(G-OF-NEW-AD)
(G-WHEN-NOT-IN-RKEYS)
(G-OF-NIL-LEMMA)
(S-IFF-WHEN-G
 (13 3 (:REWRITE S-SAME-G-STRONG))
 (10 5 (:REWRITE G-WHEN-NOT-IN-RKEYS-CHEAP))
 (6 3 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (3 3 (:TYPE-PRESCRIPTION BOOLEANP))
 (3 3 (:REWRITE CLR-DIFFERENTIAL))
 )
(NTH-OF-N-NEW-ADS2)
(INSERT-NEW-AD-INSERT-2ND-NEW-ADALT
 (28 3 (:REWRITE SET::INSERT-IDENTITY))
 (18 1 (:REWRITE SET::IN-INSERT))
 (16 16 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (8 4 (:REWRITE SET::UNION-EMPTYP-Y))
 (8 4 (:REWRITE SET::UNION-EMPTYP-X))
 (7 3 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (7 3 (:REWRITE INSERT-WHEN-EMPTY))
 (6 6 (:TYPE-PRESCRIPTION NTH-NEW-AD))
 (4 4 (:TYPE-PRESCRIPTION NEW-AD-NON-NEGATIVE))
 (4 4 (:TYPE-PRESCRIPTION INTEGERP-OF-NEW-AD))
 (3 3 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (3 1 (:REWRITE SET::NONEMPTY-MEANS-SET))
 (2 2 (:REWRITE SET::SUBSET-IN))
 (2 2 (:REWRITE NTH-NEW-AD-NOT-IN-ADS))
 (2 2 (:REWRITE SET::INSERT-NEVER-EMPTY))
 (2 1 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (1 1 (:REWRITE NTH-NEW-AD-WHEN-ZP))
 (1 1 (:REWRITE NEW-AD-NOT-MEMBERP-ADS))
 (1 1 (:REWRITE NEW-AD-KNOWN))
 (1 1 (:REWRITE SET::IN-SET))
 (1 1 (:REWRITE CLR-DIFFERENTIAL))
 )
(IN-OF-NEW-AD-AND-N-NEW-ADS2-BETTER)
(NEW-AD-OF-UNION-DOM-AND-N-NEW-ADSALT
 (22 8 (:REWRITE SET::UNION-EMPTYP-Y))
 (22 5 (:REWRITE SET::INSERT-IDENTITY))
 (14 2 (:REWRITE SET::SFIX-SET-IDENTITY))
 (12 12 (:REWRITE DEFAULT-+-2))
 (12 12 (:REWRITE DEFAULT-+-1))
 (12 5 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (12 5 (:REWRITE INSERT-WHEN-EMPTY))
 (10 10 (:REWRITE NEW-AD-KNOWN))
 (9 9 (:REWRITE NTH-NEW-AD-WHEN-ZP))
 (7 7 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (6 2 (:REWRITE SET::SFIX-WHEN-EMPTYP))
 (6 2 (:REWRITE SET::NONEMPTY-MEANS-SET))
 (4 4 (:TYPE-PRESCRIPTION SET::SETP-TYPE))
 (4 4 (:REWRITE SET::SUBSET-IN))
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (4 2 (:REWRITE SET::IN-TAIL))
 (4 2 (:REWRITE SET::EMPTYP-SFIX-CANCEL))
 (3 3 (:REWRITE NEW-AD-NOT-MEMBERP-ADS))
 (3 1 (:REWRITE NEW-ADS-SLICE-OUT-OF-ORDER-INDICES))
 (2 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE SET::IN-SET))
 (2 2 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (2 2 (:REWRITE CLR-DIFFERENTIAL))
 (2 1 (:REWRITE SET::IN-SFIX-CANCEL))
 (1 1 (:REWRITE N-NEW-ADS-AUX-WHEN-ZP))
 (1 1 (:REWRITE SET::INSERT-NEVER-EMPTY))
 )
(NEW-AD-OF-UNION-DOM-AND-N-NEW-ADSALT-BETTER)
(INSERT-OF-NEXT-AD-ONTO-UNION-OF-DOM-AND-N-NEW-ADSALT
 (23 23 (:TYPE-PRESCRIPTION SET::INSERT))
 (10 10 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (10 4 (:REWRITE SET::UNION-EMPTYP-Y))
 (8 4 (:REWRITE SET::UNION-EMPTYP-X))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE NTH-NEW-AD-WHEN-ZP))
 )
(INSERT-OF-NEXT-AD-ONTO-UNION-OF-DOM-AND-N-NEW-ADSALT-BETTER
 (23 23 (:TYPE-PRESCRIPTION SET::INSERT))
 )
(INSERT-OF-NEXT-AD-ONTO-UNION-OF-DOM-AND-N-NEW-ADSALT-BETTER-REV
 (24 24 (:TYPE-PRESCRIPTION SET::INSERT))
 (20 1 (:REWRITE SET::INSERT-IDENTITY))
 (18 18 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (18 1 (:REWRITE SET::UNION-IN))
 (16 1 (:REWRITE IN-OF-2SET))
 (15 1 (:REWRITE MEMBER-EQUAL-BECOMES-MEMBERP))
 (9 3 (:REWRITE SET::UNION-EMPTYP-Y))
 (8 2 (:REWRITE SET::UNION-EMPTYP))
 (7 3 (:REWRITE SET::UNION-EMPTYP-X))
 (6 1 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (6 1 (:REWRITE INSERT-WHEN-EMPTY))
 (3 3 (:TYPE-PRESCRIPTION MEMBERP))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 1 (:REWRITE MEMBERP-WHEN-SINGLETON-CHEAP))
 (2 1 (:REWRITE MEMBERP-WHEN-NOT-MEMBERP-OF-CDR-CHEAP))
 (2 1 (:REWRITE MEMBERP-WHEN-NOT-CONS-OF-CDR-CHEAP))
 (2 1 (:REWRITE MEMBERP-WHEN-MEMBERP-OF-CDR-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION N-NEW-ADS2))
 (1 1 (:TYPE-PRESCRIPTION LEN))
 (1 1 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (1 1 (:REWRITE NTH-NEW-AD-WHEN-ZP))
 (1 1 (:REWRITE NTH-NEW-AD-NOT-IN-ADS))
 (1 1 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-OF-TAKE))
 (1 1 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-2))
 (1 1 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-1))
 (1 1 (:REWRITE MEMBERP-WHEN-NOT-EQUAL-OF-CAR-CHEAP))
 (1 1 (:REWRITE MEMBERP-OF-CONSTANT-WHEN-NOT-MEMBER-OF-CONSTANT))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 )
(NEW-AD-NOT-EQUAL-NTH-NEW-AD2
 (1 1 (:REWRITE NTH-NEW-AD-WHEN-ZP))
 (1 1 (:REWRITE NEW-AD-NOT-EQUAL-NTH-NEW-AD-HELPER))
 (1 1 (:REWRITE NEW-AD-KNOWN))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE CLR-DIFFERENTIAL))
 )
(NEW-AD-NOT-EQUAL-NTH-NEW-AD2ALT
 (1 1 (:REWRITE NTH-NEW-AD-WHEN-ZP))
 (1 1 (:REWRITE NEW-AD-KNOWN))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 )
(NOT-MEMBERP-N-NEW-ADS2
 (10 2 (:REWRITE SET::IN-TAIL))
 (4 4 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (4 4 (:REWRITE SET::SUBSET-IN))
 (3 1 (:REWRITE SET::TAIL-WHEN-EMPTYP))
 (3 1 (:REWRITE SET::NEVER-IN-EMPTY))
 (2 2 (:TYPE-PRESCRIPTION N-NEW-ADS))
 (2 2 (:REWRITE SET::SUBSET-IN-2))
 (2 1 (:REWRITE MEMBERP-WHEN-SINGLETON-CHEAP))
 (2 1 (:REWRITE MEMBERP-WHEN-NOT-MEMBERP-OF-CDR-CHEAP))
 (2 1 (:REWRITE MEMBERP-WHEN-NOT-CONSP-CHEAP))
 (2 1 (:REWRITE MEMBERP-WHEN-NOT-CONS-OF-CDR-CHEAP))
 (2 1 (:REWRITE MEMBERP-WHEN-MEMBERP-OF-CDR-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION LEN))
 (1 1 (:REWRITE SET::SUBSET-IN-2-ALT))
 (1 1 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-OF-TAKE))
 (1 1 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-AND-NOT-INTERSECTION-EQUAL-CHEAP))
