
 (6877 9 (:REWRITE IRREDUCIBLE-LISTP-1-IMPLIES-EDP-LISTP))
 (6855 10 (:DEFINITION IRREDUCIBLE-LISTP-1))
 (6698 70 (:DEFINITION IRREDUCIBLE-PP))
 (5045 5045 (:REWRITE CLOSURE-LAWS))
 (5020 228 (:REWRITE IRREDUCIBLE-PP-IMPLIES-PRIME-PROPERTY))
 (4832 104 (:DEFINITION UNIT-PP))
 (4712 292 (:REWRITE ZERO-DIVISOR-LAW))
 (4370 28 (:DEFINITION REDUCIBLE-PP))
 (3903 409 (:REWRITE DIVIDES-P-SUFF))
 (3689 6 (:REWRITE REDUCIBLE-P-SUFF))
 (2688 2688 (:TYPE-PRESCRIPTION UNIT-P))
 (1657 1657 (:EQUIVALENCE ==_E-EQUIVALENCE-LAW))
 (1609 114 (:REWRITE DIVIDES-PP-SUFF))
 (1298 102 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
 (1164 409 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (1055 28 (:REWRITE UNIT-PP-NOT-REDUCIBLE-PP))
 (672 438 (:TYPE-PRESCRIPTION NATP-SIZE-==_E))
 (438 438 (:TYPE-PRESCRIPTION NATP-SIZE))
 (320 320 (:TYPE-PRESCRIPTION IRREDUCIBLE-PP))
 (298 114 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (282 104 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-PP))
 (267 267 (:TYPE-PRESCRIPTION DIVIDES-PP))
 (231 7 (:REWRITE IRREDUCIBLE-PP-UNIT-ASSOCIATES))
 (208 208 (:REWRITE IRREDUCIBLE-PP-IMPLIES-UNIT-PP-FACTOR))
 (194 194 (:TYPE-PRESCRIPTION BOOLEANP-DIVIDES-P))
 (190 84 (:DEFINITION MV-NTH))
 (177 177 (:REWRITE COMMUTATIVITY-LAWS-FOR-++_E-&-**_E))
 (140 10 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-P))
 (124 124 (:REWRITE DEFAULT-CAR))
 (114 114 (:REWRITE TRANSITIVITY-DIVIDES-PP))
 (114 114 (:REWRITE PRIME-PROPERTY-LEMMA))
 (104 8 (:REWRITE UNIT-ASSOCIATES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (104 8 (:REWRITE DIVIDES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (104 8 (:REWRITE DIVIDES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-LEMMA))
 (102 102 (:REWRITE IRREDUCIBLE-LISTP-1-IRREDUCIBLE-PP-MEMBER-UNIT-ASSOCIATE-PP))
 (96 46 (:LINEAR SIZE->=-SIZE-1_E))
 (77 77 (:REWRITE RIGHT-UNICITY-LAWS))
 (77 77 (:REWRITE NULLITY-LAWS))
 (74 74 (:REWRITE DEFAULT-CDR))
 (44 44 (:TYPE-PRESCRIPTION UNIT-PP))
 (31 31 (:TYPE-PRESCRIPTION IRREDUCIBLE-LISTP-1))
 (31 31 (:TYPE-PRESCRIPTION IRREDUCIBLE-LISTP))
 (28 28 (:REWRITE RIGHT-UNICITY-LAW-FOR-*_E))
 (28 28 (:REWRITE REDUCIBLE-PP-SUFF))
 (28 28 (:REWRITE LEFT-UNICITY-LAWS))
 (8 8 (:REWRITE UNIT-ASSOCIATES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP-1))
 (8 8 (:REWRITE **_E-IRREDUCIBLE-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (7 7 (:REWRITE UNIT-ASSOCIATES-PP-SUFF))
 (6 6 (:TYPE-PRESCRIPTION REDUCIBLE-PP))
 (6 6 (:REWRITE REDUCIBLE-P-SUFF-2))
 )
(UNIT-PP-UNIT-ASSOCIATES-PP-WITNESS
 (832 104 (:REWRITE UNIT-P-IMPLIES-EDP))
 (786 16 (:DEFINITION UNIT-P))
 (695 226 (:REWRITE EQUIVALENCE-LAW))
 (691 10 (:DEFINITION DIVIDES-P))
 (266 11 (:REWRITE ZERO-DIVISOR-LAW))
 (253 3 (:REWRITE IRREDUCIBLE-PP-UNIT-ASSOCIATES))
 (218 4 (:REWRITE IRREDUCIBLE-PP-IMPLIES-PRIME-PROPERTY))
 (216 216 (:REWRITE CLOSURE-LAWS))
 (156 2 (:DEFINITION IRREDUCIBLE-PP))
 (105 105 (:REWRITE MEMBER-UNIT-ASSOCIATE-PP-EDP-LISTP-IMPLIES-EDP))
 (104 104 (:TYPE-PRESCRIPTION UNIT-P))
 (96 2 (:DEFINITION REDUCIBLE-PP))
 (89 16 (:REWRITE DIVIDES-P-SUFF))
 (73 8 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-PP))
 (52 2 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
 (45 45 (:EQUIVALENCE ==_E-EQUIVALENCE-LAW))
 (32 16 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (31 3 (:REWRITE EDP-UNIT-ASSOCIATES-PP-WITNESS))
 (28 18 (:TYPE-PRESCRIPTION NATP-SIZE-==_E))
 (18 18 (:TYPE-PRESCRIPTION NATP-SIZE))
 (18 2 (:REWRITE DIVIDES-PP-SUFF))
 (16 16 (:TYPE-PRESCRIPTION BOOLEANP-DIVIDES-P))
 (16 16 (:REWRITE IRREDUCIBLE-PP-IMPLIES-UNIT-PP-FACTOR))
 (8 4 (:DEFINITION MV-NTH))
 (5 5 (:TYPE-PRESCRIPTION DIVIDES-PP))
 (5 2 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (4 4 (:TYPE-PRESCRIPTION IRREDUCIBLE-PP))
 (4 2 (:LINEAR SIZE->=-SIZE-1_E))
 (3 3 (:REWRITE UNIT-ASSOCIATES-PP-SUFF))
 (2 2 (:REWRITE UNIT-PP-NOT-REDUCIBLE-PP))
 (2 2 (:REWRITE TRANSITIVITY-DIVIDES-PP))
 (2 2 (:REWRITE REDUCIBLE-PP-SUFF))
 (2 2 (:REWRITE PRIME-PROPERTY-LEMMA))
 (2 2 (:REWRITE IRREDUCIBLE-LISTP-1-IRREDUCIBLE-PP-MEMBER-UNIT-ASSOCIATE-PP))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE COMMUTATIVITY-LAWS-FOR-++_E-&-**_E))
 (1 1 (:REWRITE RIGHT-UNICITY-LAWS))
 (1 1 (:REWRITE NULLITY-LAWS))
 )
(==_E-**_E-UNIT-ASSOCIATES-PP-WITNESS-A
 (626 1 (:REWRITE IRREDUCIBLE-PP-UNIT-ASSOCIATES))
 (580 24 (:REWRITE IRREDUCIBLE-PP-IMPLIES-PRIME-PROPERTY))
