File: lofat-remove-file%40useless-runes.lsp

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sloc: lisp: 17,818,294; java: 125,359; python: 28,122; javascript: 23,458; cpp: 18,851; ansic: 11,569; perl: 7,678; xml: 5,591; sh: 3,978; makefile: 3,840; ruby: 2,633; yacc: 1,126; ml: 763; awk: 295; csh: 233; lex: 197; php: 178; tcl: 49; asm: 23; haskell: 17
file content (4591 lines) | stat: -rw-r--r-- 223,580 bytes
parent folder | download | duplicates (2)
(D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-10
 (160 6 (:REWRITE CONSP-OF-FAT32-BUILD-INDEX-LIST))
 (116 4 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-LEFT))
 (88 11 (:REWRITE ZP-OPEN))
 (64 4 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-RIGHT))
 (26 14 (:REWRITE DEFAULT-<-2))
 (15 14 (:REWRITE DEFAULT-<-1))
 (12 12 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-FAT32-BUILD-INDEX-LIST))
 (6 6 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (4 4 (:REWRITE FLATTEN-SUBSET-NO-DUPLICATESP-LEMMA-1))
 (4 2 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (4 1 (:LINEAR NATP-OF-CLUSTER-SIZE))
 (3 1 (:LINEAR LOFAT-FS-P-CORRECTNESS-1))
 (3 1 (:LINEAR HIFAT-TO-LOFAT-INVERSION-LEMMA-19))
 (2 2 (:REWRITE INTERSECT-WITH-SUBSET . 11))
 (2 2 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (1 1 (:TYPE-PRESCRIPTION FAT32$C-P))
 (1 1 (:REWRITE LOFAT-FS-P-CORRECTNESS-1))
 )
(D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-9
 (176 6 (:REWRITE CONSP-OF-FAT32-BUILD-INDEX-LIST))
 (132 4 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-LEFT))
 (64 4 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-RIGHT))
 (56 7 (:REWRITE ZP-OPEN))
 (25 13 (:REWRITE DEFAULT-<-2))
 (20 5 (:LINEAR NATP-OF-CLUSTER-SIZE))
 (15 5 (:LINEAR LOFAT-FS-P-CORRECTNESS-1))
 (15 5 (:LINEAR HIFAT-TO-LOFAT-INVERSION-LEMMA-19))
 (14 13 (:REWRITE DEFAULT-<-1))
 (12 12 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-FAT32-BUILD-INDEX-LIST))
 (9 9 (:TYPE-PRESCRIPTION D-E-FILE-SIZE))
 (5 5 (:TYPE-PRESCRIPTION FAT32$C-P))
 (5 5 (:REWRITE LOFAT-FS-P-CORRECTNESS-1))
 (5 1 (:REWRITE FAT32-MASKED-ENTRY-P-OF-D-E-FIRST-CLUSTER))
 (4 4 (:REWRITE FLATTEN-SUBSET-NO-DUPLICATESP-LEMMA-1))
 (4 4 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (4 2 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (2 2 (:REWRITE INTERSECT-WITH-SUBSET . 11))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-70
 (2220 2 (:REWRITE SUBDIR-CONTENTS-P-WHEN-ZERO-LENGTH))
 (1904 1 (:REWRITE LEN-OF-APPEND))
 (1849 1 (:REWRITE LEN-OF-MAKE-LIST-AC))
 (1460 70 (:DEFINITION LEN))
 (1100 14 (:LINEAR MAKE-CLUSTERS-CORRECTNESS-2))
 (997 1 (:REWRITE NFIX-WHEN-NATP))