 (1 1 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-2))
 (1 1 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-1))
 (1 1 (:REWRITE MEMBERP-WHEN-NOT-EQUAL-OF-CAR-CHEAP))
 (1 1 (:REWRITE MEMBERP-OF-CONSTANT-WHEN-NOT-MEMBER-OF-CONSTANT))
 )
(NOT-MEMBERP-N-NEW-ADS2-BETTER)
(N-NEW-ADS2-AUX-OF-0)
(NEW-AD-AUX-OF-INSERT-OF-NEXT
 (16681 112 (:DEFINITION SET::DELETE))
 (5790 332 (:REWRITE SET::IN-TAIL-OR-HEAD))
 (4035 1320 (:REWRITE SET::IN-TAIL))
 (4034 206 (:REWRITE EQUAL-EQUAL-A-HEAD-HACK))
 (3619 221 (:REWRITE SET::DELETE-IN))
 (2766 2128 (:REWRITE SET::SUBSET-IN-2))
 (1916 35 (:REWRITE NEW-AD-AUX-OF-INSERT-IRREL2))
 (1750 66 (:REWRITE SET::WEAK-INSERT-INDUCTION-HELPER-3))
 (1440 16 (:REWRITE IN-OF-IF))
 (1319 869 (:REWRITE SET::TAIL-WHEN-EMPTYP))
 (1243 33 (:REWRITE NEW-AD-AUX-OF-INSERT-IRREL))
 (1140 229 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (1126 104 (:REWRITE SET::WEAK-INSERT-INDUCTION-HELPER-1))
 (1094 52 (:REWRITE SET::WEAK-INSERT-INDUCTION-HELPER-2))
 (1022 324 (:REWRITE SET::EMPTYP-SUBSET-2))
 (989 229 (:REWRITE SET::INSERT-IDENTITY))
 (798 732 (:REWRITE SET::TAIL-PRESERVES-EMPTYP))
 (793 262 (:REWRITE SET::DELETE-PRESERVES-EMPTYP))
 (606 556 (:REWRITE SET::SUBSET-TRANSITIVE))
 (574 475 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (487 487 (:REWRITE CLR-DIFFERENTIAL))
 (464 1 (:REWRITE NEW-AD-AUX-OF-DELETE-IRREL2))
 (445 445 (:REWRITE SUBSET-HACK))
 (425 40 (:REWRITE SET::SUBSET-INSERT-X))
 (416 320 (:REWRITE SET::EMPTYP-SUBSET))
 (374 334 (:REWRITE HEAD-WHEN-EMPTY))
 (372 332 (:REWRITE SET::HEAD-WHEN-EMPTYP))
 (320 320 (:TYPE-PRESCRIPTION SET::INSERT))
 (278 278 (:REWRITE SET::PICK-A-POINT-SUBSET-CONSTRAINT-HELPER))
 (262 236 (:REWRITE DEFAULT-+-2))
 (236 236 (:REWRITE DEFAULT-+-1))
 (176 104 (:REWRITE SET::HEAD-INSERT-EMPTYP))
 (138 13 (:REWRITE SET::IN-SFIX-CANCEL))
 (135 135 (:REWRITE NEW-AD-NOT-BOUND-HELPER2))
 (128 128 (:REWRITE SET::HEAD-UNIQUE))
 (113 113 (:REWRITE SET::INSERT-NEVER-EMPTY))
 (104 52 (:REWRITE SET::TAIL-INSERT-EMPTYP))
 (84 67 (:REWRITE DEFAULT-<-1))
 (75 31 (:REWRITE SET::SFIX-WHEN-EMPTYP))
 (68 67 (:REWRITE DEFAULT-<-2))
 (66 10 (:REWRITE SUBSET-OF-INSERT-IRREL))
 (50 50 (:TYPE-PRESCRIPTION BOOLEANP))
 (42 21 (:REWRITE SET::EMPTYP-SFIX-CANCEL))
 (29 29 (:REWRITE SET::IN-SET))
 (12 6 (:REWRITE SET::TAIL-SFIX-CANCEL))
 (10 10 (:REWRITE SET::SUBSET-TAIL))
 (6 2 (:REWRITE SET::SUBSET-SFIX-CANCEL-X))
 )
(N-NEW-ADS2-AUX-OF-INSERT-NEW-AD-GEN
 (196 6 (:REWRITE N-NEW-ADS2-AUX-OF-INSERT-IRREL2))
 (126 68 (:REWRITE DEFAULT-+-2))
 (68 68 (:REWRITE DEFAULT-+-1))
 (58 58 (:REWRITE NEW-AD-AUX-KNOWN))
 (36 15 (:REWRITE ZP-OPEN))
 (26 20 (:REWRITE DEFAULT-<-1))
 (23 23 (:TYPE-PRESCRIPTION MEMBERP))
 (21 21 (:TYPE-PRESCRIPTION SET::INSERT))
 (21 7 (:REWRITE FOLD-CONSTS-IN-+))
 (20 20 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (20 20 (:REWRITE DEFAULT-<-2))
 (15 5 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (15 5 (:REWRITE INSERT-WHEN-EMPTY))
 (15 5 (:REWRITE SET::INSERT-IDENTITY))
 (13 1 (:REWRITE NEW-AD-AUX-OF-INSERT-IRREL))
 (12 6 (:REWRITE MEMBERP-WHEN-SINGLETON-CHEAP))
 (12 6 (:REWRITE MEMBERP-WHEN-NOT-MEMBERP-OF-CDR-CHEAP))
 (12 6 (:REWRITE MEMBERP-WHEN-NOT-CONSP-CHEAP))
 (12 6 (:REWRITE MEMBERP-WHEN-NOT-CONS-OF-CDR-CHEAP))
 (12 6 (:REWRITE MEMBERP-WHEN-MEMBERP-OF-CDR-CHEAP))
 (12 4 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (12 1 (:REWRITE NEW-AD-AUX-OF-INSERT-IRREL2))
 (6 6 (:TYPE-PRESCRIPTION LEN))
 (6 6 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-OF-TAKE))
 (6 6 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-AND-NOT-INTERSECTION-EQUAL-CHEAP))
 (6 6 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-2))
 (6 6 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-1))
 (6 6 (:REWRITE MEMBERP-WHEN-NOT-EQUAL-OF-CAR-CHEAP))
 (6 6 (:REWRITE MEMBERP-OF-CONSTANT-WHEN-NOT-MEMBER-OF-CONSTANT))
 (5 5 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (5 5 (:REWRITE NEW-AD-NOT-BOUND-HELPER2))
 (4 4 (:TYPE-PRESCRIPTION BOOLEANP))
 (4 4 (:REWRITE CLR-DIFFERENTIAL))
 (4 2 (:REWRITE DEFAULT-CDR))
 (4 2 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE MEMBERP-OF-CONS-SAME))
 )
(N-NEW-ADS2-AUX-OF-INSERT-NEW-AD-GEN-HACK
 (18 2 (:DEFINITION N-NEW-ADS2-AUX))
 (12 6 (:REWRITE DEFAULT-+-2))
 (6 6 (:REWRITE DEFAULT-+-1))
 (5 5 (:REWRITE NEW-AD-AUX-KNOWN))
 (4 4 (:TYPE-PRESCRIPTION NEW-AD-AUX))
 (4 4 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (3 1 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (3 1 (:REWRITE INSERT-WHEN-EMPTY))
 (3 1 (:REWRITE SET::INSERT-IDENTITY))
 (2 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (1 1 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (1 1 (:REWRITE NEW-AD-NOT-BOUND-HELPER2))
 )
(NEW-AD-AUX-OF-UNION-IRREL
 (8365 71 (:DEFINITION SET::DELETE))
 (5521 8 (:REWRITE NEW-AD-AUX-OF-DELETE-IRREL2))
 (4798 1097 (:REWRITE SET::IN-TAIL))
 (4439 142 (:REWRITE SET::DELETE-NONMEMBER-CANCEL))
 (4340 4340 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (4022 137 (:REWRITE SET::DELETE-IN))
 (3399 71 (:REWRITE EQUAL-EQUAL-A-HEAD-HACK))
 (2776 1208 (:REWRITE SET::SUBSET-IN-2))
 (1795 569 (:REWRITE SET::NEVER-IN-EMPTY))
 (1727 676 (:REWRITE SET::TAIL-WHEN-EMPTYP))
 (1165 504 (:REWRITE SET::EMPTYP-SUBSET-2))
 (1079 504 (:REWRITE SET::EMPTYP-SUBSET))
 (1026 284 (:REWRITE SET::UNION-EMPTYP))
 (1012 142 (:REWRITE SET::IN-TAIL-OR-HEAD))
 (1008 1008 (:REWRITE SET::SUBSET-TRANSITIVE))