 (464 4 (:DEFINITION IRREDUCIBLE-PP))
 (462 60 (:REWRITE UNIT-P-IMPLIES-EDP))
 (421 11 (:DEFINITION UNIT-P))
 (382 11 (:DEFINITION UNIT-PP))
 (352 124 (:REWRITE EQUIVALENCE-LAW))
 (293 9 (:DEFINITION DIVIDES-P))
 (214 2 (:DEFINITION REDUCIBLE-PP))
 (170 12 (:REWRITE DIVIDES-PP-SUFF))
 (134 134 (:REWRITE CLOSURE-LAWS))
 (119 11 (:REWRITE DIVIDES-P-SUFF))
 (115 6 (:REWRITE ZERO-DIVISOR-LAW))
 (104 4 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
 (70 70 (:REWRITE MEMBER-UNIT-ASSOCIATE-PP-EDP-LISTP-IMPLIES-EDP))
 (60 60 (:TYPE-PRESCRIPTION UNIT-P))
 (56 36 (:TYPE-PRESCRIPTION NATP-SIZE-==_E))
 (50 4 (:REWRITE UNIT-PP-NOT-REDUCIBLE-PP))
 (37 6 (:REWRITE INVERSE-CANCELLATION-LAWS-**_E))
 (36 36 (:TYPE-PRESCRIPTION NATP-SIZE))
 (34 12 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (31 11 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-PP))
 (25 11 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (24 24 (:TYPE-PRESCRIPTION IRREDUCIBLE-PP))
 (22 22 (:REWRITE IRREDUCIBLE-PP-IMPLIES-UNIT-PP-FACTOR))
 (20 20 (:TYPE-PRESCRIPTION DIVIDES-PP))
 (13 13 (:TYPE-PRESCRIPTION UNIT-PP))
 (12 12 (:REWRITE TRANSITIVITY-DIVIDES-PP))
 (12 12 (:REWRITE PRIME-PROPERTY-LEMMA))
 (10 10 (:REWRITE RIGHT-UNICITY-LAWS))
 (9 9 (:REWRITE NULLITY-LAWS))
 (8 8 (:TYPE-PRESCRIPTION BOOLEANP-DIVIDES-P))
 (8 4 (:LINEAR SIZE->=-SIZE-1_E))
 (8 4 (:DEFINITION MV-NTH))
 (6 2 (:REWRITE PROJECTION-LAWS))
 (4 4 (:REWRITE IRREDUCIBLE-LISTP-1-IRREDUCIBLE-PP-MEMBER-UNIT-ASSOCIATE-PP))
 (2 2 (:REWRITE REDUCIBLE-PP-SUFF))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE UNIT-ASSOCIATES-PP-SUFF))
 )
(UNIT-ASSOCIATES-PP-**_E-1
 (1104 193 (:REWRITE UNIT-P-IMPLIES-EDP))
 (1101 2 (:REWRITE IRREDUCIBLE-PP-UNIT-ASSOCIATES))
 (911 25 (:DEFINITION UNIT-P))
 (818 8 (:REWRITE IRREDUCIBLE-PP-IMPLIES-PRIME-PROPERTY))
 (778 231 (:REWRITE EQUIVALENCE-LAW))
 (680 8 (:DEFINITION IRREDUCIBLE-PP))
 (626 19 (:DEFINITION DIVIDES-P))
 (416 12 (:DEFINITION REDUCIBLE-PP))
 (363 2 (:REWRITE DIVIDES-PP-**_E))
 (270 25 (:REWRITE DIVIDES-P-SUFF))
 (224 208 (:REWRITE CLOSURE-LAWS))
 (213 213 (:REWRITE MEMBER-UNIT-ASSOCIATE-PP-EDP-LISTP-IMPLIES-EDP))
 (197 4 (:REWRITE DIVIDES-PP-SUFF))
 (193 193 (:TYPE-PRESCRIPTION UNIT-P))
 (191 8 (:REWRITE ZERO-DIVISOR-LAW))
 (166 48 (:REWRITE INVERSE-CANCELLATION-LAWS-**_E))
 (140 12 (:REWRITE REDUCIBLE-PP-**_E))
 (114 8 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
 (105 39 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-PP))
 (101 10 (:REWRITE ASSOCIATIVITY-LAWS-FOR-++_E-&-**_E))
 (99 25 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (78 78 (:REWRITE IRREDUCIBLE-PP-IMPLIES-UNIT-PP-FACTOR))
 (48 24 (:DEFINITION MV-NTH))
 (46 36 (:TYPE-PRESCRIPTION NATP-SIZE-==_E))
 (43 4 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (36 36 (:TYPE-PRESCRIPTION NATP-SIZE))
 (22 6 (:REWRITE UNIT-PP-CLOSURE-**_E))
 (22 6 (:REWRITE REDUCIBLE-PP-**_E-1))
 (20 20 (:TYPE-PRESCRIPTION BOOLEANP-DIVIDES-P))
 (15 5 (:REWRITE ZERO-DIVISOR-LAW-FOR-**_E))
 (12 12 (:TYPE-PRESCRIPTION REDUCIBLE-PP))
 (12 12 (:REWRITE REDUCIBLE-PP-SUFF))
 (12 12 (:REWRITE DEFAULT-CDR))
 (12 12 (:REWRITE DEFAULT-CAR))
 (8 8 (:TYPE-PRESCRIPTION IRREDUCIBLE-PP))
 (8 8 (:REWRITE UNIT-PP-NOT-REDUCIBLE-PP))
 (8 8 (:REWRITE IRREDUCIBLE-LISTP-1-IRREDUCIBLE-PP-MEMBER-UNIT-ASSOCIATE-PP))
 (8 4 (:REWRITE RIGHT-UNICITY-LAWS))
 (8 4 (:REWRITE PROJECTION-LAWS))
 (8 4 (:LINEAR SIZE->=-SIZE-1_E))
 (7 7 (:TYPE-PRESCRIPTION DIVIDES-PP))
 (7 3 (:REWRITE NULLITY-LAWS))
 (6 1 (:REWRITE CANCELLATION-LAWS-FOR-**_E))
 (4 4 (:REWRITE TRANSITIVITY-DIVIDES-PP))
 (4 4 (:REWRITE PRIME-PROPERTY-LEMMA))
 (4 4 (:REWRITE ==_E-**_E-UNIT-ASSOCIATES-PP-WITNESS))
 (4 2 (:LINEAR SIZE-<-SIZE-**_E))
 (4 2 (:LINEAR SIZE-**_E))
 (2 2 (:REWRITE UNIT-ASSOCIATES-PP-SUFF))
 )
(UNIT-ASSOCIATES-PP-==_E-**_E-2
 (5109 4 (:REWRITE IRREDUCIBLE-PP-UNIT-ASSOCIATES))
 (4384 226 (:REWRITE IRREDUCIBLE-PP-IMPLIES-PRIME-PROPERTY))
 (3968 22 (:DEFINITION IRREDUCIBLE-PP))
 (2915 105 (:DEFINITION UNIT-PP))
 (2264 30 (:DEFINITION REDUCIBLE-PP))
 (1932 327 (:REWRITE UNIT-P-IMPLIES-EDP))
 (1724 113 (:REWRITE DIVIDES-PP-SUFF))
 (1587 49 (:DEFINITION UNIT-P))
 (1320 1320 (:EQUIVALENCE ==_E-EQUIVALENCE-LAW))
 (1267 41 (:DEFINITION DIVIDES-P))
 (1239 460 (:REWRITE EQUIVALENCE-LAW))
 (1077 4 (:REWRITE DIVIDES-PP-**_E))
 (836 28 (:REWRITE REDUCIBLE-PP-**_E))
 (572 572 (:REWRITE CLOSURE-LAWS))
