(COARSE-INDUCTION-SCHEME
 (14792 7396 (:TYPE-PRESCRIPTION NTH-CHARACTER-LISTP))
 (12125 12125 (:TYPE-PRESCRIPTION FLSZ1))
 (7944 3854 (:REWRITE DEFAULT-+-2))
 (7396 7396 (:TYPE-PRESCRIPTION CHARACTER-LISTP))
 (6777 6417 (:REWRITE DEFAULT-CDR))
 (6506 6458 (:REWRITE DEFAULT-CAR))
 (5117 3854 (:REWRITE DEFAULT-+-1))
 (4610 1617 (:REWRITE DEFAULT-<-1))
 (4220 1617 (:REWRITE DEFAULT-<-2))
 (3752 442 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (3007 136 (:DEFINITION SYMBOL-TO-FIXNAT-ALISTP))
 (2251 629 (:REWRITE INTEGERP-IMPLIES-REAL/RATIONALP))
 (2072 518 (:DEFINITION INTEGER-ABS))
 (2072 259 (:DEFINITION LENGTH))
 (2048 136 (:DEFINITION FIXNAT-GUARD))
 (1640 272 (:DEFINITION UNSIGNED-BYTE-P))
 (1594 797 (:DEFINITION NTH))
 (1368 272 (:DEFINITION INTEGER-RANGE-P))
 (1092 136 (:REWRITE SMALL-NAT-IMPLIES-FIXNAT))
 (876 218 (:TYPE-PRESCRIPTION TRUE-LISTP-NTHCDR-TYPE-PRESCRIPTION))
 (832 398 (:REWRITE DEFAULT-*-2))
 (518 518 (:REWRITE DEFAULT-UNARY-MINUS))
 (416 64 (:REWRITE ZP-OPEN))
 (398 398 (:REWRITE DEFAULT-*-1))
 (259 259 (:REWRITE DEFAULT-REALPART))
 (259 259 (:REWRITE DEFAULT-NUMERATOR))
 (259 259 (:REWRITE DEFAULT-IMAGPART))
 (259 259 (:REWRITE DEFAULT-DENOMINATOR))
 (259 259 (:REWRITE DEFAULT-COERCE-2))
 (259 259 (:REWRITE DEFAULT-COERCE-1))
 (136 136 (:TYPE-PRESCRIPTION UNSIGNED-BYTE-P))
 (72 72 (:REWRITE NTHCDR-NIL))
 (48 48 (:TYPE-PRESCRIPTION INTEGERP-MAX-WIDTH))
 )
(FLAG::FLAG-EQUIV-LEMMA)
(COARSE-INDUCTION-SCHEME-EQUIVALENCES)
(FINE-INDUCTION-SCHEME
 (20516 10258 (:TYPE-PRESCRIPTION NTH-CHARACTER-LISTP))
 (15716 15716 (:TYPE-PRESCRIPTION FLSZ1))
 (14220 14220 (:REWRITE DEFAULT-CAR))
 (13959 13863 (:REWRITE DEFAULT-CDR))
 (12933 6433 (:REWRITE DEFAULT-+-2))
 (10258 10258 (:TYPE-PRESCRIPTION CHARACTER-LISTP))
 (8258 6433 (:REWRITE DEFAULT-+-1))
 (5746 1510 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (5580 2143 (:REWRITE DEFAULT-<-2))
 (4956 2143 (:REWRITE DEFAULT-<-1))
 (3266 1633 (:DEFINITION NTH))
 (2983 1348 (:REWRITE INTEGERP-IMPLIES-REAL/RATIONALP))
 (2472 111 (:DEFINITION SYMBOL-TO-FIXNAT-ALISTP))
 (1681 111 (:DEFINITION FIXNAT-GUARD))
 (1520 380 (:DEFINITION INTEGER-ABS))
 (1520 190 (:DEFINITION LENGTH))
 (1348 222 (:DEFINITION UNSIGNED-BYTE-P))
 (1152 547 (:REWRITE DEFAULT-*-2))
 (1148 636 (:REWRITE DEFAULT-UNARY-MINUS))
 (1126 222 (:DEFINITION INTEGER-RANGE-P))
 (896 111 (:REWRITE SMALL-NAT-IMPLIES-FIXNAT))
 (547 547 (:REWRITE DEFAULT-*-1))
 (208 104 (:TYPE-PRESCRIPTION TRUE-LISTP-NTHCDR-TYPE-PRESCRIPTION))