 (591 5 (:REWRITE IN-OF-IF))
 (586 289 (:REWRITE SET::TAIL-PRESERVES-EMPTYP))
 (564 564 (:REWRITE SUBSET-HACK))
 (504 504 (:REWRITE SET::PICK-A-POINT-SUBSET-CONSTRAINT-HELPER))
 (497 71 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (429 143 (:REWRITE SET::DELETE-PRESERVES-EMPTYP))
 (426 71 (:REWRITE SET::INSERT-IDENTITY))
 (417 142 (:REWRITE SET::HEAD-WHEN-EMPTYP))
 (417 142 (:REWRITE HEAD-WHEN-EMPTY))
 (355 71 (:REWRITE INSERT-WHEN-EMPTY))
 (216 207 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (207 207 (:REWRITE CLR-DIFFERENTIAL))
 (113 113 (:REWRITE DEFAULT-+-2))
 (113 113 (:REWRITE DEFAULT-+-1))
 (71 71 (:REWRITE SET::HEAD-UNIQUE))
 (36 11 (:REWRITE SET::UNION-EMPTYP-X))
 (33 11 (:REWRITE SET::UNION-EMPTYP-Y))
 (26 18 (:REWRITE DEFAULT-<-1))
 (18 18 (:REWRITE DEFAULT-<-2))
 )
(N-NEW-ADS2-AUX-OF-DELETE-IRREL
 (255 5 (:DEFINITION SET::DELETE))
 (135 10 (:REWRITE SET::DELETE-NONMEMBER-CANCEL))
 (61 4 (:REWRITE NEW-AD-AUX-OF-DELETE-IRREL2))
 (60 60 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (50 50 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (40 40 (:REWRITE SET::SUBSET-IN))
 (35 10 (:REWRITE SET::NEVER-IN-EMPTY))
 (35 5 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (35 5 (:REWRITE EQUAL-EQUAL-A-HEAD-HACK))
 (30 15 (:REWRITE SET::IN-TAIL))
 (30 10 (:REWRITE SET::DELETE-PRESERVES-EMPTYP))
 (30 5 (:REWRITE SET::INSERT-IDENTITY))
 (25 5 (:REWRITE INSERT-WHEN-EMPTY))
 (24 24 (:REWRITE NEW-AD-AUX-KNOWN))
 (23 15 (:REWRITE DEFAULT-+-2))
 (22 17 (:REWRITE DEFAULT-<-1))
 (20 20 (:REWRITE SET::SUBSET-IN-2))
 (20 5 (:REWRITE SET::DELETE-IN))
 (17 17 (:REWRITE DEFAULT-<-2))
 (16 16 (:TYPE-PRESCRIPTION NEW-AD-AUX))
 (15 15 (:REWRITE DEFAULT-+-1))
 (14 8 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (10 10 (:REWRITE SET::TAIL-WHEN-EMPTYP))
 (10 10 (:REWRITE SET::TAIL-PRESERVES-EMPTYP))
 (10 10 (:REWRITE SET::SUBSET-IN-2-ALT))
 (10 10 (:REWRITE SET::IN-TAIL-OR-HEAD))
 (10 10 (:REWRITE SET::HEAD-WHEN-EMPTYP))
 (10 10 (:REWRITE HEAD-WHEN-EMPTY))
 (10 7 (:REWRITE ZP-OPEN))
 (8 8 (:REWRITE CLR-DIFFERENTIAL))
 (5 5 (:REWRITE SET::HEAD-UNIQUE))
 (3 3 (:TYPE-PRESCRIPTION BOOLEANP))
 (3 1 (:REWRITE FOLD-CONSTS-IN-+))
 (1 1 (:TYPE-PRESCRIPTION NATP))
 )
(MEMBERP-OF-N-NEW-ADS2-AUX-IRREL
 (45 6 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-2))
 (38 1 (:DEFINITION SUBSETP-EQUAL))
 (16 16 (:TYPE-PRESCRIPTION NEW-AD-AUX))
 (16 16 (:TYPE-PRESCRIPTION N-NEW-ADS2-AUX))
 (15 1 (:REWRITE MEMBER-EQUAL-BECOMES-MEMBERP))
 (12 12 (:REWRITE DEFAULT-<-2))
 (12 12 (:REWRITE DEFAULT-<-1))
 (12 6 (:REWRITE MEMBERP-WHEN-SINGLETON-CHEAP))
 (12 6 (:REWRITE MEMBERP-WHEN-NOT-MEMBERP-OF-CDR-CHEAP))
 (12 6 (:REWRITE MEMBERP-WHEN-MEMBERP-OF-CDR-CHEAP))
 (10 5 (:REWRITE MEMBERP-WHEN-NOT-CONSP-CHEAP))
 (10 2 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (9 1 (:REWRITE DEFAULT-CDR))
 (8 8 (:TYPE-PRESCRIPTION LEN))
 (7 7 (:REWRITE NEW-AD-AUX-KNOWN))
 (6 6 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-OF-TAKE))
 (6 6 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-1))
 (6 6 (:REWRITE MEMBERP-WHEN-NOT-EQUAL-OF-CAR-CHEAP))
 (6 6 (:REWRITE MEMBERP-OF-CONSTANT-WHEN-NOT-MEMBER-OF-CONSTANT))
 (6 4 (:REWRITE DEFAULT-+-2))
 (5 5 (:TYPE-PRESCRIPTION SUBSETP-EQUAL))
 (5 5 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-AND-NOT-INTERSECTION-EQUAL-CHEAP))
 (4 4 (:REWRITE ZP-OPEN))
 (4 4 (:REWRITE DEFAULT-+-1))
 (4 2 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE LEN-OF-N-NEW-ADS2-AUX))
 (2 2 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (2 1 (:REWRITE CAR-OF-N-NEW-ADS2-AUX))
 )
(MEMBERP-OF-NEW-AD-AUX-AND-N-NEW-ADS2-AUX-IRREL
 (462 3 (:DEFINITION NEW-AD-AUX))
 (309 3 (:DEFINITION SET::DELETE))
 (156 6 (:REWRITE SET::IN-TAIL-OR-HEAD))
 (126 60 (:REWRITE SET::SUBSET-IN))
 (126 6 (:REWRITE NEW-AD-AUX-IS-CURRENT-TRY))
 (90 27 (:REWRITE SET::IN-TAIL))
 (90 6 (:REWRITE SET::DELETE-IN))
 (78 78 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (72 72 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (51 21 (:REWRITE SET::NEVER-IN-EMPTY))
 (42 42 (:REWRITE SET::SUBSET-IN-2))
 (37 37 (:TYPE-PRESCRIPTION NEW-AD-AUX))
 (36 6 (:REWRITE SET::DELETE-NONMEMBER-CANCEL))
 (36 3 (:REWRITE EQUAL-EQUAL-A-HEAD-HACK))
 (33 21 (:REWRITE SET::TAIL-WHEN-EMPTYP))
 (24 24 (:REWRITE SET::SUBSET-IN-2-ALT))
 (24 6 (:REWRITE SET::EMPTYP-SUBSET-2))
 (21 3 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (18 6 (:REWRITE SET::DELETE-PRESERVES-EMPTYP))
 (18 3 (:REWRITE SET::INSERT-IDENTITY))
 (15 15 (:REWRITE SET::TAIL-PRESERVES-EMPTYP))
 (15 3 (:REWRITE INSERT-WHEN-EMPTY))
 (12 12 (:TYPE-PRESCRIPTION SET::SUBSET-TYPE))
 (12 12 (:REWRITE SET::SUBSET-TRANSITIVE))
 (9 9 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (9 9 (:REWRITE CLR-DIFFERENTIAL))
 (6 6 (:REWRITE SUBSET-HACK))
 (6 6 (:REWRITE SET::PICK-A-POINT-SUBSET-CONSTRAINT-HELPER))
 (6 6 (:REWRITE NEW-AD-AUX-KNOWN))
 (6 6 (:REWRITE SET::HEAD-WHEN-EMPTYP))
 (6 6 (:REWRITE HEAD-WHEN-EMPTY))
 (6 6 (:REWRITE SET::EMPTYP-SUBSET))
 (5 4 (:REWRITE DEFAULT-<-1))
 (4 4 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE SET::HEAD-UNIQUE))
 (3 3 (:REWRITE DEFAULT-+-2))
 (3 3 (:REWRITE DEFAULT-+-1))
 )
(N-NEW-ADS2-AUX-OF-SFIX
 (99 15 (:REWRITE DEFAULT-+-2))
 (42 6 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (41 39 (:TYPE-PRESCRIPTION INTEGERP-OF-NEW-AD-AUX))
 (39 39 (:TYPE-PRESCRIPTION NEW-AD-AUX))
 (35 5 (:REWRITE SET::SFIX-SET-IDENTITY))