 (433 21 (:REWRITE ZERO-DIVISOR-LAW))
 (419 46 (:REWRITE ASSOCIATIVITY-LAWS-FOR-++_E-&-**_E))
 (399 19 (:REWRITE UNIT-PP-CLOSURE-**_E))
 (370 113 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (360 156 (:REWRITE INVERSE-CANCELLATION-LAWS-**_E))
 (350 22 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
 (327 327 (:TYPE-PRESCRIPTION UNIT-P))
 (327 327 (:REWRITE MEMBER-UNIT-ASSOCIATE-PP-EDP-LISTP-IMPLIES-EDP))
 (284 105 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-PP))
 (279 49 (:REWRITE DIVIDES-P-SUFF))
 (226 226 (:TYPE-PRESCRIPTION IRREDUCIBLE-PP))
 (210 210 (:REWRITE IRREDUCIBLE-PP-IMPLIES-UNIT-PP-FACTOR))
 (201 201 (:TYPE-PRESCRIPTION DIVIDES-PP))
 (188 22 (:REWRITE UNIT-PP-NOT-REDUCIBLE-PP))
 (159 159 (:TYPE-PRESCRIPTION UNIT-PP))
 (154 14 (:REWRITE REDUCIBLE-PP-**_E-1))
 (144 112 (:TYPE-PRESCRIPTION NATP-SIZE-==_E))
 (120 60 (:DEFINITION MV-NTH))
 (113 113 (:REWRITE TRANSITIVITY-DIVIDES-PP))
 (113 113 (:REWRITE PRIME-PROPERTY-LEMMA))
 (112 112 (:TYPE-PRESCRIPTION NATP-SIZE))
 (83 49 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (73 73 (:REWRITE CLOSURE-LAWS-FOR-++_E-&-**_E))
 (63 21 (:REWRITE ZERO-DIVISOR-LAW-FOR-**_E))
 (51 39 (:REWRITE RIGHT-UNICITY-LAWS))
 (45 37 (:REWRITE NULLITY-LAWS))
 (32 32 (:TYPE-PRESCRIPTION BOOLEANP-DIVIDES-P))
 (30 30 (:REWRITE REDUCIBLE-PP-SUFF))
 (30 30 (:REWRITE DEFAULT-CDR))
 (30 30 (:REWRITE DEFAULT-CAR))
 (28 28 (:TYPE-PRESCRIPTION REDUCIBLE-PP))
 (28 14 (:REWRITE PROJECTION-LAWS))
 (24 12 (:LINEAR SIZE->=-SIZE-1_E))
 (22 22 (:REWRITE IRREDUCIBLE-LISTP-1-IRREDUCIBLE-PP-MEMBER-UNIT-ASSOCIATE-PP))
 (18 3 (:REWRITE CANCELLATION-LAWS-FOR-**_E))
 (12 6 (:LINEAR SIZE-<-SIZE-**_E))
 (12 6 (:LINEAR SIZE-**_E))
 (4 4 (:REWRITE UNIT-ASSOCIATES-PP-SUFF))
 )
(UNIT-ASSOCIATES-PP-**_E-**_E-LST-DELETE-ONE-UNIT-ASSOCIATE-LEMMA
 (2608 432 (:REWRITE UNIT-P-IMPLIES-EDP))
 (2242 68 (:DEFINITION UNIT-P))
 (2184 7 (:REWRITE IRREDUCIBLE-PP-UNIT-ASSOCIATES))
 (2004 54 (:DEFINITION DIVIDES-P))
 (1760 591 (:REWRITE EQUIVALENCE-LAW))
 (1602 14 (:REWRITE IRREDUCIBLE-PP-IMPLIES-PRIME-PROPERTY))
 (1544 26 (:DEFINITION IRREDUCIBLE-PP))
 (1245 5 (:DEFINITION **_E-LST))
 (975 28 (:DEFINITION REDUCIBLE-PP))
 (939 3 (:DEFINITION DELETE-ONE-UNIT-ASSOCIATE-PP))
 (635 25 (:REWRITE ZERO-DIVISOR-LAW))
 (507 499 (:REWRITE CLOSURE-LAWS))
 (432 432 (:TYPE-PRESCRIPTION UNIT-P))
 (378 12 (:REWRITE INVERSE-CANCELLATION-LAWS-**_E))
 (334 28 (:REWRITE IRREDUCIBLE-LISTP-1-IRREDUCIBLE-PP-MEMBER-UNIT-ASSOCIATE-PP))
 (326 2 (:REWRITE DIVIDES-PP-MEMBER-UNIT-ASSOCIATE-PP-**_E-LST))
 (322 8 (:DEFINITION IRREDUCIBLE-LISTP-1))
 (288 2 (:REWRITE DIVIDES-PP-**_E))
 (270 270 (:TYPE-PRESCRIPTION UNIT-PP))
 (226 85 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-PP))
 (223 223 (:EQUIVALENCE ==_E-EQUIVALENCE-LAW))
 (210 28 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
 (194 68 (:REWRITE DIVIDES-P-SUFF))
 (170 170 (:REWRITE IRREDUCIBLE-PP-IMPLIES-UNIT-PP-FACTOR))
 (163 2 (:DEFINITION MEMBER-UNIT-ASSOCIATE-PP))
 (126 68 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (114 7 (:REWRITE DIVIDES-PP-SUFF))
 (112 56 (:DEFINITION MV-NTH))
 (111 35 (:REWRITE COMMUTATIVITY-LAWS-FOR-++_E-&-**_E))
 (98 4 (:REWRITE UNIT-ASSOCIATES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (98 4 (:REWRITE DIVIDES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (98 4 (:REWRITE DIVIDES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-LEMMA))
 (90 16 (:REWRITE REDUCIBLE-PP-**_E))
 (72 72 (:TYPE-PRESCRIPTION NATP-SIZE-==_E))
 (72 72 (:TYPE-PRESCRIPTION NATP-SIZE))
 (65 7 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (57 57 (:REWRITE DEFAULT-CAR))
 (54 54 (:REWRITE DEFAULT-CDR))
 (46 46 (:TYPE-PRESCRIPTION IRREDUCIBLE-LISTP-1))
 (42 26 (:REWRITE CLOSURE-LAWS-FOR-++_E-&-**_E))
 (40 8 (:REWRITE REDUCIBLE-PP-**_E-LST))
 (36 36 (:TYPE-PRESCRIPTION BOOLEANP-DIVIDES-P))
 (32 32 (:TYPE-PRESCRIPTION IRREDUCIBLE-PP))
 (28 28 (:REWRITE REDUCIBLE-PP-SUFF))
 (26 26 (:REWRITE UNIT-PP-NOT-REDUCIBLE-PP))
 (20 6 (:REWRITE UNIT-PP-CLOSURE-**_E))
 (18 8 (:REWRITE REDUCIBLE-PP-**_E-1))
 (16 8 (:LINEAR SIZE->=-SIZE-1_E))
 (15 15 (:TYPE-PRESCRIPTION DIVIDES-PP))
 (11 4 (:REWRITE RIGHT-UNICITY-LAWS))
 (7 7 (:REWRITE UNIT-ASSOCIATES-PP-SUFF))
 (7 7 (:REWRITE TRANSITIVITY-DIVIDES-PP))
 (7 7 (:REWRITE PRIME-PROPERTY-LEMMA))
 (7 1 (:REWRITE PROJECTION-LAWS))
 (6 3 (:REWRITE NULLITY-LAWS))