 (190 190 (:REWRITE DEFAULT-REALPART))
 (190 190 (:REWRITE DEFAULT-NUMERATOR))
 (190 190 (:REWRITE DEFAULT-IMAGPART))
 (190 190 (:REWRITE DEFAULT-DENOMINATOR))
 (190 190 (:REWRITE DEFAULT-COERCE-2))
 (190 190 (:REWRITE DEFAULT-COERCE-1))
 (111 111 (:TYPE-PRESCRIPTION UNSIGNED-BYTE-P))
 (96 64 (:REWRITE RATIONALP-+))
 (48 48 (:TYPE-PRESCRIPTION INTEGERP-MAX-WIDTH))
 (35 35 (:REWRITE NTHCDR-NIL))
 )
(FLAG::FLAG-EQUIV-LEMMA)
(FINE-INDUCTION-SCHEME-EQUIVALENCES)
(ABOUT-IMACH
 (4 4 (:TYPE-PRESCRIPTION MERGE-SORT-LEXORDER))
 )
(FIND-ALL-CALLS-OF-ANY)
(ALL-FNNAMES-INTERSECT-FNS)
(COMPUTED-HINT
 (2 2 (:TYPE-PRESCRIPTION LAST))
 )
(FLAG-LEMMA-FOR-THM-1-PPR1
 (73359 5950 (:REWRITE DEFAULT-+-2))
 (27690 5950 (:REWRITE DEFAULT-+-1))
 (24629 12561 (:REWRITE DEFAULT-CDR))
 (18486 4207 (:REWRITE DEFAULT-<-1))
 (17294 8647 (:TYPE-PRESCRIPTION NTH-CHARACTER-LISTP))
 (15421 13557 (:REWRITE DEFAULT-CAR))
 (8647 8647 (:TYPE-PRESCRIPTION CHARACTER-LISTP))
 (8211 288 (:REWRITE DEFAULT-UNARY-MINUS))
 (6120 4207 (:REWRITE DEFAULT-<-2))
 (5716 5716 (:TYPE-PRESCRIPTION NATP))
 (4708 308 (:REWRITE MAX-WIDTH-OPENER))
 (4180 509 (:REWRITE SMALL-NAT-IMPLIES-FIXNAT))
 (4104 2027 (:TYPE-PRESCRIPTION MAX))
 (3438 1719 (:DEFINITION NTH))
 (2100 50 (:REWRITE CONSP-CDDR-PPR1))
 (1032 408 (:TYPE-PRESCRIPTION TRUE-LISTP-NTHCDR-TYPE-PRESCRIPTION))
 (540 108 (:DEFINITION LEN))
 (236 236 (:REWRITE NTHCDR-NIL))
 (178 98 (:DEFINITION TRUE-LISTP))
 (120 60 (:REWRITE NOT-CDDDR-PPR1-FLAT-NOT-EVISCERATION-MARK))
 (60 20 (:DEFINITION KEYWORDP))
 (36 36 (:REWRITE NOT-CDDDR-PPR1-FLAT-NIL))
 (20 20 (:TYPE-PRESCRIPTION STRINGP-SYMBOL-PACKAGE-NAME))
 (20 20 (:REWRITE DEFAULT-SYMBOL-PACKAGE-NAME))
 (5 5 (:REWRITE PPR11-NEVER-DOT))
 )
(FLAG-LEMMA-FOR-THM-2-PPR1
 (3047520 72560 (:REWRITE CONSP-CDDR-PPR1))
 (1972396 1202196 (:REWRITE DEFAULT-CDR))
 (1745913 945281 (:REWRITE DEFAULT-CAR))
 (837566 418783 (:TYPE-PRESCRIPTION NTH-CHARACTER-LISTP))
 (633240 78486 (:REWRITE SMALL-NAT-IMPLIES-FIXNAT))
 (508657 438695 (:REWRITE DEFAULT-<-1))
 (452566 438695 (:REWRITE DEFAULT-<-2))
 (418783 418783 (:TYPE-PRESCRIPTION CHARACTER-LISTP))
 (345050 345050 (:TYPE-PRESCRIPTION NATP))
 (219906 109953 (:DEFINITION NTH))
 (138960 108766 (:REWRITE DEFAULT-+-2))
 (113034 108766 (:REWRITE DEFAULT-+-1))
 (100608 87072 (:REWRITE NOT-CDDDR-PPR1-FLAT-NOT-EVISCERATION-MARK))
 (54958 2649 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (54656 26336 (:TYPE-PRESCRIPTION MAX))
 (38772 38772 (:REWRITE NOT-CDDDR-PPR1-FLAT-NIL))