 (20 20 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (15 15 (:REWRITE DEFAULT-+-1))
 (15 5 (:REWRITE SET::SFIX-WHEN-EMPTYP))
 (15 5 (:REWRITE SET::NONEMPTY-MEANS-SET))
 (12 12 (:REWRITE NEW-AD-AUX-KNOWN))
 (10 10 (:TYPE-PRESCRIPTION SET::SETP-TYPE))
 (10 7 (:REWRITE ZP-OPEN))
 (9 3 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (5 5 (:REWRITE SET::IN-SET))
 (3 3 (:TYPE-PRESCRIPTION BOOLEANP))
 (3 3 (:REWRITE CLR-DIFFERENTIAL))
 (3 1 (:REWRITE FOLD-CONSTS-IN-+))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 )
(ADDRESS-HACK-BBBOZO-BETTER-HELPER
 (76 4 (:REWRITE SET::INSERT-IDENTITY))
 (50 4 (:REWRITE MEMBERP-OF-N-NEW-ADS2-AUX-IRREL))
 (36 2 (:REWRITE SET::UNION-IN))
 (31 31 (:REWRITE NEW-AD-AUX-KNOWN))
 (30 1 (:REWRITE N-NEW-ADS2-AUX-OF-INSERT-IRREL2))
 (26 20 (:REWRITE DEFAULT-+-2))
 (25 25 (:TYPE-PRESCRIPTION NEW-AD-AUX))
 (25 25 (:TYPE-PRESCRIPTION MEMBERP))
 (20 20 (:REWRITE DEFAULT-+-1))
 (18 4 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (18 4 (:REWRITE INSERT-WHEN-EMPTY))
 (17 14 (:REWRITE DEFAULT-<-1))
 (17 5 (:REWRITE NTHCDR-WHEN-NOT-POSP))
 (16 8 (:REWRITE MEMBERP-WHEN-SINGLETON-CHEAP))
 (16 8 (:REWRITE MEMBERP-WHEN-NOT-MEMBERP-OF-CDR-CHEAP))
 (16 8 (:REWRITE MEMBERP-WHEN-NOT-CONS-OF-CDR-CHEAP))
 (16 8 (:REWRITE MEMBERP-WHEN-MEMBERP-OF-CDR-CHEAP))
 (16 4 (:REWRITE SET::UNION-EMPTYP))
 (14 14 (:REWRITE DEFAULT-<-2))
 (11 5 (:REWRITE SET::UNION-EMPTYP-X))
 (11 1 (:REWRITE N-NEW-ADS2-AUX-OF-INSERT-IRREL))
 (10 5 (:REWRITE NTHCDR-WHEN-NOT-CONSP-CHEAP))
 (9 3 (:DEFINITION POSP))
 (8 8 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-OF-TAKE))
 (8 8 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-2))
 (8 8 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-1))
 (8 8 (:REWRITE MEMBERP-WHEN-NOT-EQUAL-OF-CAR-CHEAP))
 (8 8 (:REWRITE MEMBERP-OF-CONSTANT-WHEN-NOT-MEMBER-OF-CONSTANT))
 (8 4 (:REWRITE MEMBERP-WHEN-NOT-CONSP-CHEAP))
 (8 3 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (7 1 (:REWRITE SET::SFIX-SET-IDENTITY))
 (5 5 (:REWRITE NTHCDR-WHEN-EQUAL-OF-LEN))
 (4 4 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-AND-NOT-INTERSECTION-EQUAL-CHEAP))
 (4 4 (:REWRITE FOLD-CONSTS-IN-+))
 (3 3 (:TYPE-PRESCRIPTION POSP))
 (3 3 (:REWRITE CLR-DIFFERENTIAL))
 (3 1 (:REWRITE SET::SFIX-WHEN-EMPTYP))
 (3 1 (:REWRITE SET::NONEMPTY-MEANS-SET))
 (2 2 (:TYPE-PRESCRIPTION SET::SETP-TYPE))
 (2 2 (:TYPE-PRESCRIPTION BOOLEANP))
 (2 2 (:REWRITE NEW-AD-NOT-BOUND-HELPER2))
 (2 2 (:REWRITE SET::INSERT-NEVER-EMPTY))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE SET::IN-SET))
 )
(ADDRESS-HACK-BBBOZO-BETTER
 (13 3 (:REWRITE N-NEW-ADS2-AUX-WHEN-ZP))
 (7 2 (:REWRITE ZP-OPEN))
 (6 2 (:REWRITE NTHCDR-WHEN-NOT-POSP))
 (5 5 (:REWRITE DEFAULT-<-2))
 (5 5 (:REWRITE DEFAULT-<-1))
 (5 5 (:REWRITE DEFAULT-+-2))
 (5 5 (:REWRITE DEFAULT-+-1))
 (4 4 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (4 2 (:REWRITE NTHCDR-WHEN-NOT-CONSP-CHEAP))
 (3 3 (:TYPE-PRESCRIPTION ZP))
 (3 1 (:REWRITE SET::UNION-EMPTYP-Y))
 (3 1 (:REWRITE SET::UNION-EMPTYP-X))
 (3 1 (:DEFINITION POSP))
 (2 2 (:REWRITE NTHCDR-WHEN-EQUAL-OF-LEN))
 (1 1 (:TYPE-PRESCRIPTION POSP))
 )
(MEMBERP-OF-NTH-NEW-AD-AND-NEW-ADS-SLICE2
 (7 7 (:REWRITE DEFAULT-<-2))
 (7 7 (:REWRITE DEFAULT-<-1))
 (3 1 (:REWRITE NEW-ADS-SLICE-OUT-OF-ORDER-INDICES))
 (3 1 (:REWRITE MEMBERP-WHEN-NOT-CONSP-CHEAP))
 (3 1 (:REWRITE MEMBERP-WHEN-NOT-CONS-OF-CDR-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION NEW-ADS-TYPE))
 (2 2 (:TYPE-PRESCRIPTION NEW-ADS-SLICE))
 (2 1 (:REWRITE MEMBERP-WHEN-SINGLETON-CHEAP))
 (2 1 (:REWRITE MEMBERP-WHEN-NOT-MEMBERP-OF-CDR-CHEAP))
 (2 1 (:REWRITE MEMBERP-WHEN-MEMBERP-OF-CDR-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION LEN))
 (1 1 (:REWRITE NTH-NEW-AD-WHEN-ZP))
 (1 1 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-OF-TAKE))
 (1 1 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-AND-NOT-INTERSECTION-EQUAL-CHEAP))
 (1 1 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-2))
 (1 1 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-1))
 (1 1 (:REWRITE MEMBERP-WHEN-NOT-EQUAL-OF-CAR-CHEAP))
 (1 1 (:REWRITE MEMBERP-OF-CONSTANT-WHEN-NOT-MEMBER-OF-CONSTANT))
 )
(NOT-MEMBERP-OF-NEW-ADS-SLICE2
 (10 2 (:REWRITE SET::IN-TAIL))
 (5 1 (:REWRITE NTHCDR-WHEN-NOT-POSP))
 (4 4 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (4 4 (:REWRITE SET::SUBSET-IN))
 (3 1 (:REWRITE SET::TAIL-WHEN-EMPTYP))
 (3 1 (:REWRITE SET::NEVER-IN-EMPTY))
 (3 1 (:REWRITE MEMBERP-WHEN-NOT-CONS-OF-CDR-CHEAP))
 (3 1 (:DEFINITION POSP))
 (2 2 (:TYPE-PRESCRIPTION N-NEW-ADS2))
 (2 2 (:REWRITE SET::SUBSET-IN-2))
 (2 1 (:TYPE-PRESCRIPTION TRUE-LISTP-NTHCDR-TYPE-PRESCRIPTION))
 (2 1 (:REWRITE NTHCDR-WHEN-NOT-CONSP-CHEAP))
 (2 1 (:REWRITE MEMBERP-WHEN-SINGLETON-CHEAP))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:TYPE-PRESCRIPTION POSP))
 (1 1 (:REWRITE SET::SUBSET-IN-2-ALT))
 (1 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1 1 (:REWRITE NTHCDR-WHEN-EQUAL-OF-LEN))
 (1 1 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-OF-TAKE))
 (1 1 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-AND-NOT-INTERSECTION-EQUAL-CHEAP))
 (1 1 (:REWRITE MEMBERP-WHEN-NOT-EQUAL-OF-CAR-CHEAP))
 (1 1 (:REWRITE MEMBERP-OF-CONSTANT-WHEN-NOT-MEMBER-OF-CONSTANT))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(NOT-MEMBERP-OF-CDR-WHEN-INFIRSTN-AND-UNIQUE
 (6552 133 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-2))