 (4 4 (:TYPE-PRESCRIPTION REDUCIBLE-PP))
 (4 4 (:REWRITE UNIT-ASSOCIATES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP-1))
 (4 4 (:REWRITE **_E-IRREDUCIBLE-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (2 2 (:REWRITE ZERO-DIVISOR-LAW-FOR-**_E))
 (2 2 (:REWRITE **_E-IRREDUCIBLE-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP-LEMMA))
 )
(UNIT-ASSOCIATES-PP-**_E-**_E-LST-DELETE-ONE-UNIT-ASSOCIATE
 (39527 987 (:DEFINITION UNIT-P))
 (39194 15211 (:REWRITE EQUIVALENCE-LAW))
 (32908 20 (:DEFINITION IRREDUCIBLE-P))
 (30272 762 (:DEFINITION DIVIDES-P))
 (27410 6672 (:REWRITE UNIT-P-IMPLIES-EDP))
 (18089 20 (:DEFINITION REDUCIBLE-P))
 (13762 136 (:DEFINITION IRREDUCIBLE-PP))
 (11123 685 (:REWRITE ZERO-DIVISOR-LAW))
 (11060 11044 (:REWRITE CLOSURE-LAWS))
 (9304 990 (:REWRITE DIVIDES-P-SUFF))
 (9215 24 (:REWRITE IRREDUCIBLE-PP-UNIT-ASSOCIATES))
 (9039 20 (:REWRITE REDUCIBLE-P-SUFF))
 (8572 160 (:DEFINITION REDUCIBLE-PP))
 (7160 52 (:REWRITE IRREDUCIBLE-PP-IMPLIES-PRIME-PROPERTY))
 (6933 6933 (:TYPE-PRESCRIPTION UNIT-P))
 (6785 48 (:DEFINITION IRREDUCIBLE-LISTP-1))
 (5039 37 (:REWRITE IRREDUCIBLE-LISTP-1-IMPLIES-EDP-LISTP))
 (3154 987 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (1952 136 (:REWRITE IRREDUCIBLE-LISTP-1-IRREDUCIBLE-PP-MEMBER-UNIT-ASSOCIATE-PP))
 (1811 16 (:REWRITE UNIT-ASSOCIATES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (1811 16 (:REWRITE DIVIDES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (1811 16 (:REWRITE DIVIDES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-LEMMA))
 (1787 1787 (:TYPE-PRESCRIPTION UNIT-PP))
 (1419 544 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-PP))
 (1271 1271 (:EQUIVALENCE ==_E-EQUIVALENCE-LAW))
 (1242 136 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
 (1088 1088 (:REWRITE IRREDUCIBLE-PP-IMPLIES-UNIT-PP-FACTOR))
 (910 455 (:DEFINITION MV-NTH))
 (880 72 (:REWRITE REDUCIBLE-PP-**_E))
 (848 6 (:REWRITE DIVIDES-PP-**_E))
 (740 26 (:REWRITE DIVIDES-PP-SUFF))
 (706 6 (:REWRITE DIVIDES-PP-MEMBER-UNIT-ASSOCIATE-PP-**_E-LST))
 (701 701 (:REWRITE DEFAULT-CAR))
 (616 616 (:TYPE-PRESCRIPTION BOOLEANP-DIVIDES-P))
 (391 391 (:REWRITE DEFAULT-CDR))
 (320 26 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (264 12 (:REWRITE ASSOCIATIVITY-LAWS-FOR-++_E-&-**_E))
 (246 126 (:REWRITE CLOSURE-LAWS-FOR-++_E-&-**_E))
 (245 209 (:TYPE-PRESCRIPTION NATP-SIZE-==_E))
 (227 227 (:TYPE-PRESCRIPTION IRREDUCIBLE-LISTP-1))
 (220 20 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-P))
 (209 209 (:TYPE-PRESCRIPTION NATP-SIZE))
 (174 166 (:REWRITE COMMUTATIVITY-LAWS-FOR-++_E-&-**_E))
 (160 160 (:REWRITE REDUCIBLE-PP-SUFF))
 (156 36 (:REWRITE REDUCIBLE-PP-**_E-1))
 (140 38 (:REWRITE UNIT-PP-CLOSURE-**_E))
 (136 136 (:REWRITE UNIT-PP-NOT-REDUCIBLE-PP))
 (100 100 (:TYPE-PRESCRIPTION IRREDUCIBLE-PP))
 (88 12 (:REWRITE INVERSE-CANCELLATION-LAWS-**_E))
 (78 22 (:REWRITE RIGHT-UNICITY-LAWS))
 (62 19 (:REWRITE NULLITY-LAWS))
 (60 8 (:REWRITE ZERO-DIVISOR-LAW-FOR-**_E))
 (56 56 (:REWRITE RIGHT-UNICITY-LAW-FOR-*_E))
 (56 56 (:REWRITE LEFT-UNICITY-LAWS))
 (51 51 (:TYPE-PRESCRIPTION DIVIDES-PP))
 (49 23 (:LINEAR SIZE->=-SIZE-1_E))
 (41 5 (:REWRITE CANCELLATION-LAWS-FOR-**_E))
 (32 32 (:TYPE-PRESCRIPTION REDUCIBLE-PP))
 (26 26 (:REWRITE TRANSITIVITY-DIVIDES-PP))
 (26 26 (:REWRITE PRIME-PROPERTY-LEMMA))
 (24 24 (:REWRITE UNIT-ASSOCIATES-PP-SUFF))
 (24 12 (:REWRITE REDUCIBLE-PP-**_E-LST))
 (20 20 (:REWRITE REDUCIBLE-P-SUFF-2))
 (20 5 (:REWRITE PROJECTION-LAWS))
 (16 16 (:REWRITE UNIT-ASSOCIATES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP-1))
 (16 16 (:REWRITE **_E-IRREDUCIBLE-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (6 6 (:REWRITE **_E-IRREDUCIBLE-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP-LEMMA))
 )
(UNIT-ASSOCIATES-PP-**_E-CANCELLATION
 (9716 1415 (:REWRITE UNIT-P-IMPLIES-EDP))
 (8686 182 (:DEFINITION UNIT-P))
 (7294 2484 (:REWRITE EQUIVALENCE-LAW))
 (6707 142 (:DEFINITION DIVIDES-P))
 (3956 59 (:REWRITE IRREDUCIBLE-PP-UNIT-ASSOCIATES))
 (3321 31 (:DEFINITION IRREDUCIBLE-PP))
 (2598 74 (:REWRITE IRREDUCIBLE-PP-IMPLIES-PRIME-PROPERTY))
 (2286 104 (:REWRITE ZERO-DIVISOR-LAW))
 (2055 2007 (:REWRITE CLOSURE-LAWS))
 (1861 47 (:DEFINITION REDUCIBLE-PP))
 (1858 182 (:REWRITE DIVIDES-P-SUFF))
 (1660 328 (:REWRITE IRREDUCIBLE-PP-IMPLIES-UNIT-PP-FACTOR))
 (1417 1417 (:REWRITE MEMBER-UNIT-ASSOCIATE-PP-EDP-LISTP-IMPLIES-EDP))
