(LCNF::PKG-FUNCTIONAL-INSTANCE-PAIRS)
(LCNF::PKG-FUNCTIONAL-INSTANCE)
(LCNF::REL)
(LCNF::FN)
(LCNF::REL-WELL-FOUNDED-RELATION-ON-MP)
(LCNF::REL-TRANSITIVE)
(LCNF::LEGAL)
(LCNF::REDUCE-ONE-STEP)
(LCNF::REDUCIBLE)
(LCNF::TRANSFORM-LOCAL-PEAK)
(LCNF::LEGAL-REDUCIBLE-1)
(LCNF::LEGAL-REDUCIBLE-2)
(LCNF::PROOF-STEP-P)
(LCNF::EQUIV-P)
(LCNF::EQUIV-P-TYPE)
(LCNF::LOCAL-CONFLUENCE)
(LCNF::NOETHERIAN)
(LCNF::EXISTS-REL-BIGGER)
(LCNF::FORALL-EXISTS-REL-BIGGER)
(LCNF::MUL-REL)
(LCNF::MAP-FN-E0-ORD)
(LCNF::MAP-FN-OP)
(LCNF::REL-WELL-FOUNDED-RELATION-ON-MP-REWRITE)
(LCNF::|MULTISET-EXTENSION-OF-REL-WELL-FOUNDED-Lemma|
 (105 5 (:DEFINITION MUL::INSERT-E0-ORD-<))
 (70 5 (:DEFINITION E0-ORD-<))
 (68 68 (:REWRITE DEFAULT-CAR))
 (56 56 (:REWRITE DEFAULT-CDR))
 (32 4 (:DEFINITION MULTISET-DIFF))
 (20 4 (:DEFINITION REMOVE-ONE))
 (15 15 (:REWRITE DEFAULT-<-2))
 (15 15 (:REWRITE DEFAULT-<-1))
 (5 5 (:REWRITE DEFAULT-+-2))
 (5 5 (:REWRITE DEFAULT-+-1))
 )
(LCNF::MULTISET-EXTENSION-OF-REL-WELL-FOUNDED
 (54 2 (:DEFINITION LCNF::MAP-FN-E0-ORD))
 (42 2 (:DEFINITION MUL::INSERT-E0-ORD-<))
 (32 4 (:DEFINITION MULTISET-DIFF))
 (30 30 (:REWRITE DEFAULT-CAR))
 (28 2 (:DEFINITION E0-ORD-<))
 (26 26 (:REWRITE DEFAULT-CDR))
 (20 4 (:DEFINITION REMOVE-ONE))
 (9 2 (:DEFINITION LCNF::EXISTS-REL-BIGGER))
 (6 6 (:REWRITE DEFAULT-<-2))
 (6 6 (:REWRITE DEFAULT-<-1))
 (6 2 (:DEFINITION MUL::ADD1-IF-INTEGER))
 (4 4 (:TYPE-PRESCRIPTION LCNF::MAP-FN-E0-ORD))
 (4 4 (:TYPE-PRESCRIPTION E0-ORD-<))
 (4 2 (:DEFINITION TRUE-LISTP))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(LCNF::EQUAL-SET-IMPLIES-IFF-FORALL-EXISTS-REL-BIGGER-1)
(LCNF::EQUAL-SET-IMPLIES-IFF-FORALL-EXISTS-REL-BIGGER-2)
(LCNF::EXISTS-LOCAL-PEAK
 (72 32 (:REWRITE DEFAULT-+-2))
 (46 32 (:REWRITE DEFAULT-+-1))
 (16 16 (:REWRITE DEFAULT-CDR))
 (16 4 (:REWRITE COMMUTATIVITY-OF-+))
 (16 4 (:DEFINITION INTEGER-ABS))
 (16 2 (:DEFINITION LENGTH))
 (12 12 (:REWRITE FOLD-CONSTS-IN-+))
 (12 12 (:REWRITE DEFAULT-CAR))
 (10 6 (:REWRITE DEFAULT-<-2))
 (10 2 (:DEFINITION LEN))
 (8 6 (:REWRITE DEFAULT-<-1))
 (4 4 (:REWRITE DEFAULT-UNARY-MINUS))
 (2 2 (:TYPE-PRESCRIPTION LEN))
 (2 2 (:REWRITE DEFAULT-REALPART))
 (2 2 (:REWRITE DEFAULT-NUMERATOR))
 (2 2 (:REWRITE DEFAULT-IMAGPART))
 (2 2 (:REWRITE DEFAULT-DENOMINATOR))
 (2 2 (:REWRITE DEFAULT-COERCE-2))
 (2 2 (:REWRITE DEFAULT-COERCE-1))
 )
(LCNF::REPLACE-LOCAL-PEAK
 (72 32 (:REWRITE DEFAULT-+-2))
 (46 32 (:REWRITE DEFAULT-+-1))
 (16 16 (:REWRITE DEFAULT-CDR))
 (16 4 (:REWRITE COMMUTATIVITY-OF-+))