 (6376 60 (:DEFINITION SUBSETP-EQUAL))
 (2652 15 (:REWRITE NOT-MEMBERP-OF-TAKE))
 (2135 134 (:REWRITE DEFAULT-CDR))
 (1771 66 (:REWRITE LEN-OF-NTHCDR))
 (869 33 (:REWRITE CAR-OF-NTHCDR))
 (770 33 (:DEFINITION NTH))
 (741 236 (:DEFINITION NFIX))
 (657 66 (:REWRITE CONSP-OF-NTHCDR))
 (609 477 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (609 58 (:REWRITE COMMUTATIVITY-2-OF-+))
 (589 567 (:REWRITE DEFAULT-+-2))
 (583 567 (:REWRITE DEFAULT-+-1))
 (558 530 (:REWRITE DEFAULT-<-2))
 (552 530 (:REWRITE DEFAULT-<-1))
 (396 198 (:TYPE-PRESCRIPTION TRUE-LISTP-NTHCDR-TYPE-PRESCRIPTION))
 (386 36 (:REWRITE TAKE-DOES-NOTHING))
 (375 26 (:REWRITE MEMBERP-OF-CDR-WHEN-NOT-MEMBERP))
 (366 18 (:REWRITE CDR-OF-TAKE))
 (316 65 (:REWRITE DEFAULT-CAR))
 (315 169 (:REWRITE FOLD-CONSTS-IN-+))
 (266 133 (:REWRITE MEMBERP-WHEN-NOT-MEMBERP-OF-CDR-CHEAP))
 (266 133 (:REWRITE MEMBERP-WHEN-MEMBERP-OF-CDR-CHEAP))
 (250 134 (:REWRITE MEMBERP-WHEN-SINGLETON-CHEAP))
 (247 247 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (238 238 (:TYPE-PRESCRIPTION SUBSETP-EQUAL))
 (238 147 (:REWRITE MEMBERP-WHEN-NOT-CONS-OF-CDR-CHEAP))
 (218 147 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-OF-TAKE))
 (198 198 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (160 34 (:REWRITE DISTRIBUTIVITY-OF-MINUS-OVER-+))
 (147 147 (:REWRITE MEMBERP-OF-CONSTANT-WHEN-NOT-MEMBER-OF-CONSTANT))
 (137 27 (:REWRITE CAR-OF-TAKE-STRONG))
 (134 134 (:REWRITE MEMBERP-WHEN-NOT-EQUAL-OF-CAR-CHEAP))
 (133 133 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-1))
 (132 12 (:REWRITE MEMBERP-OF-NTH-AND-TAKE))
 (131 50 (:REWRITE ZP-OPEN))
 (110 76 (:REWRITE MEMBERP-WHEN-NOT-CONSP-CHEAP))
 (104 24 (:REWRITE NTHCDR-WHEN-NOT-POSP))
 (100 100 (:REWRITE DEFAULT-UNARY-MINUS))
 (97 11 (:REWRITE MEMBERP-NTH-OF-SELF))
 (86 86 (:TYPE-PRESCRIPTION TAKE))
 (85 85 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (77 77 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-AND-NOT-INTERSECTION-EQUAL-CHEAP))
 (60 20 (:DEFINITION POSP))
 (53 27 (:REWRITE CONSP-OF-TAKE))
 (48 24 (:REWRITE UNICITY-OF-0))
 (44 41 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (41 41 (:REWRITE CLR-DIFFERENTIAL))
 (37 2 (:REWRITE MEMBERP-OF-CONS-IRREL-STRONG))
 (33 33 (:REWRITE NTH-WHEN-EQUAL-OF-TAKE-AND-CONSTANT))
 (33 33 (:REWRITE NTH-WHEN-EQUAL-OF-FIRSTN-AND-CONSTANT))
 (25 13 (:REWRITE MEMBERP-OF-CAR-SAME))
 (24 24 (:REWRITE NTHCDR-WHEN-NOT-CONSP-CHEAP))
 (24 24 (:REWRITE NTHCDR-WHEN-EQUAL-OF-LEN))
 (24 24 (:DEFINITION FIX))
 (20 20 (:TYPE-PRESCRIPTION POSP))
 (18 3 (:REWRITE EQUAL-OF-LEN-AND-0))
 (14 14 (:REWRITE CONSP-OF-CDR-WHEN-LEN-KNOWN))
 (14 1 (:LINEAR LEN-OF-CDR-LINEAR-STRONG))
 (13 1 (:REWRITE FIRSTN-WHEN-<=-OF-LEN))
 (10 1 (:LINEAR LEN-OF-CDR-LINEAR))
 (7 1 (:REWRITE NOT-EQUAL-NTH-WHEN-NOT-MEMBERP-CHEAP))
 (5 5 (:REWRITE SUBSETP-EQUAL-OF-TAKE-AND-TAKE))
 (3 3 (:TYPE-PRESCRIPTION BOOLEANP))
 (2 2 (:REWRITE LEN-OF-CDDR-WHEN-EQUAL-OF-LEN))
 (2 2 (:REWRITE CAR-CONS))
 (1 1 (:REWRITE CDR-CONS))
 )
(NOT-MEMBERP-NTH-NEW-AD-NEW-ADS-SLICE
 (365 14 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-2))
 (349 3 (:DEFINITION SUBSETP-EQUAL))
 (136 10 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (110 110 (:REWRITE DEFAULT-<-2))
 (110 110 (:REWRITE DEFAULT-<-1))
 (90 4 (:REWRITE DEFAULT-CDR))
 (84 3 (:REWRITE CAR-OF-NTHCDR))
 (76 5 (:REWRITE LEN-OF-NTHCDR))
 (73 34 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (72 3 (:REWRITE MEMBER-EQUAL-BECOMES-MEMBERP))
 (56 2 (:DEFINITION NTH))
 (45 5 (:REWRITE CONSP-OF-NTHCDR))
 (42 21 (:TYPE-PRESCRIPTION TRUE-LISTP-NTHCDR-TYPE-PRESCRIPTION))
 (32 16 (:REWRITE MEMBERP-WHEN-SINGLETON-CHEAP))
 (30 1 (:REWRITE MEMBERP-NTH-OF-SELF))
 (28 14 (:REWRITE MEMBERP-WHEN-NOT-MEMBERP-OF-CDR-CHEAP))
 (28 14 (:REWRITE MEMBERP-WHEN-MEMBERP-OF-CDR-CHEAP))
 (26 26 (:REWRITE DEFAULT-+-2))
 (26 26 (:REWRITE DEFAULT-+-1))
 (25 11 (:REWRITE MEMBERP-WHEN-NOT-CONSP-CHEAP))
 (25 5 (:REWRITE NOT-MEMBERP-OF-CDR-WHEN-INFIRSTN-AND-UNIQUE))
 (22 8 (:REWRITE NOT-MEMBERP-N-NEW-ADS2))
 (19 3 (:REWRITE NTH-OF-N-NEW-ADS))
 (16 16 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-OF-TAKE))
 (16 16 (:REWRITE MEMBERP-WHEN-NOT-EQUAL-OF-CAR-CHEAP))
 (16 16 (:REWRITE MEMBERP-OF-CONSTANT-WHEN-NOT-MEMBER-OF-CONSTANT))
 (15 5 (:DEFINITION POSP))
 (14 14 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-1))
 (14 7 (:REWRITE NTHCDR-WHEN-NOT-CONSP-CHEAP))
 (13 13 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-AND-NOT-INTERSECTION-EQUAL-CHEAP))
 (13 5 (:REWRITE FOLD-CONSTS-IN-+))
 (11 11 (:TYPE-PRESCRIPTION SUBSETP-EQUAL))
 (11 1 (:REWRITE FIRSTN-WHEN-<=-OF-LEN))
 (10 10 (:REWRITE NTH-NEW-AD-WHEN-ZP))
 (10 10 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (8 2 (:REWRITE ZP-OPEN))
 (7 7 (:TYPE-PRESCRIPTION NATP))
 (7 7 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (7 7 (:REWRITE NTHCDR-WHEN-EQUAL-OF-LEN))
 (7 7 (:REWRITE NTH-NEW-AD-NOT-IN-ADS))
 (7 1 (:REWRITE TAKE-DOES-NOTHING))
 (7 1 (:REWRITE MEMBERP-OF-NTH-AND-NTHCDR))
 (6 6 (:REWRITE DEFAULT-UNARY-MINUS))
 (6 1 (:REWRITE COMMUTATIVITY-2-OF-+))
 (5 5 (:TYPE-PRESCRIPTION POSP))
 (5 5 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (4 2 (:REWRITE CAR-OF-N-NEW-ADS))
 (4 1 (:REWRITE DISTRIBUTIVITY-OF-MINUS-OVER-+))
 (3 3 (:REWRITE NTH-WHEN-EQUAL-OF-TAKE-AND-CONSTANT))
 (3 3 (:REWRITE NTH-WHEN-EQUAL-OF-FIRSTN-AND-CONSTANT))
 (2 2 (:REWRITE NEW-AD-KNOWN))
 (2 1 (:REWRITE UNICITY-OF-0))