 (1415 1415 (:TYPE-PRESCRIPTION UNIT-P))
 (1375 164 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-PP))
 (1335 234 (:REWRITE INVERSE-CANCELLATION-LAWS-**_E))
 (1215 48 (:REWRITE DIVIDES-PP-**_E))
 (875 37 (:REWRITE DIVIDES-PP-SUFF))
 (640 48 (:REWRITE REDUCIBLE-PP-**_E))
 (552 182 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (489 33 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
 (447 39 (:REWRITE ASSOCIATIVITY-LAWS-FOR-++_E-&-**_E))
 (264 227 (:TYPE-PRESCRIPTION NATP-SIZE-==_E))
 (188 94 (:DEFINITION MV-NTH))
 (185 47 (:REWRITE REDUCIBLE-PP-SUFF))
 (183 183 (:TYPE-PRESCRIPTION NATP-SIZE))
 (158 37 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (152 24 (:REWRITE UNIT-PP-CLOSURE-**_E))
 (152 24 (:REWRITE REDUCIBLE-PP-**_E-1))
 (144 144 (:TYPE-PRESCRIPTION DIVIDES-PP))
 (118 118 (:TYPE-PRESCRIPTION BOOLEANP-DIVIDES-P))
 (102 102 (:TYPE-PRESCRIPTION IRREDUCIBLE-PP))
 (69 23 (:LINEAR SIZE->=-SIZE-1_E))
 (59 59 (:REWRITE UNIT-ASSOCIATES-PP-SUFF))
 (57 19 (:REWRITE ZERO-DIVISOR-LAW-FOR-**_E))
 (48 48 (:TYPE-PRESCRIPTION REDUCIBLE-PP))
 (47 47 (:REWRITE DEFAULT-CDR))
 (47 47 (:REWRITE DEFAULT-CAR))
 (37 37 (:REWRITE TRANSITIVITY-DIVIDES-PP))
 (37 37 (:REWRITE PRIME-PROPERTY-LEMMA))
 (33 33 (:REWRITE IRREDUCIBLE-LISTP-1-IRREDUCIBLE-PP-MEMBER-UNIT-ASSOCIATE-PP))
 (31 31 (:REWRITE UNIT-PP-NOT-REDUCIBLE-PP))
 (28 8 (:LINEAR SIZE-<-SIZE-**_E))
 (27 15 (:REWRITE PROJECTION-LAWS))
 (24 12 (:REWRITE RIGHT-UNICITY-LAWS))
 (24 12 (:REWRITE NULLITY-LAWS))
 (18 8 (:LINEAR SIZE-**_E))
 )
(UNIT-ASSOCIATES-PP-**_E-**_E-LST-DELETE-ONE-UNIT-ASSOCIATE-PP-CANCELLATION
 (2444 71 (:DEFINITION UNIT-P))
 (2315 357 (:REWRITE UNIT-P-IMPLIES-EDP))
 (2131 51 (:DEFINITION DIVIDES-P))
 (1954 744 (:REWRITE EQUIVALENCE-LAW))
 (1274 6 (:DEFINITION **_E-LST))
 (1147 7 (:REWRITE IRREDUCIBLE-PP-UNIT-ASSOCIATES))
 (699 32 (:REWRITE ZERO-DIVISOR-LAW))
 (686 2 (:REWRITE IRREDUCIBLE-LISTP-IMPLIES-EDP-LISTP))
 (680 2 (:DEFINITION IRREDUCIBLE-LISTP))
 (663 2 (:DEFINITION IRREDUCIBLE-P))
 (625 625 (:REWRITE CLOSURE-LAWS))
 (542 8 (:REWRITE IRREDUCIBLE-PP-IMPLIES-PRIME-PROPERTY))
 (390 390 (:TYPE-PRESCRIPTION UNIT-P))
 (365 2 (:REWRITE DIVIDES-PP-MEMBER-UNIT-ASSOCIATE-PP-**_E-LST))
 (357 357 (:REWRITE MEMBER-UNIT-ASSOCIATE-PP-EDP-LISTP-IMPLIES-EDP))
 (340 2 (:DEFINITION DELETE-ONE-UNIT-ASSOCIATE-PP))
 (298 26 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
 (288 71 (:REWRITE DIVIDES-P-SUFF))
 (277 2 (:DEFINITION REDUCIBLE-P))
 (275 2 (:REWRITE REDUCIBLE-P-SUFF))
 (187 5 (:REWRITE UNIT-ASSOCIATES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (182 177 (:TYPE-PRESCRIPTION NATP-SIZE-==_E))
 (142 25 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-PP))
 (139 2 (:DEFINITION MEMBER-UNIT-ASSOCIATE-PP))
 (118 71 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (111 111 (:TYPE-PRESCRIPTION NATP-SIZE))
 (102 4 (:REWRITE DIVIDES-PP-SUFF))
 (78 4 (:REWRITE DIVIDES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (78 4 (:REWRITE DIVIDES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-LEMMA))
 (72 4 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (71 23 (:LINEAR SIZE->=-SIZE-1_E))
 (53 17 (:REWRITE REDUCIBLE-PP-**_E-LST))
 (50 50 (:REWRITE IRREDUCIBLE-PP-IMPLIES-UNIT-PP-FACTOR))
 (40 40 (:TYPE-PRESCRIPTION BOOLEANP-DIVIDES-P))
 (26 26 (:REWRITE IRREDUCIBLE-LISTP-1-IRREDUCIBLE-PP-MEMBER-UNIT-ASSOCIATE-PP))
 (24 24 (:REWRITE UNIT-PP-NOT-REDUCIBLE-PP))
 (24 24 (:REWRITE REDUCIBLE-PP-SUFF))
 (24 24 (:REWRITE DEFAULT-CAR))
 (22 2 (:DEFINITION IRREDUCIBLE-LISTP-1))
 (18 18 (:REWRITE DEFAULT-CDR))
 (12 4 (:REWRITE RIGHT-UNICITY-LAWS))
 (10 10 (:TYPE-PRESCRIPTION IRREDUCIBLE-LISTP))
 (10 10 (:TYPE-PRESCRIPTION DIVIDES-PP))
 (10 2 (:REWRITE COMMUTATIVITY-LAWS-FOR-++_E-&-**_E))
 (8 4 (:DEFINITION MV-NTH))
 (7 7 (:REWRITE UNIT-ASSOCIATES-PP-SUFF))
 (7 3 (:REWRITE NULLITY-LAWS))
 (7 1 (:REWRITE PROJECTION-LAWS))
 (5 5 (:REWRITE UNIT-ASSOCIATES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP-1))
 (5 2 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-P))
 (4 4 (:REWRITE TRANSITIVITY-DIVIDES-PP))
 (4 4 (:REWRITE PRIME-PROPERTY-LEMMA))
 (4 2 (:REWRITE IRREDUCIBLE-LISTP-1-DELETE-ONE-UNIT-ASSOCIATE-PP))
 (3 3 (:REWRITE **_E-IRREDUCIBLE-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP-LEMMA))
 (2 2 (:REWRITE REDUCIBLE-P-SUFF-2))
 )
(IRREDUCIBLE-FACTORIZATION-UNIQUENESS-GENERAL-1
