(INV-P-P-IMPLIES-SUFF-PROC
     (133 7
          (:REWRITE MY-SUBSETP-PREVIOUS-REDUCTION))
     (83 83
         (:REWRITE LEXICOGRAPHIC-POS-IMPLIES-EVERYTHING-<-CAR-QUEUE))
     (83 83
         (:REWRITE DISJOINT-IMPLIES-ONE-NOT-MEMBER-SYMMETRIC))
     (83 83
         (:REWRITE DISJOINT-IMPLIES-ONE-NOT-MEMBER))
     (70 70 (:REWRITE DEFAULT-CAR))
     (61 61 (:REWRITE DEFAULT-CDR))
     (39 39 (:REWRITE MY-SUBSETP-IS-TRANSITIVE))
     (30 2
         (:REWRITE NOT-MEMBERP-PREVIOUS-REDUCTION))
     (21 11 (:REWRITE DEFAULT-+-2))
     (19 16 (:REWRITE DEFAULT-<-1))
     (17 16 (:REWRITE DEFAULT-<-2))
     (14 14
         (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
     (11 11 (:REWRITE DEFAULT-+-1))
     (2 2
        (:REWRITE LEXICOGRAPHIC-POS-LEX<-REDUCTION)))
(INDUCT-ON-KEYS
     (6 1 (:DEFINITION MEMBERP))
     (4 1 (:DEFINITION INV-P-KEYS))
     (2 2
        (:REWRITE LEXICOGRAPHIC-POS-IMPLIES-EVERYTHING-<-CAR-QUEUE))
     (2 2
        (:REWRITE DISJOINT-IMPLIES-ONE-NOT-MEMBER-SYMMETRIC))
     (2 2
        (:REWRITE DISJOINT-IMPLIES-ONE-NOT-MEMBER))
     (2 2 (:REWRITE DEFAULT-CDR))
     (2 2 (:REWRITE DEFAULT-CAR)))
(INV-P-KEYS-TO-CAR-QUEUE-IF-SUBSET
     (30 5 (:DEFINITION MEMBERP))
     (14 14 (:REWRITE DEFAULT-CAR))
     (12 12 (:REWRITE DEFAULT-CDR))
     (12 3 (:DEFINITION INV-P-KEYS))
     (10 10
         (:REWRITE LEXICOGRAPHIC-POS-IMPLIES-EVERYTHING-<-CAR-QUEUE))
     (10 10
         (:REWRITE DISJOINT-IMPLIES-ONE-NOT-MEMBER-SYMMETRIC))
     (10 10
         (:REWRITE DISJOINT-IMPLIES-ONE-NOT-MEMBER))
     (8 8 (:REWRITE MY-SUBSETP-IS-TRANSITIVE)))
(INV-B-C-SUFFICIENT->>
     (158 6 (:DEFINITION ORDEREDP))
     (108 4 (:REWRITE ORDERED-IMPLIES-UNIQUE))
     (86 22 (:REWRITE <<-TRICHOTOMY))
     (82 2 (:DEFINITION UNIQUEP))
     (58 10 (:REWRITE <<-ASYMMETRIC))
     (56 56 (:TYPE-PRESCRIPTION <<))
     (54 54 (:REWRITE DEFAULT-CDR))
     (48 48 (:REWRITE DEFAULT-CAR))
     (32 4 (:DEFINITION MY-SUBSETP))
     (30 6 (:REWRITE LEX<-TOTAL))
     (27 3 (:REWRITE LEX<-ASYMMETRIC))
     (22 22 (:REWRITE <<-TRANSITIVE))
     (20 2 (:DEFINITION LEGAL-STATUS-LISTP))
     (16 2 (:DEFINITION CHOOSING-POS))
     (14 12 (:REWRITE DEFAULT-<-1))
     (12 12 (:REWRITE DEFAULT-<-2))
     (12 2 (:DEFINITION Q<MAX))
     (12 2 (:DEFINITION MEMBERP))
     (12 2 (:DEFINITION INV-P-KEYS))
     (10 2 (:DEFINITION LEGAL-STATUS))
     (8 8
        (:REWRITE LEXICOGRAPHIC-POS-IMPLIES-EVERYTHING-<-CAR-QUEUE))
     (8 8
        (:REWRITE DISJOINT-IMPLIES-ONE-NOT-MEMBER-SYMMETRIC))
     (8 8
        (:REWRITE DISJOINT-IMPLIES-ONE-NOT-MEMBER))
     (6 6 (:TYPE-PRESCRIPTION NATP))
     (6 6 (:REWRITE LEX<-TRANSITIVE))
     (6 2 (:DEFINITION CHOOSING-BUCKET))
     (6 2 (:DEFINITION B=MAX))
     (2 2
        (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
     (2 2 (:DEFINITION WAIT-STATUS))
     (2 2 (:DEFINITION INTERESTED-STATUS))
     (2 2 (:DEFINITION IDLE-STATUS))
     (2 2 (:DEFINITION GO-STATUS)))
(FAIR-INV-B-C-SUFFICIENT->>
     (158 6 (:DEFINITION ORDEREDP))
     (108 4 (:REWRITE ORDERED-IMPLIES-UNIQUE))
     (86 22 (:REWRITE <<-TRICHOTOMY))