 (1 1 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (1 1 (:REWRITE CLR-DIFFERENTIAL))
 (1 1 (:DEFINITION FIX))
 )
(NEW-AD-NOT-MEMBERP-OF-NEW-ADS-SLICE2
 (4 3 (:REWRITE DEFAULT-<-1))
 (4 2 (:TYPE-PRESCRIPTION NEW-ADS-TYPE))
 (4 1 (:REWRITE NEW-ADS-SLICE-OUT-OF-ORDER-INDICES))
 (4 1 (:REWRITE MEMBERP-WHEN-NOT-CONSP-CHEAP))
 (4 1 (:REWRITE MEMBERP-WHEN-NOT-CONS-OF-CDR-CHEAP))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 1 (:REWRITE NOT-MEMBERP-OF-NEW-ADS-SLICE2))
 (2 2 (:TYPE-PRESCRIPTION NEW-ADS-SLICE))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (2 1 (:REWRITE MEMBERP-WHEN-SINGLETON-CHEAP))
 (2 1 (:REWRITE MEMBERP-WHEN-NOT-MEMBERP-OF-CDR-CHEAP))
 (2 1 (:REWRITE MEMBERP-WHEN-MEMBERP-OF-CDR-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION LEN))
 (1 1 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (1 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1 1 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-OF-TAKE))
 (1 1 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-AND-NOT-INTERSECTION-EQUAL-CHEAP))
 (1 1 (:REWRITE NEW-AD-NOT-MEMBERP-ADS))
 (1 1 (:REWRITE NEW-AD-KNOWN))
 (1 1 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-2))
 (1 1 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-1))
 (1 1 (:REWRITE MEMBERP-WHEN-NOT-EQUAL-OF-CAR-CHEAP))
 (1 1 (:REWRITE MEMBERP-OF-CONSTANT-WHEN-NOT-MEMBER-OF-CONSTANT))
 )
(UNION-COMMUTATIVE-2-2SET-OF-NEW-ADS-SLICE
 (32 11 (:REWRITE SET::UNION-EMPTYP-Y))
 (24 24 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (17 11 (:REWRITE SET::UNION-EMPTYP-X))
 (12 3 (:REWRITE SET::UNION-EMPTYP))
 (6 2 (:REWRITE NEW-ADS-SLICE-OUT-OF-ORDER-INDICES))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 )
(NOT-MEMBERP-OF-FIRSTN-WHEN-MEMBERP-OF-NTHCDR-AND-UNIQUE
 (20 1 (:DEFINITION NTHCDR))
 (10 2 (:REWRITE NTHCDR-WHEN-NOT-POSP))
 (6 2 (:DEFINITION POSP))
 (6 1 (:REWRITE DEFAULT-CDR))
 (5 4 (:REWRITE DEFAULT-<-1))
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 1 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (3 1 (:REWRITE COMMUTATIVITY-OF-+))
 (2 2 (:TYPE-PRESCRIPTION POSP))
 (2 2 (:REWRITE NTHCDR-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE NTHCDR-WHEN-EQUAL-OF-LEN))
 (2 2 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (1 1 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 )
(MEMBERP-OF-NEW-AD-AUX-AND-N-NEW-ADS2-AUX
 (58 6 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-2))
 (51 1 (:DEFINITION SUBSETP-EQUAL))
 (43 43 (:TYPE-PRESCRIPTION INTEGERP-OF-NEW-AD-AUX))
 (36 3 (:REWRITE MEMBERP-OF-NEW-AD-AUX-AND-N-NEW-ADS2-AUX-IRREL))
 (33 3 (:REWRITE MEMBERP-OF-N-NEW-ADS2-AUX-IRREL))
 (21 21 (:REWRITE NEW-AD-AUX-KNOWN))
 (20 14 (:REWRITE DEFAULT-<-1))
 (19 12 (:REWRITE DEFAULT-+-2))
 (18 6 (:LINEAR NEW-AD-AUX-BOUND))
 (16 1 (:REWRITE MEMBER-EQUAL-BECOMES-MEMBERP))
 (14 14 (:TYPE-PRESCRIPTION N-NEW-ADS2-AUX))
 (14 14 (:REWRITE DEFAULT-<-2))
 (14 2 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (12 12 (:REWRITE DEFAULT-+-1))
 (12 6 (:REWRITE MEMBERP-WHEN-SINGLETON-CHEAP))
 (12 6 (:REWRITE MEMBERP-WHEN-NOT-MEMBERP-OF-CDR-CHEAP))
 (12 6 (:REWRITE MEMBERP-WHEN-MEMBERP-OF-CDR-CHEAP))
 (11 6 (:REWRITE MEMBERP-WHEN-NOT-CONS-OF-CDR-CHEAP))
 (11 1 (:REWRITE DEFAULT-CDR))
 (9 5 (:REWRITE MEMBERP-WHEN-NOT-CONSP-CHEAP))
 (8 8 (:TYPE-PRESCRIPTION LEN))
 (8 2 (:REWRITE ZP-OPEN))
 (8 1 (:REWRITE CONSP-OF-N-NEW-ADS2-AUX))
 (6 6 (:TYPE-PRESCRIPTION SUBSETP-EQUAL))
 (6 6 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-OF-TAKE))
 (6 6 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-1))
 (6 6 (:REWRITE MEMBERP-WHEN-NOT-EQUAL-OF-CAR-CHEAP))
 (6 6 (:REWRITE MEMBERP-OF-CONSTANT-WHEN-NOT-MEMBER-OF-CONSTANT))
 (5 5 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-AND-NOT-INTERSECTION-EQUAL-CHEAP))
 (4 4 (:REWRITE N-NEW-ADS2-AUX-WHEN-ZP))
 (4 2 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (3 1 (:REWRITE FOLD-CONSTS-IN-+))
 (2 2 (:REWRITE LEN-OF-N-NEW-ADS2-AUX))
 (2 2 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (2 1 (:REWRITE CAR-OF-N-NEW-ADS2-AUX))
 (1 1 (:REWRITE CONSP-WHEN-LEN-GREATER))
 )
(UNIQUE-OF-N-NEW-ADS2-AUX
 (150 3 (:REWRITE MEMBERP-OF-CDR-WHEN-NOT-MEMBERP))
 (45 3 (:REWRITE MEMBERP-OF-N-NEW-ADS2-AUX-IRREL))
 (38 6 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (36 8 (:REWRITE DEFAULT-CDR))
 (26 18 (:REWRITE DEFAULT-<-1))
 (21 21 (:TYPE-PRESCRIPTION MEMBERP))
 (20 18 (:REWRITE DEFAULT-<-2))
 (18 18 (:REWRITE NEW-AD-AUX-KNOWN))
 (14 3 (:REWRITE CONSP-OF-N-NEW-ADS2-AUX))
 (12 12 (:TYPE-PRESCRIPTION LEN))
 (12 6 (:REWRITE MEMBERP-WHEN-SINGLETON-CHEAP))
 (12 6 (:REWRITE MEMBERP-WHEN-NOT-MEMBERP-OF-CDR-CHEAP))
 (12 6 (:REWRITE MEMBERP-WHEN-NOT-CONSP-CHEAP))
 (12 6 (:REWRITE MEMBERP-WHEN-NOT-CONS-OF-CDR-CHEAP))
 (12 6 (:REWRITE MEMBERP-WHEN-MEMBERP-OF-CDR-CHEAP))
 (12 6 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (9 6 (:REWRITE ZP-OPEN))
 (7 7 (:TYPE-PRESCRIPTION NEW-AD-AUX))
 (6 6 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-OF-TAKE))
 (6 6 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-AND-NOT-INTERSECTION-EQUAL-CHEAP))
 (6 6 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-2))
 (6 6 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-1))
 (6 6 (:REWRITE MEMBERP-WHEN-NOT-EQUAL-OF-CAR-CHEAP))
 (6 6 (:REWRITE MEMBERP-OF-CONSTANT-WHEN-NOT-MEMBER-OF-CONSTANT))
 (6 6 (:REWRITE LEN-OF-N-NEW-ADS2-AUX))
 (6 6 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (6 4 (:REWRITE DEFAULT-+-2))