 (7579 1235 (:REWRITE UNIT-P-IMPLIES-EDP))
 (7258 206 (:DEFINITION UNIT-P))
 (6612 160 (:DEFINITION DIVIDES-P))
 (5771 2052 (:REWRITE EQUIVALENCE-LAW))
 (3869 25 (:REWRITE IRREDUCIBLE-PP-UNIT-ASSOCIATES))
 (2139 91 (:REWRITE ZERO-DIVISOR-LAW))
 (1842 1842 (:REWRITE CLOSURE-LAWS))
 (1582 7 (:REWRITE DIVIDES-PP-MEMBER-UNIT-ASSOCIATE-PP-**_E-LST))
 (1352 1352 (:TYPE-PRESCRIPTION UNIT-P))
 (1329 9 (:REWRITE IRREDUCIBLE-LISTP-IMPLIES-EDP-LISTP))
 (1302 9 (:DEFINITION IRREDUCIBLE-LISTP))
 (1296 34 (:REWRITE IRREDUCIBLE-PP-IMPLIES-PRIME-PROPERTY))
 (1236 9 (:DEFINITION IRREDUCIBLE-P))
 (1235 1235 (:REWRITE MEMBER-UNIT-ASSOCIATE-PP-EDP-LISTP-IMPLIES-EDP))
 (884 20 (:REWRITE UNIT-ASSOCIATES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (817 100 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
 (564 9 (:DEFINITION REDUCIBLE-P))
 (554 206 (:REWRITE DIVIDES-P-SUFF))
 (470 16 (:REWRITE DIVIDES-PP-SUFF))
 (470 4 (:DEFINITION DELETE-ONE-UNIT-ASSOCIATE-PP))
 (428 9 (:REWRITE REDUCIBLE-P-SUFF))
 (422 18 (:REWRITE DIVIDES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (422 18 (:REWRITE DIVIDES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-LEMMA))
 (331 106 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-PP))
 (330 206 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (268 268 (:EQUIVALENCE ==_E-EQUIVALENCE-LAW))
 (236 17 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (212 212 (:REWRITE IRREDUCIBLE-PP-IMPLIES-UNIT-PP-FACTOR))
 (188 153 (:TYPE-PRESCRIPTION NATP-SIZE-==_E))
 (166 6 (:REWRITE ASSOCIATIVITY-LAWS-FOR-++_E-&-**_E))
 (153 153 (:TYPE-PRESCRIPTION NATP-SIZE))
 (145 1 (:DEFINITION EDP-LISTP))
 (129 129 (:REWRITE EDP-**_E-LST))
 (108 108 (:REWRITE IRREDUCIBLE-LISTP-1-IRREDUCIBLE-PP-MEMBER-UNIT-ASSOCIATE-PP))
 (104 104 (:REWRITE REDUCIBLE-PP-SUFF))
 (100 100 (:REWRITE UNIT-PP-NOT-REDUCIBLE-PP))
 (94 94 (:REWRITE DEFAULT-CAR))
 (92 92 (:TYPE-PRESCRIPTION BOOLEANP-DIVIDES-P))
 (88 12 (:REWRITE INVERSE-CANCELLATION-LAWS-**_E))
 (76 32 (:REWRITE REDUCIBLE-PP-**_E))
 (72 40 (:REWRITE CLOSURE-LAWS-FOR-++_E-&-**_E))
 (59 59 (:REWRITE DEFAULT-CDR))
 (52 16 (:REWRITE REDUCIBLE-PP-**_E-1))
 (45 45 (:TYPE-PRESCRIPTION IRREDUCIBLE-LISTP))
 (41 9 (:REWRITE RIGHT-UNICITY-LAWS))
 (40 40 (:TYPE-PRESCRIPTION DIVIDES-PP))
 (39 17 (:LINEAR SIZE->=-SIZE-1_E))
 (38 10 (:REWRITE NULLITY-LAWS))
 (36 32 (:REWRITE REDUCIBLE-PP-**_E-LST))
 (36 18 (:DEFINITION MV-NTH))
 (25 25 (:REWRITE UNIT-ASSOCIATES-PP-SUFF))
 (19 7 (:REWRITE COMMUTATIVITY-LAWS-FOR-++_E-&-**_E))
 (18 1 (:REWRITE LEAST-DIVIDES-PP=1_E))
 (17 17 (:REWRITE TRANSITIVITY-DIVIDES-PP))
 (17 17 (:REWRITE PRIME-PROPERTY-LEMMA))
 (16 16 (:REWRITE UNIT-PP-CLOSURE-**_E))
 (14 2 (:REWRITE ZERO-DIVISOR-LAW-FOR-**_E))
 (12 9 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-P))
 (9 9 (:REWRITE REDUCIBLE-P-SUFF-2))
 (9 9 (:REWRITE **_E-IRREDUCIBLE-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP-LEMMA))
 (8 8 (:REWRITE NOT-IRREDUCIBLE-PP-1_E))
 (7 1 (:REWRITE PROJECTION-LAWS))
 (2 2 (:REWRITE |1_E-0_E|))
 (2 1 (:REWRITE IRREDUCIBLE-LISTP-1-DELETE-ONE-UNIT-ASSOCIATE-PP))
 (1 1 (:REWRITE UNIT-PP-1_E))
 )
(IRREDUCIBLE-LISTP-=-IRREDUCIBLE-LISTP-1
 (23529 6900 (:REWRITE EQUIVALENCE-LAW))
 (22313 435 (:DEFINITION UNIT-P))
 (21909 2 (:DEFINITION IRREDUCIBLE-P))
 (16419 329 (:DEFINITION DIVIDES-P))
 (14496 2 (:DEFINITION REDUCIBLE-P))
 (14076 3155 (:REWRITE UNIT-P-IMPLIES-EDP))
 (8985 265 (:REWRITE ZERO-DIVISOR-LAW))
 (7727 435 (:REWRITE DIVIDES-P-SUFF))
 (6614 6494 (:REWRITE CLOSURE-LAWS))
 (4594 10 (:DEFINITION IRREDUCIBLE-PP))
 (3738 2 (:REWRITE REDUCIBLE-P-SUFF))
 (3468 10 (:DEFINITION REDUCIBLE-PP))
 (3175 3175 (:TYPE-PRESCRIPTION UNIT-P))
 (3155 3155 (:REWRITE MEMBER-UNIT-ASSOCIATE-PP-EDP-LISTP-IMPLIES-EDP))
 (3018 38 (:DEFINITION UNIT-PP))
 (2858 76 (:REWRITE IRREDUCIBLE-PP-IMPLIES-PRIME-PROPERTY))
 (1253 435 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (674 10 (:REWRITE UNIT-PP-NOT-REDUCIBLE-PP))
 (644 24 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
 (618 38 (:REWRITE DIVIDES-PP-SUFF))
 (304 224 (:TYPE-PRESCRIPTION NATP-SIZE-==_E))
 (224 7 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-P))
 (204 31 (:LINEAR SIZE->=-SIZE-1_E))
 (196 196 (:TYPE-PRESCRIPTION BOOLEANP-DIVIDES-P))
 (189 189 (:TYPE-PRESCRIPTION NATP-SIZE))
 (114 38 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-PP))