 (30423 2433 (:REWRITE INTEGERP-IMPLIES-REAL/RATIONALP))
 (23304 7768 (:DEFINITION KEYWORDP))
 (18432 9216 (:TYPE-PRESCRIPTION TRUE-LISTP-NTHCDR-TYPE-PRESCRIPTION))
 (12810 6560 (:REWRITE MAX-WIDTH-OPENER))
 (8030 8030 (:REWRITE NTHCDR-NIL))
 (7768 7768 (:TYPE-PRESCRIPTION STRINGP-SYMBOL-PACKAGE-NAME))
 (7768 7768 (:REWRITE DEFAULT-SYMBOL-PACKAGE-NAME))
 (7256 7256 (:REWRITE PPR11-NEVER-DOT))
 (6104 438 (:REWRITE INTEGERP-MAX-WIDTH))
 (5888 4616 (:REWRITE DEFAULT-UNARY-MINUS))
 )
(THM-2-PPR1)
(THM-2-PPR1-LST)
(FLAG-LEMMA-FOR-THM-3-PPR1
 (1014638 109560 (:REWRITE DEFAULT-+-2))
 (656588 23666 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (483234 322076 (:REWRITE DEFAULT-CDR))
 (406768 109560 (:REWRITE DEFAULT-+-1))
 (386306 193153 (:TYPE-PRESCRIPTION NTH-CHARACTER-LISTP))
 (355028 20114 (:REWRITE INTEGERP-IMPLIES-REAL/RATIONALP))
 (332766 310996 (:REWRITE DEFAULT-CAR))
 (247815 66723 (:REWRITE DEFAULT-<-1))
 (193153 193153 (:TYPE-PRESCRIPTION CHARACTER-LISTP))
 (175807 175807 (:TYPE-PRESCRIPTION NATP))
 (112924 6012 (:REWRITE DEFAULT-UNARY-MINUS))
 (100093 66723 (:REWRITE DEFAULT-<-2))
 (88086 44043 (:DEFINITION NTH))
 (63936 6430 (:REWRITE MAX-WIDTH-OPENER))
 (57020 2982 (:REWRITE INTEGERP-MAX-WIDTH))
 (46520 21116 (:TYPE-PRESCRIPTION MAX))
 (43824 5123 (:REWRITE SMALL-NAT-IMPLIES-FIXNAT))
 (38172 17598 (:TYPE-PRESCRIPTION TRUE-LISTP-NTHCDR-TYPE-PRESCRIPTION))
 (18480 440 (:REWRITE CONSP-CDDR-PPR1))
 (7262 7262 (:REWRITE NTHCDR-NIL))
 (1314 438 (:DEFINITION KEYWORDP))
 (528 528 (:REWRITE NOT-CDDDR-PPR1-FLAT-NOT-EVISCERATION-MARK))
 (438 438 (:TYPE-PRESCRIPTION STRINGP-SYMBOL-PACKAGE-NAME))
 (438 438 (:REWRITE DEFAULT-SYMBOL-PACKAGE-NAME))
 (264 264 (:REWRITE NOT-CDDDR-PPR1-FLAT-NIL))
 (44 44 (:REWRITE PPR11-NEVER-DOT))
 )
(THM-3-PPR1)
(THM-3-PPR1-LST)
(FLAG-LEMMA-FOR-THM-4-PPR1
 (927360 22080 (:REWRITE CONSP-CDDR-PPR1))
 (893572 509414 (:REWRITE DEFAULT-CDR))
 (677712 413332 (:REWRITE DEFAULT-CAR))
 (417488 208744 (:TYPE-PRESCRIPTION NTH-CHARACTER-LISTP))
 (208920 25742 (:REWRITE SMALL-NAT-IMPLIES-FIXNAT))
 (208744 208744 (:TYPE-PRESCRIPTION CHARACTER-LISTP))
 (201313 161987 (:REWRITE DEFAULT-<-1))
 (192451 192451 (:TYPE-PRESCRIPTION NATP))
 (170294 161987 (:REWRITE DEFAULT-<-2))
 (95134 47567 (:DEFINITION NTH))
 (91582 73144 (:REWRITE DEFAULT-+-2))
 (81448 39924 (:TYPE-PRESCRIPTION MAX))
 (77000 73144 (:REWRITE DEFAULT-+-1))
 (35136 26496 (:REWRITE NOT-CDDDR-PPR1-FLAT-NOT-EVISCERATION-MARK))