 (6 3 (:REWRITE CAR-OF-N-NEW-ADS2-AUX))
 (4 4 (:REWRITE DEFAULT-+-1))
 (3 3 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (2 1 (:REWRITE DEFAULT-CAR))
 )
(MEMBERP-WHEN-MEMBERP-OF-FIRSTN
 (14 1 (:REWRITE FIRSTN-WHEN-<=-OF-LEN))
 (8 6 (:REWRITE DEFAULT-<-1))
 (8 4 (:REWRITE MEMBERP-WHEN-NOT-CONS-OF-CDR-CHEAP))
 (7 6 (:REWRITE DEFAULT-<-2))
 (6 3 (:REWRITE MEMBERP-WHEN-SINGLETON-CHEAP))
 (5 5 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (5 1 (:REWRITE MEMBERP-WHEN-NOT-CONSP-CHEAP))
 (4 4 (:REWRITE MEMBERP-OF-CONSTANT-WHEN-NOT-MEMBER-OF-CONSTANT))
 (4 4 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (3 3 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-AND-NOT-INTERSECTION-EQUAL-CHEAP))
 (3 3 (:REWRITE MEMBERP-WHEN-NOT-EQUAL-OF-CAR-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION TAKE))
 (2 1 (:REWRITE MEMBERP-WHEN-NOT-MEMBERP-OF-CDR-CHEAP))
 (2 1 (:REWRITE MEMBERP-WHEN-MEMBERP-OF-CDR-CHEAP))
 (1 1 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-1))
 (1 1 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (1 1 (:REWRITE CLR-DIFFERENTIAL))
 )
(MEMBERP-OF-NTH-NEW-AD-AND-N-NEW-ADS-BETTER
 (588 21 (:DEFINITION NTH))
 (210 42 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (189 21 (:REWRITE DEFAULT-CDR))
 (148 74 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (117 100 (:REWRITE DEFAULT-<-1))
 (100 100 (:REWRITE DEFAULT-<-2))
 (96 33 (:REWRITE ZP-OPEN))
 (87 51 (:REWRITE N-NEW-ADS2-AUX-WHEN-ZP))
 (81 6 (:REWRITE NOT-MEMBERP-OF-NTHCDR))
 (68 17 (:REWRITE MEMBERP-OF-N-NEW-ADS2-AUX-IRREL))
 (66 66 (:REWRITE DEFAULT-+-2))
 (66 66 (:REWRITE DEFAULT-+-1))
 (63 21 (:REWRITE FOLD-CONSTS-IN-+))
 (54 22 (:REWRITE MEMBERP-WHEN-NOT-CONS-OF-CDR-CHEAP))
 (45 5 (:REWRITE MEMBERP-NTH-OF-SELF))
 (44 22 (:REWRITE MEMBERP-WHEN-SINGLETON-CHEAP))
 (44 4 (:REWRITE FIRSTN-WHEN-<=-OF-LEN))
 (42 42 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (42 21 (:REWRITE CAR-OF-N-NEW-ADS2-AUX))
 (41 17 (:REWRITE MEMBERP-WHEN-NOT-CONSP-CHEAP))
 (34 17 (:REWRITE MEMBERP-WHEN-NOT-MEMBERP-OF-CDR-CHEAP))
 (34 17 (:REWRITE MEMBERP-WHEN-MEMBERP-OF-CDR-CHEAP))
 (27 27 (:REWRITE MEMBERP-WHEN-MEMBERP-OF-FIRSTN))
 (24 24 (:TYPE-PRESCRIPTION ZP))
 (22 22 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-OF-TAKE))
 (22 22 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-AND-NOT-INTERSECTION-EQUAL-CHEAP))
 (22 22 (:REWRITE MEMBERP-WHEN-NOT-EQUAL-OF-CAR-CHEAP))
 (22 22 (:REWRITE MEMBERP-OF-CONSTANT-WHEN-NOT-MEMBER-OF-CONSTANT))
 (21 21 (:REWRITE NTH-WHEN-EQUAL-OF-TAKE-AND-CONSTANT))
 (21 21 (:REWRITE NTH-WHEN-EQUAL-OF-FIRSTN-AND-CONSTANT))
 (21 21 (:REWRITE NEW-AD-AUX-KNOWN))
 (21 5 (:REWRITE NTHCDR-WHEN-NOT-POSP))
 (18 9 (:TYPE-PRESCRIPTION TRUE-LISTP-NTHCDR-TYPE-PRESCRIPTION))
 (17 17 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (17 17 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-1))
 (10 5 (:REWRITE NTHCDR-WHEN-NOT-CONSP-CHEAP))
 (8 8 (:REWRITE NTH-NEW-AD2-WHEN-ZP))
 (8 4 (:LINEAR LEN-POSITIVE-WHEN-CONSP-LINEAR-CHEAP))
 (6 6 (:REWRITE CLR-DIFFERENTIAL))
 (5 5 (:REWRITE NTHCDR-WHEN-EQUAL-OF-LEN))
 (4 4 (:TYPE-PRESCRIPTION POSP))
 )
(NEW-AD-UNION-2SET-N-NEW-ADS-BETTER)
(NTH-NEW-AD-OF-UNION-DOM-N-NEW-ADS-BETTER)
(TAKE-OF-N-NEW-ADS2
 (9 3 (:REWRITE N-NEW-ADS2-AUX-WHEN-ZP))
 (7 1 (:REWRITE TAKE-DOES-NOTHING))
 (4 4 (:TYPE-PRESCRIPTION ZP))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE ZP-OPEN))
 (2 1 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION LEN))
 (1 1 (:REWRITE LEN-OF-N-NEW-ADS2-AUX))
 (1 1 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (1 1 (:REWRITE CLR-DIFFERENTIAL))
 )
(UNION-OF-NEW-ADS-SLICE-AND-2SET-OF-N-NEW-ADS-BETTER
 (119 14 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (52 52 (:REWRITE DEFAULT-<-2))
 (52 52 (:REWRITE DEFAULT-<-1))
 (44 4 (:REWRITE DEFAULT-CAR))
 (43 11 (:REWRITE NTHCDR-WHEN-NOT-POSP))
 (41 20 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (40 40 (:REWRITE DEFAULT-+-2))
 (40 40 (:REWRITE DEFAULT-+-1))
 (32 4 (:REWRITE CONSP-OF-N-NEW-ADS2))
 (30 8 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (29 1 (:REWRITE LEN-OF-NTHCDR))
 (22 22 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (22 11 (:REWRITE NTHCDR-WHEN-NOT-CONSP-CHEAP))
 (18 6 (:REWRITE SET::UNION-EMPTYP-Y))
 (16 6 (:REWRITE SET::UNION-EMPTYP-X))
 (16 4 (:REWRITE ZP-OPEN))
 (14 14 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (11 11 (:REWRITE NTHCDR-WHEN-EQUAL-OF-LEN))
 (8 8 (:TYPE-PRESCRIPTION POSP))
 (8 8 (:REWRITE CLR-DIFFERENTIAL))
 (7 7 (:TYPE-PRESCRIPTION SET::INSERT))
 (7 7 (:TYPE-PRESCRIPTION BOOLEANP))
 (7 1 (:REWRITE TAKE-DOES-NOTHING))
 (6 6 (:REWRITE CONSP-WHEN-LEN-GREATER))
 (4 4 (:REWRITE DEFAULT-UNARY-MINUS))
 (2 2 (:REWRITE NTH-NEW-AD-WHEN-ZP))
 )
(INSERT-OF-NEW-AD-OF-INSERT-OF-NTH-NEW-AD
 (84 6 (:REWRITE SET::INSERT-IDENTITY))
 (61 2 (:REWRITE SET::IN-INSERT))
 (44 44 (:TYPE-PRESCRIPTION SET::INSERT))
 (21 6 (:REWRITE SET::IN-TAIL))
 (17 17 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (16 16 (:REWRITE SET::SUBSET-IN))
 (12 6 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (12 6 (:REWRITE INSERT-WHEN-EMPTY))
 (11 11 (:TYPE-PRESCRIPTION NTH-NEW-AD))
 (10 10 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (9 9 (:TYPE-PRESCRIPTION NEW-AD-NON-NEGATIVE))
 (9 9 (:TYPE-PRESCRIPTION INTEGERP-OF-NEW-AD))
 (5 2 (:REWRITE NTH-NEW-AD-WHEN-ZP))
 (5 2 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (4 4 (:REWRITE SET::INSERT-NEVER-EMPTY))