 (114 38 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (86 86 (:TYPE-PRESCRIPTION DIVIDES-PP))
 (76 76 (:REWRITE IRREDUCIBLE-PP-IMPLIES-UNIT-PP-FACTOR))
 (66 66 (:REWRITE COMMUTATIVITY-LAWS-FOR-++_E-&-**_E))
 (62 28 (:DEFINITION MV-NTH))
 (38 38 (:REWRITE TRANSITIVITY-DIVIDES-PP))
 (38 38 (:REWRITE RIGHT-UNICITY-LAWS))
 (38 38 (:REWRITE PRIME-PROPERTY-LEMMA))
 (38 38 (:REWRITE NULLITY-LAWS))
 (38 14 (:REWRITE RIGHT-UNICITY-LAW-FOR-*_E))
 (32 32 (:REWRITE DEFAULT-CAR))
 (24 24 (:REWRITE IRREDUCIBLE-LISTP-1-IRREDUCIBLE-PP-MEMBER-UNIT-ASSOCIATE-PP))
 (20 20 (:REWRITE DEFAULT-CDR))
 (10 10 (:REWRITE REDUCIBLE-PP-SUFF))
 (5 5 (:REWRITE |1_E-0_E|))
 (2 2 (:REWRITE REDUCIBLE-P-SUFF-2))
 )
(IRREDUCIBLE-FACTORIZATION-UNIQUENESS-GENERAL
 (45908 13340 (:REWRITE EQUIVALENCE-LAW))
 (27752 6232 (:REWRITE UNIT-P-IMPLIES-EDP))
 (18066 540 (:REWRITE ZERO-DIVISOR-LAW))
 (15484 922 (:REWRITE DIVIDES-P-SUFF))
 (13292 13052 (:REWRITE CLOSURE-LAWS))
 (7284 4 (:REWRITE REDUCIBLE-P-SUFF))
 (6272 6272 (:TYPE-PRESCRIPTION UNIT-P))
 (6252 6236 (:REWRITE MEMBER-UNIT-ASSOCIATE-PP-EDP-LISTP-IMPLIES-EDP))
 (3996 322 (:REWRITE IRREDUCIBLE-PP-IMPLIES-PRIME-PROPERTY))
 (3329 5 (:DEFINITION MEMBER-UNIT-ASSOCIATE-PP))
 (3146 10 (:REWRITE IRREDUCIBLE-PP-UNIT-ASSOCIATES))
 (2624 922 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (2094 106 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
 (1922 1922 (:EQUIVALENCE ==_E-EQUIVALENCE-LAW))
 (1861 161 (:REWRITE DIVIDES-PP-SUFF))
 (1668 10 (:REWRITE UNIT-ASSOCIATES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (1668 10 (:REWRITE DIVIDES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (1668 10 (:REWRITE DIVIDES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-LEMMA))
 (1423 4 (:REWRITE IRREDUCIBLE-FACTORIZATION-UNIQUENESS-GENERAL-1))
 (1140 42 (:REWRITE UNIT-PP-NOT-REDUCIBLE-PP))
 (1122 3 (:REWRITE DIVIDES-PP-MEMBER-UNIT-ASSOCIATE-PP-**_E-LST))
 (968 6 (:DEFINITION **_E-LST))
 (888 584 (:TYPE-PRESCRIPTION NATP-SIZE-==_E))
 (864 864 (:TYPE-PRESCRIPTION BOOLEANP-DIVIDES-P))
 (584 584 (:TYPE-PRESCRIPTION NATP-SIZE))
 (501 161 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (480 480 (:TYPE-PRESCRIPTION IRREDUCIBLE-PP))
 (410 154 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-PP))
 (308 308 (:REWRITE IRREDUCIBLE-PP-IMPLIES-UNIT-PP-FACTOR))
 (164 64 (:LINEAR SIZE->=-SIZE-1_E))
 (161 161 (:REWRITE TRANSITIVITY-DIVIDES-PP))
 (161 161 (:REWRITE PRIME-PROPERTY-LEMMA))
 (125 109 (:REWRITE RIGHT-UNICITY-LAWS))
 (125 109 (:REWRITE NULLITY-LAWS))
 (110 110 (:REWRITE IRREDUCIBLE-LISTP-1-IRREDUCIBLE-PP-MEMBER-UNIT-ASSOCIATE-PP))
 (106 2 (:DEFINITION DELETE-ONE-UNIT-ASSOCIATE-PP))
 (104 104 (:REWRITE DEFAULT-CAR))
 (90 90 (:TYPE-PRESCRIPTION UNIT-PP))
 (87 87 (:REWRITE DEFAULT-CDR))
 (80 4 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-P))
 (76 28 (:REWRITE RIGHT-UNICITY-LAW-FOR-*_E))
 (52 52 (:REWRITE EDP-**_E-LST))
 (42 42 (:REWRITE REDUCIBLE-PP-SUFF))
 (18 18 (:REWRITE REDUCIBLE-PP-**_E-LST))
 (15 15 (:TYPE-PRESCRIPTION EDP-LISTP))
 (10 10 (:REWRITE UNIT-ASSOCIATES-PP-SUFF))
 (10 10 (:REWRITE UNIT-ASSOCIATES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP-1))
 (10 10 (:REWRITE **_E-IRREDUCIBLE-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (7 7 (:REWRITE IRREDUCIBLE-LISTP-IMPLIES-EDP-LISTP))
 (7 1 (:DEFINITION DELETE-ONE-UNIT-ASSOCIATE))
 (5 1 (:DEFINITION MEMBER-UNIT-ASSOCIATE))
 (4 4 (:REWRITE REDUCIBLE-P-SUFF-2))
 (4 4 (:REWRITE PROJECTION-LAWS))
 (3 3 (:REWRITE UNIT-ASSOCIATES-P-SUFF))
 (3 3 (:REWRITE **_E-IRREDUCIBLE-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP-LEMMA))
 )
(IRREDUCIBLE-FACTORIZATION-UNIQUENESS-1
 (564 78 (:REWRITE UNIT-P-IMPLIES-EDP))
 (530 10 (:DEFINITION UNIT-P))
 (506 6 (:DEFINITION DIVIDES-P))
 (464 148 (:REWRITE EQUIVALENCE-LAW))
 (178 8 (:REWRITE ZERO-DIVISOR-LAW))
 (140 140 (:REWRITE CLOSURE-LAWS))
 (78 78 (:TYPE-PRESCRIPTION UNIT-P))
 (78 78 (:REWRITE MEMBER-UNIT-ASSOCIATE-PP-EDP-LISTP-IMPLIES-EDP))
 (72 2 (:REWRITE IRREDUCIBLE-PP-UNIT-ASSOCIATES))
 (50 2 (:DEFINITION IRREDUCIBLE-LISTP-1))
 (42 4 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
 (32 1 (:REWRITE DIVIDES-PP-MEMBER-UNIT-ASSOCIATE-PP-**_E-LST))
 (22 10 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (22 10 (:REWRITE DIVIDES-P-SUFF))
 (17 1 (:REWRITE DIVIDES-PP-SUFF))
 (17 1 (:DEFINITION MEMBER-UNIT-ASSOCIATE-PP))
 (12 12 (:TYPE-PRESCRIPTION IRREDUCIBLE-PP))