 (26290 2327 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (15216 7608 (:TYPE-PRESCRIPTION TRUE-LISTP-NTHCDR-TYPE-PRESCRIPTION))
 (13247 2099 (:REWRITE INTEGERP-IMPLIES-REAL/RATIONALP))
 (12672 12672 (:REWRITE NOT-CDDDR-PPR1-FLAT-NIL))
 (8486 4820 (:REWRITE MAX-WIDTH-OPENER))
 (8118 2706 (:DEFINITION KEYWORDP))
 (6236 4020 (:REWRITE DEFAULT-UNARY-MINUS))
 (6128 6128 (:REWRITE NTHCDR-NIL))
 (2706 2706 (:TYPE-PRESCRIPTION STRINGP-SYMBOL-PACKAGE-NAME))
 (2706 2706 (:REWRITE DEFAULT-SYMBOL-PACKAGE-NAME))
 (2208 2208 (:REWRITE PPR11-NEVER-DOT))
 (432 36 (:REWRITE INTEGERP-MAX-WIDTH))
 )
(THM-4-PPR1)
(THM-4-PPR1-LST)
(PPR1-LST-NIL)
(FLAG-LEMMA-FOR-THM-5-PPR1
 (903840 21520 (:REWRITE CONSP-CDDR-PPR1))
 (868810 500438 (:REWRITE DEFAULT-CDR))
 (663138 406420 (:REWRITE DEFAULT-CAR))
 (407322 203661 (:TYPE-PRESCRIPTION NTH-CHARACTER-LISTP))
 (203661 203661 (:TYPE-PRESCRIPTION CHARACTER-LISTP))
 (203536 25087 (:REWRITE SMALL-NAT-IMPLIES-FIXNAT))
 (196221 158201 (:REWRITE DEFAULT-<-1))
 (185860 185860 (:TYPE-PRESCRIPTION NATP))
 (166246 158201 (:REWRITE DEFAULT-<-2))
 (93724 46862 (:DEFINITION NTH))
 (86842 69664 (:REWRITE DEFAULT-+-2))
 (79864 39164 (:TYPE-PRESCRIPTION MAX))
 (73090 69664 (:REWRITE DEFAULT-+-1))
 (34464 25824 (:REWRITE NOT-CDDDR-PPR1-FLAT-NOT-EVISCERATION-MARK))
 (25426 2317 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (15216 7608 (:TYPE-PRESCRIPTION TRUE-LISTP-NTHCDR-TYPE-PRESCRIPTION))
 (12779 2081 (:REWRITE INTEGERP-IMPLIES-REAL/RATIONALP))
 (12384 12384 (:REWRITE NOT-CDDDR-PPR1-FLAT-NIL))
 (7926 2642 (:DEFINITION KEYWORDP))
 (6602 4140 (:REWRITE MAX-WIDTH-OPENER))
 (6128 6128 (:REWRITE NTHCDR-NIL))
 (5704 3780 (:REWRITE DEFAULT-UNARY-MINUS))
 (2642 2642 (:TYPE-PRESCRIPTION STRINGP-SYMBOL-PACKAGE-NAME))
 (2642 2642 (:REWRITE DEFAULT-SYMBOL-PACKAGE-NAME))
 (2152 2152 (:REWRITE PPR11-NEVER-DOT))
 (368 36 (:REWRITE INTEGERP-MAX-WIDTH))
 )
(THM-5-PPR1)
(THM-5-PPR1-LST)
(FLAG-LEMMA-FOR-THM-6-PPR1
 (1833720 43660 (:REWRITE CONSP-CDDR-PPR1))
 (1274554 793970 (:REWRITE DEFAULT-CDR))
 (1122521 635305 (:REWRITE DEFAULT-CAR))
 (624976 312488 (:TYPE-PRESCRIPTION NTH-CHARACTER-LISTP))
 (393544 48596 (:REWRITE SMALL-NAT-IMPLIES-FIXNAT))
 (336053 281289 (:REWRITE DEFAULT-<-1))
 (312488 312488 (:TYPE-PRESCRIPTION CHARACTER-LISTP))
 (291970 281289 (:REWRITE DEFAULT-<-2))
 (281704 281704 (:TYPE-PRESCRIPTION NATP))
 (148082 74041 (:DEFINITION NTH))
 (96914 79876 (:REWRITE DEFAULT-+-2))
 (82166 79876 (:REWRITE DEFAULT-+-1))