 (16 4 (:DEFINITION INTEGER-ABS))
 (16 2 (:DEFINITION LENGTH))
 (12 12 (:REWRITE FOLD-CONSTS-IN-+))
 (12 12 (:REWRITE DEFAULT-CAR))
 (10 6 (:REWRITE DEFAULT-<-2))
 (10 5 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (10 2 (:DEFINITION LEN))
 (8 6 (:REWRITE DEFAULT-<-1))
 (5 5 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (5 5 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (4 4 (:REWRITE DEFAULT-UNARY-MINUS))
 (2 2 (:TYPE-PRESCRIPTION LEN))
 (2 2 (:REWRITE DEFAULT-REALPART))
 (2 2 (:REWRITE DEFAULT-NUMERATOR))
 (2 2 (:REWRITE DEFAULT-IMAGPART))
 (2 2 (:REWRITE DEFAULT-DENOMINATOR))
 (2 2 (:REWRITE DEFAULT-COERCE-2))
 (2 2 (:REWRITE DEFAULT-COERCE-1))
 )
(LCNF::TRANSFORM-TO-VALLEY-ADMISSION
 (221 221 (:REWRITE DEFAULT-CDR))
 (209 209 (:REWRITE DEFAULT-CAR))
 (46 46 (:REWRITE LCNF::LEGAL-REDUCIBLE-2))
 (42 14 (:DEFINITION BINARY-APPEND))
 (40 20 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (32 4 (:DEFINITION MULTISET-DIFF))
 (20 20 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (20 20 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (20 4 (:DEFINITION REMOVE-ONE))
 )
(LCNF::TRANSFORM-TO-VALLEY)
(LCNF::EQUIV-P-X-Y-TRANSFORM-TO-VALLEY
 (115 5 (:DEFINITION LCNF::EXISTS-LOCAL-PEAK))
 (85 5 (:DEFINITION LCNF::REPLACE-LOCAL-PEAK))
 (70 70 (:REWRITE DEFAULT-CDR))
 (65 65 (:REWRITE DEFAULT-CAR))
 (40 10 (:DEFINITION LCNF::PROOF-STEP-P))
 (20 20 (:TYPE-PRESCRIPTION R-STEP-P))
 (20 20 (:REWRITE LCNF::LEGAL-REDUCIBLE-2))
 (15 5 (:DEFINITION BINARY-APPEND))
 )
(LCNF::VALLEY-TRANSFORM-TO-VALLEY)
(LCNF::PROOF-IRREDUCIBLE)
(LCNF::NORMALIZING-1
 (21 18 (:TYPE-PRESCRIPTION LAST))
 (10 10 (:TYPE-PRESCRIPTION R-STEP-P))
 )
(LCNF::NORMALIZING-2)
(LCNF::NORMAL-FORM)
(LCNF::R-EQUIVALENT)
(LCNF::NORMAL-FORM-AUX)
(LCNF::NORMAL-FORM-AUX-NORMAL-FORM
 (13 13 (:REWRITE DEFAULT-CDR))
 (11 6 (:REWRITE DEFAULT-CAR))
 (5 5 (:TYPE-PRESCRIPTION LAST))
 )
(LCNF::R-EQUIV)
(LCNF::R-EQUIVALENT-COMPLETE
 (124 2 (:DEFINITION LCNF::TRANSFORM-TO-VALLEY))
 (86 2 (:DEFINITION LCNF::EXISTS-LOCAL-PEAK))
 (72 68 (:REWRITE DEFAULT-CAR))
 (43 43 (:REWRITE DEFAULT-CDR))
 (35 35 (:REWRITE LCNF::LEGAL-REDUCIBLE-2))
 (34 2 (:DEFINITION LCNF::REPLACE-LOCAL-PEAK))
 (12 4 (:DEFINITION LAST))
 (6 2 (:DEFINITION BINARY-APPEND))
 (4 4 (:TYPE-PRESCRIPTION LAST))
 (2 2 (:TYPE-PRESCRIPTION LCNF::EXISTS-LOCAL-PEAK))
 )
(LCNF::MAKE-PROOF-COMMON-N-F
 (5 5 (:TYPE-PRESCRIPTION BINARY-APPEND))
 )
(LCNF::R-EQUIVALENT-SOUND
 (3 3 (:TYPE-PRESCRIPTION BINARY-APPEND))
 )