 (11 11 (:REWRITE DEFAULT-CAR))
 (10 2 (:REWRITE IRREDUCIBLE-PP-IMPLIES-PRIME-PROPERTY))
 (8 8 (:TYPE-PRESCRIPTION BOOLEANP-DIVIDES-P))
 (7 7 (:REWRITE DEFAULT-CDR))
 (7 1 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (5 5 (:TYPE-PRESCRIPTION MEMBER-UNIT-ASSOCIATE-PP))
 (4 4 (:REWRITE IRREDUCIBLE-LISTP-1-IRREDUCIBLE-PP-MEMBER-UNIT-ASSOCIATE-PP))
 (4 2 (:REWRITE UNIT-ASSOCIATES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (4 2 (:REWRITE DIVIDES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (4 2 (:REWRITE DIVIDES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-LEMMA))
 (3 3 (:TYPE-PRESCRIPTION DIVIDES-PP))
 (2 2 (:REWRITE UNIT-ASSOCIATES-PP-SUFF))
 (2 2 (:REWRITE UNIT-ASSOCIATES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP-1))
 (2 2 (:REWRITE PROJECTION-LAWS))
 (2 2 (:REWRITE EDP-**_E-LST))
 (2 2 (:REWRITE COMMUTATIVITY-LAWS-FOR-++_E-&-**_E))
 (2 2 (:REWRITE **_E-IRREDUCIBLE-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (2 1 (:REWRITE IRREDUCIBLE-LISTP-IMPLIES-EDP-LISTP))
 (1 1 (:TYPE-PRESCRIPTION IRREDUCIBLE-LISTP))
 (1 1 (:TYPE-PRESCRIPTION EDP-LISTP))
 (1 1 (:REWRITE TRANSITIVITY-DIVIDES-PP))
 (1 1 (:REWRITE RIGHT-UNICITY-LAWS))
 (1 1 (:REWRITE PRIME-PROPERTY-LEMMA))
 (1 1 (:REWRITE NULLITY-LAWS))
 (1 1 (:REWRITE IRREDUCIBLE-LISTP-1-IMPLIES-EDP-LISTP))
 (1 1 (:REWRITE **_E-IRREDUCIBLE-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP-LEMMA))
 )
(IRREDUCIBLE-FACTORIZATION-UNIQUENESS
 (48180 14082 (:REWRITE EQUIVALENCE-LAW))
 (28725 6491 (:REWRITE UNIT-P-IMPLIES-EDP))
 (18616 574 (:REWRITE ZERO-DIVISOR-LAW))
 (16044 963 (:REWRITE DIVIDES-P-SUFF))
 (13819 13579 (:REWRITE CLOSURE-LAWS))
 (7776 5 (:REWRITE REDUCIBLE-P-SUFF))
 (6541 6541 (:TYPE-PRESCRIPTION UNIT-P))
 (6511 6495 (:REWRITE MEMBER-UNIT-ASSOCIATE-PP-EDP-LISTP-IMPLIES-EDP))
 (3224 228 (:REWRITE IRREDUCIBLE-PP-IMPLIES-PRIME-PROPERTY))
 (2808 4 (:DEFINITION MEMBER-UNIT-ASSOCIATE-PP))
 (2793 963 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-P))
 (2300 2 (:REWRITE IRREDUCIBLE-FACTORIZATION-UNIQUENESS-GENERAL))
 (1984 92 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-PP))
 (1784 4 (:REWRITE IRREDUCIBLE-FACTORIZATION-UNIQUENESS-GENERAL-1))
 (1482 114 (:REWRITE DIVIDES-PP-SUFF))
 (1364 8 (:REWRITE IRREDUCIBLE-PP-UNIT-ASSOCIATES))
 (1320 8 (:REWRITE UNIT-ASSOCIATES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (1320 8 (:REWRITE DIVIDES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (1320 8 (:REWRITE DIVIDES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-LEMMA))
 (1088 8 (:DEFINITION **_E-LST))
 (1060 28 (:REWRITE UNIT-PP-NOT-REDUCIBLE-PP))
 (892 892 (:TYPE-PRESCRIPTION BOOLEANP-DIVIDES-P))
 (852 548 (:TYPE-PRESCRIPTION NATP-SIZE-==_E))
 (548 548 (:TYPE-PRESCRIPTION NATP-SIZE))
 (380 380 (:TYPE-PRESCRIPTION IRREDUCIBLE-PP))
 (362 114 (:REWRITE RR_E=0-IMPLIES-DIVIDES-PP))
 (304 108 (:REWRITE SIZE=SIZE-1_E-IMPLIES-UNIT-PP))
 (216 216 (:REWRITE IRREDUCIBLE-PP-IMPLIES-UNIT-PP-FACTOR))
 (156 60 (:LINEAR SIZE->=-SIZE-1_E))
 (114 114 (:REWRITE TRANSITIVITY-DIVIDES-PP))
 (114 114 (:REWRITE PRIME-PROPERTY-LEMMA))
 (106 2 (:DEFINITION DELETE-ONE-UNIT-ASSOCIATE-PP))
 (104 96 (:REWRITE RIGHT-UNICITY-LAWS))
 (104 96 (:REWRITE NULLITY-LAWS))
 (99 99 (:REWRITE DEFAULT-CAR))
 (96 96 (:REWRITE IRREDUCIBLE-LISTP-1-IRREDUCIBLE-PP-MEMBER-UNIT-ASSOCIATE-PP))
 (96 5 (:REWRITE SIZE-IMPLIES-IRREDUCIBLE-P))
 (80 32 (:REWRITE RIGHT-UNICITY-LAW-FOR-*_E))
 (78 78 (:REWRITE DEFAULT-CDR))
 (60 2 (:REWRITE DIVIDES-PP-MEMBER-UNIT-ASSOCIATE-PP-**_E-LST))
 (44 44 (:TYPE-PRESCRIPTION UNIT-PP))
 (36 36 (:REWRITE EDP-**_E-LST))
 (28 28 (:REWRITE REDUCIBLE-PP-SUFF))
 (14 14 (:TYPE-PRESCRIPTION EDP-LISTP))
 (8 8 (:REWRITE UNIT-ASSOCIATES-PP-SUFF))
 (8 8 (:REWRITE UNIT-ASSOCIATES-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP-1))
 (8 8 (:REWRITE **_E-IRREDUCIBLE-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP))
 (7 1 (:DEFINITION DELETE-ONE-UNIT-ASSOCIATE))
 (6 6 (:REWRITE IRREDUCIBLE-LISTP-IMPLIES-EDP-LISTP))
 (5 5 (:REWRITE REDUCIBLE-P-SUFF-2))
 (5 1 (:DEFINITION MEMBER-UNIT-ASSOCIATE))
 (4 4 (:TYPE-PRESCRIPTION UNIT-ASSOCIATES-PP))
 (4 4 (:TYPE-PRESCRIPTION BOOLEANP-UNIT-ASSOCIATES-P))
 (4 4 (:REWRITE REDUCIBLE-PP-**_E-LST))
 (4 4 (:REWRITE LEFT-UNICITY-LAWS))
 (3 3 (:REWRITE UNIT-ASSOCIATES-P-SUFF))
 (2 2 (:REWRITE **_E-IRREDUCIBLE-PP-**_E-LST-IMPLIES-MEMBER-UNIT-ASSOCIATE-PP-LEMMA))
 )