 (64104 52392 (:REWRITE NOT-CDDDR-PPR1-FLAT-NOT-EVISCERATION-MARK))
 (47608 23004 (:TYPE-PRESCRIPTION MAX))
 (35498 1759 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (24684 24684 (:REWRITE NOT-CDDDR-PPR1-FLAT-NIL))
 (17923 1711 (:REWRITE INTEGERP-IMPLIES-REAL/RATIONALP))
 (17712 8856 (:TYPE-PRESCRIPTION TRUE-LISTP-NTHCDR-TYPE-PRESCRIPTION))
 (14328 4776 (:DEFINITION KEYWORDP))
 (7884 4676 (:REWRITE MAX-WIDTH-OPENER))
 (6960 6960 (:REWRITE NTHCDR-NIL))
 (6072 4404 (:REWRITE DEFAULT-UNARY-MINUS))
 (4776 4776 (:TYPE-PRESCRIPTION STRINGP-SYMBOL-PACKAGE-NAME))
 (4776 4776 (:REWRITE DEFAULT-SYMBOL-PACKAGE-NAME))
 (4366 4366 (:REWRITE PPR11-NEVER-DOT))
 (396 36 (:REWRITE INTEGERP-MAX-WIDTH))
 )
(THM-6-PPR1)
(THM-6-PPR1-LST)
(INTEGERP-MAX)
(NONNEG-MAX
 (12 4 (:REWRITE DEFAULT-<-1))
 (10 5 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (6 4 (:REWRITE DEFAULT-<-2))
 (5 5 (:REWRITE INTEGERP-IMPLIES-REAL/RATIONALP))
 )
(MAX-UPPER-BOUND
 (62 62 (:TYPE-PRESCRIPTION MAX))
 (20 10 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (18 6 (:REWRITE DEFAULT-<-1))
 (14 6 (:REWRITE DEFAULT-<-2))
 (10 10 (:REWRITE INTEGERP-IMPLIES-REAL/RATIONALP))
 (10 2 (:LINEAR NONNEG-MAX))
 )
(FLAG-LEMMA-FOR-THM-7-PPR1
 (835816 457842 (:REWRITE DEFAULT-CDR))
 (759360 18080 (:REWRITE CONSP-CDDR-PPR1))
 (596440 372516 (:REWRITE DEFAULT-CAR))
 (395888 197944 (:TYPE-PRESCRIPTION NTH-CHARACTER-LISTP))
 (197944 197944 (:TYPE-PRESCRIPTION CHARACTER-LISTP))
 (191695 191695 (:TYPE-PRESCRIPTION NATP))
 (179333 140231 (:REWRITE DEFAULT-<-1))
 (177192 21746 (:REWRITE SMALL-NAT-IMPLIES-FIXNAT))
 (146950 140231 (:REWRITE DEFAULT-<-2))
 (92686 72564 (:REWRITE DEFAULT-+-2))
 (84982 42491 (:DEFINITION NTH))
 (76876 72564 (:REWRITE DEFAULT-+-1))
 (28890 2923 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (25632 21696 (:REWRITE NOT-CDDDR-PPR1-FLAT-NOT-EVISCERATION-MARK))
 (15744 7872 (:TYPE-PRESCRIPTION TRUE-LISTP-NTHCDR-TYPE-PRESCRIPTION))
 (14555 2711 (:REWRITE INTEGERP-IMPLIES-REAL/RATIONALP))
 (10272 10272 (:REWRITE NOT-CDDDR-PPR1-FLAT-NIL))
 (8486 4708 (:REWRITE MAX-WIDTH-OPENER))
 (7062 2354 (:DEFINITION KEYWORDP))
 (6492 4564 (:REWRITE DEFAULT-UNARY-MINUS))
 (6384 6384 (:REWRITE NTHCDR-NIL))
 (2354 2354 (:TYPE-PRESCRIPTION STRINGP-SYMBOL-PACKAGE-NAME))
 (2354 2354 (:REWRITE DEFAULT-SYMBOL-PACKAGE-NAME))
 (1808 1808 (:REWRITE PPR11-NEVER-DOT))
 (480 48 (:REWRITE SMALL-NAT-MAX-DIFFERENCE-0))
 (432 36 (:REWRITE INTEGERP-MAX-WIDTH))
 (48 48 (:REWRITE INTEGERP-MAX))
 )
(THM-7-PPR1)
(THM-7-PPR1-LST)