     (82 2 (:DEFINITION UNIQUEP))
     (64 6 (:DEFINITION MY-SUBSETP))
     (58 58 (:REWRITE DEFAULT-CDR))
     (58 10 (:REWRITE <<-ASYMMETRIC))
     (56 56 (:TYPE-PRESCRIPTION <<))
     (52 52 (:REWRITE DEFAULT-CAR))
     (30 6 (:REWRITE LEX<-TOTAL))
     (27 3 (:REWRITE LEX<-ASYMMETRIC))
     (24 4 (:DEFINITION MEMBERP))
     (22 22 (:REWRITE <<-TRANSITIVE))
     (20 2 (:DEFINITION LEGAL-STATUS-LISTP))
     (16 2 (:DEFINITION CHOOSING-POS))
     (14 12 (:REWRITE DEFAULT-<-1))
     (12 12
         (:REWRITE LEXICOGRAPHIC-POS-IMPLIES-EVERYTHING-<-CAR-QUEUE))
     (12 12
         (:REWRITE DISJOINT-IMPLIES-ONE-NOT-MEMBER-SYMMETRIC))
     (12 12
         (:REWRITE DISJOINT-IMPLIES-ONE-NOT-MEMBER))
     (12 12 (:REWRITE DEFAULT-<-2))
     (12 2 (:DEFINITION Q<MAX))
     (12 2 (:DEFINITION INV-P-KEYS))
     (10 2 (:DEFINITION LEGAL-STATUS))
     (6 6 (:TYPE-PRESCRIPTION NATP))
     (6 6 (:REWRITE LEX<-TRANSITIVE))
     (6 2 (:DEFINITION CHOOSING-BUCKET))
     (6 2 (:DEFINITION B=MAX))
     (2 2
        (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
     (2 2 (:DEFINITION WAIT-STATUS))
     (2 2 (:DEFINITION INTERESTED-STATUS))
     (2 2 (:DEFINITION IDLE-STATUS))
     (2 2 (:DEFINITION GO-STATUS)))
(INV-P-P-SUFF-PROC-C-S
     (15 15
         (:REWRITE LEXICOGRAPHIC-POS-IMPLIES-EVERYTHING-<-CAR-QUEUE))
     (15 15
         (:REWRITE DISJOINT-IMPLIES-ONE-NOT-MEMBER-SYMMETRIC))
     (15 15
         (:REWRITE DISJOINT-IMPLIES-ONE-NOT-MEMBER))
     (9 9 (:REWRITE DEFAULT-CAR))
     (7 7 (:REWRITE DEFAULT-CDR)))
(INDUCT-ON-KEYS-C-S
     (14 14 (:REWRITE DEFAULT-CAR))
     (7 7
        (:REWRITE LEXICOGRAPHIC-POS-IMPLIES-EVERYTHING-<-CAR-QUEUE))
     (7 7
        (:REWRITE DISJOINT-IMPLIES-ONE-NOT-MEMBER-SYMMETRIC))
     (7 7
        (:REWRITE DISJOINT-IMPLIES-ONE-NOT-MEMBER))
     (4 4 (:REWRITE DEFAULT-CDR)))
(KEYS-NOT-NIL-TO-NOT-QUEUE
     (74 74 (:REWRITE DEFAULT-CAR))
     (61 61
         (:REWRITE LEXICOGRAPHIC-POS-IMPLIES-EVERYTHING-<-CAR-QUEUE))
     (61 61
         (:REWRITE DISJOINT-IMPLIES-ONE-NOT-MEMBER-SYMMETRIC))
     (61 61
         (:REWRITE DISJOINT-IMPLIES-ONE-NOT-MEMBER))
     (54 54 (:REWRITE DEFAULT-CDR))
     (21 21 (:REWRITE MY-SUBSETP-IS-TRANSITIVE)))
(INV-C-S-SUFFICIENT
     (316 12 (:DEFINITION ORDEREDP))
     (216 8 (:REWRITE ORDERED-IMPLIES-UNIQUE))
     (172 44 (:REWRITE <<-TRICHOTOMY))
     (164 4 (:DEFINITION UNIQUEP))
     (116 20 (:REWRITE <<-ASYMMETRIC))
     (112 112 (:TYPE-PRESCRIPTION <<))
     (64 64 (:REWRITE DEFAULT-CDR))
     (64 8 (:DEFINITION MY-SUBSETP))
     (52 52 (:REWRITE DEFAULT-CAR))
     (44 44 (:REWRITE <<-TRANSITIVE))
     (24 4 (:DEFINITION MEMBERP))
     (24 4 (:DEFINITION INV-P-KEYS-C-S))
     (20 4 (:DEFINITION KEYS-NOT-NIL))
     (17 17
         (:REWRITE LEXICOGRAPHIC-POS-IMPLIES-EVERYTHING-<-CAR-QUEUE))
     (17 17
         (:REWRITE DISJOINT-IMPLIES-ONE-NOT-MEMBER-SYMMETRIC))
     (17 17
         (:REWRITE DISJOINT-IMPLIES-ONE-NOT-MEMBER))
     (16 16 (:REWRITE MY-SUBSETP-IS-TRANSITIVE))
     (10 10 (:TYPE-PRESCRIPTION INV-P-P-C-S))
     (9 3 (:REWRITE INV-P-P-SUFF-PROC-C-S)))