 (4 2 (:REWRITE SET::TAIL-WHEN-EMPTYP))
 (2 2 (:TYPE-PRESCRIPTION ZP))
 (2 2 (:REWRITE NEW-AD-KNOWN))
 (2 2 (:REWRITE CLR-DIFFERENTIAL))
 (1 1 (:REWRITE ZP-OPEN))
 )
(INSERT-OF-NTH-NEW-AD-OF-INSERT-OF-NTH-NEW-AD
 (85 6 (:REWRITE SET::INSERT-IDENTITY))
 (76 76 (:TYPE-PRESCRIPTION SET::INSERT))
 (62 2 (:REWRITE SET::IN-INSERT))
 (21 6 (:REWRITE SET::IN-TAIL))
 (20 20 (:TYPE-PRESCRIPTION NTH-NEW-AD))
 (17 17 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (16 16 (:REWRITE SET::SUBSET-IN))
 (15 3 (:REWRITE INSERT-NTH-NEW-AD-INSERT-NTH-NEW-AD-ADJACENT))
 (12 6 (:REWRITE SET::INSERT-WHEN-EMPTYP))
 (12 6 (:REWRITE INSERT-WHEN-EMPTY))
 (10 10 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (10 4 (:REWRITE NTH-NEW-AD-WHEN-ZP))
 (10 2 (:REWRITE EQUAL-NTH-NEW-AD-NTH-NEW-AD))
 (8 4 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (6 2 (:DEFINITION POSP))
 (4 4 (:TYPE-PRESCRIPTION ZP))
 (4 4 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (4 4 (:REWRITE SET::INSERT-NEVER-EMPTY))
 (4 4 (:REWRITE CLR-DIFFERENTIAL))
 (4 3 (:REWRITE DEFAULT-<-2))
 (4 3 (:REWRITE DEFAULT-<-1))
 (4 2 (:REWRITE SET::TAIL-WHEN-EMPTYP))
 (4 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:TYPE-PRESCRIPTION POSP))
 (2 2 (:TYPE-PRESCRIPTION BOOLEANP))
 (2 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE DEFAULT-+-1))
 )
(MEMBERP-OF-NTH-NEW-AD-AND-N-NEW-ADS-AUX
 (196 9 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-2))
 (186 2 (:DEFINITION SUBSETP-EQUAL))
 (108 2 (:REWRITE MEMBER-EQUAL-BECOMES-MEMBERP))
 (56 8 (:REWRITE CONSP-FROM-LEN-CHEAP))
 (49 49 (:TYPE-PRESCRIPTION N-NEW-ADS-AUX))
 (41 2 (:REWRITE MEMBERP-OF-CONS-IRREL-STRONG))
 (29 29 (:REWRITE DEFAULT-<-2))
 (29 29 (:REWRITE DEFAULT-<-1))
 (22 2 (:REWRITE DEFAULT-CDR))
 (22 2 (:REWRITE DEFAULT-CAR))
 (20 6 (:REWRITE N-NEW-ADS-AUX-WHEN-ZP))
 (20 2 (:REWRITE MEMBERP-OF-CAR-SAME))
 (18 9 (:REWRITE MEMBERP-WHEN-SINGLETON-CHEAP))
 (18 9 (:REWRITE MEMBERP-WHEN-NOT-MEMBERP-OF-CDR-CHEAP))
 (18 9 (:REWRITE MEMBERP-WHEN-NOT-CONS-OF-CDR-CHEAP))
 (18 9 (:REWRITE MEMBERP-WHEN-MEMBERP-OF-CDR-CHEAP))
 (17 17 (:TYPE-PRESCRIPTION LEN))
 (16 8 (:REWRITE LEN-WHEN-NOT-CONSP-CHEAP))
 (12 6 (:REWRITE MEMBERP-WHEN-NOT-CONSP-CHEAP))
 (12 2 (:REWRITE ZP-OPEN))
 (10 10 (:TYPE-PRESCRIPTION SUBSETP-EQUAL))
 (9 9 (:REWRITE NTH-NEW-AD-WHEN-ZP))
 (9 9 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-OF-TAKE))
 (9 9 (:REWRITE MEMBERP-WHEN-SUBSETP-EQUAL-1))
 (9 9 (:REWRITE MEMBERP-WHEN-NOT-EQUAL-OF-CAR-CHEAP))
 (9 9 (:REWRITE MEMBERP-WHEN-MEMBERP-OF-FIRSTN))
 (9 9 (:REWRITE MEMBERP-OF-CONSTANT-WHEN-NOT-MEMBER-OF-CONSTANT))
 (8 8 (:REWRITE LEN-OF-N-NEW-ADS-AUX))
 (8 8 (:REWRITE CONSP-WHEN-LEN-EQUAL-CONSTANT))
 (8 4 (:REWRITE NOT-MEMBERP-NTH-NEW-AD-N-NEW-ADS))
 (8 4 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (7 1 (:REWRITE NOT-EQUAL-NTH-NEW-AD-WHEN-BOUND-ALT))
 (7 1 (:REWRITE NOT-EQUAL-NTH-NEW-AD-WHEN-BOUND))
 (6 6 (:TYPE-PRESCRIPTION SET::IN-TYPE))
 (6 6 (:REWRITE NOT-MEMBERP-WHEN-MEMBERP-AND-NOT-INTERSECTION-EQUAL-CHEAP))
 (6 6 (:REWRITE CLR-DIFFERENTIAL))
 (6 2 (:REWRITE CONSP-OF-N-NEW-ADS-AUX))
 (4 4 (:REWRITE SET::SUBSET-IN))
 (4 2 (:REWRITE SET::IN-TAIL))
 (3 3 (:REWRITE DEFAULT-+-2))
 (3 3 (:REWRITE DEFAULT-+-1))
 (2 2 (:TYPE-PRESCRIPTION ZP))
 (2 2 (:TYPE-PRESCRIPTION BOOLEANP))
 (2 2 (:REWRITE CONSP-WHEN-LEN-GREATER))
 )
(MEMBERP-OF-NTH-NEW-AD-AND-N-NEW-ADS
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE NTH-NEW-AD-WHEN-ZP))
 (1 1 (:REWRITE N-NEW-ADS-AUX-WHEN-ZP))
 )
(INSERT-OF-NTH-NEW-AD-WHEN-ALREADY-THERE-LEMMA
 (27 27 (:TYPE-PRESCRIPTION SET::INSERT))
 (12 12 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (8 4 (:REWRITE SET::UNION-EMPTYP-Y))
 (8 4 (:REWRITE SET::UNION-EMPTYP-X))
 (6 1 (:REWRITE INSERT-WHEN-EMPTY))
 (5 1 (:REWRITE INSERT-OF-NEXT-AD-ONTO-UNION-OF-DOM-AND-N-NEW-ADS))
 (4 1 (:REWRITE SET::UNION-EMPTYP))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE NTH-NEW-AD-WHEN-ZP))
 (1 1 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE CLR-DIFFERENTIAL))
 )
(INSERT-OF-NTH-NEW-AD-WHEN-ALREADY-THERE-LEMMA-ALT
 (27 27 (:TYPE-PRESCRIPTION SET::INSERT))
 (8 8 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (6 1 (:REWRITE INSERT-WHEN-EMPTY))
 (5 1 (:REWRITE INSERT-OF-NEXT-AD-ONTO-UNION-OF-DOM-AND-N-NEW-ADS))
 (4 2 (:REWRITE SET::UNION-EMPTYP-Y))
 (4 2 (:REWRITE SET::UNION-EMPTYP-X))
 (4 1 (:REWRITE SET::UNION-EMPTYP))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE NTH-NEW-AD-WHEN-ZP))
 (1 1 (:REWRITE EQUAL-OF-BOOLEANS-CHEAP))
 (1 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE CLR-DIFFERENTIAL))
 )
(INSERT-OF-NEW-AD-WHEN-ALREADY-THERE-LEMMA
 (21 21 (:TYPE-PRESCRIPTION SET::INSERT))
 (12 12 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (8 4 (:REWRITE SET::UNION-EMPTYP-Y))
 (8 4 (:REWRITE SET::UNION-EMPTYP-X))
 (6 1 (:REWRITE INSERT-WHEN-EMPTY))
 (4 1 (:REWRITE SET::UNION-EMPTYP))
 (1 1 (:REWRITE NEW-AD-KNOWN))
 (1 1 (:REWRITE MEMBERP-WHEN-MEMBERP-OF-FIRSTN))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 )
(INSERT-OF-NEW-AD-WHEN-ALREADY-THERE-LEMMA-ALT
 (21 21 (:TYPE-PRESCRIPTION SET::INSERT))
 (8 8 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (6 1 (:REWRITE INSERT-WHEN-EMPTY))
 (4 2 (:REWRITE SET::UNION-EMPTYP-Y))
 (4 2 (:REWRITE SET::UNION-EMPTYP-X))
 (4 1 (:REWRITE SET::UNION-EMPTYP))
 (1 1 (:REWRITE NEW-AD-KNOWN))
 (1 1 (:REWRITE MEMBERP-WHEN-MEMBERP-OF-FIRSTN))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 )