 (983 1 (:DEFINITION NATP))
 (941 3 (:REWRITE MOD-DOES-NOTHING))
 (906 13 (:LINEAR LEN-OF-EXPLODE-WHEN-M1-FILE-CONTENTS-P-1))
 (869 24 (:REWRITE ZP-OPEN))
 (868 6 (:REWRITE REARRANGE-NEGATIVE-COEFS-<))
 (857 1 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (840 1 (:REWRITE CONSP-OF-MAKE-LIST-AC))
 (774 112 (:REWRITE STR::CONSP-OF-EXPLODE))
 (576 2 (:REWRITE NONNEG-+))
 (531 13 (:REWRITE M1-FILE-CONTENTS-P-WHEN-STRINGP))
 (453 13 (:REWRITE LEN-OF-NATS=>CHARS))
 (447 1 (:REWRITE NFIX-WHEN-ZP))
 (440 13 (:REWRITE LEN-OF-CLEAR-D-E))
 (427 13 (:LINEAR LENGTH-OF-D-E-CC-CONTENTS . 2))
 (343 1 (:DEFINITION NFIX))
 (294 70 (:REWRITE DEFAULT-CDR))
 (292 2 (:REWRITE PRODUCT-LESS-THAN-ZERO))
 (234 13 (:LINEAR LENGTH-OF-D-E-CC-CONTENTS . 3))
 (223 95 (:REWRITE DEFAULT-+-2))
 (192 56 (:REWRITE FAT32-FILENAME-P-CORRECTNESS-1))
 (168 168 (:TYPE-PRESCRIPTION STR::TRUE-LISTP-OF-EXPLODE))
 (161 7 (:LINEAR MAKE-CLUSTERS-CORRECTNESS-3))
 (131 95 (:REWRITE DEFAULT-+-1))
 (112 56 (:REWRITE STR::EXPLODE-WHEN-NOT-STRINGP))
 (84 28 (:TYPE-PRESCRIPTION MAKE-CLUSTERS-OF-NIL))
 (83 36 (:REWRITE DEFAULT-<-2))
 (82 1 (:DEFINITION MAKE-LIST-AC))
 (80 7 (:REWRITE COMMUTATIVITY-OF-+))
 (78 78 (:TYPE-PRESCRIPTION INTEGERP-OF-D-E-CC-CONTENTS))
 (78 13 (:DEFINITION UNSIGNED-BYTE-P))
 (71 71 (:REWRITE EXPT-COMPARE-EQUAL))
 (71 71 (:REWRITE EQUAL-OF-PREDS-REWRITE))
 (71 71 (:REWRITE EQUAL-MULTIPLY-THROUGH-BY-INVERTED-FACTOR-FROM-RIGHT-HAND-SIDE))
 (71 71 (:REWRITE EQUAL-MULTIPLY-THROUGH-BY-INVERTED-FACTOR-FROM-LEFT-HAND-SIDE))
 (71 71 (:REWRITE CANCEL-COMMON-FACTORS-IN-EQUAL))
 (71 71 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (71 71 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (70 70 (:REWRITE FAT32-FILENAME-P-WHEN-MEMBER-EQUAL-OF-FAT32-FILENAME-LIST-P))
 (56 28 (:REWRITE DEFAULT-*-2))
 (53 36 (:REWRITE DEFAULT-<-1))
 (52 52 (:TYPE-PRESCRIPTION HIFAT-BOUNDED-FILE-ALIST-P))
 (52 22 (:LINEAR LOFAT-FS-P-CORRECTNESS-1))
 (52 22 (:LINEAR HIFAT-TO-LOFAT-INVERSION-LEMMA-19))
 (52 13 (:DEFINITION INTEGER-RANGE-P))
 (47 47 (:TYPE-PRESCRIPTION NATS=>STRING))
 (46 28 (:REWRITE DEFAULT-*-1))
 (44 44 (:REWRITE NON-INTEGERP-<-INTEGERP))
 (44 44 (:REWRITE INTEGERP-<-NON-INTEGERP))
 (44 44 (:REWRITE EXPT-COMPARE))
 (44 44 (:REWRITE CANCEL-COMMON-FACTORS-IN-<))
 (42 42 (:REWRITE LESS-THAN-MULTIPLY-THROUGH-BY-INVERTED-FACTOR-FROM-RIGHT-HAND-SIDE))
 (42 42 (:REWRITE LESS-THAN-MULTIPLY-THROUGH-BY-INVERTED-FACTOR-FROM-LEFT-HAND-SIDE))
 (39 13 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-5))
 (39 13 (:LINEAR LEN-WHEN-HIFAT-BOUNDED-FILE-ALIST-P . 2))
 (39 13 (:LINEAR LEN-WHEN-HIFAT-BOUNDED-FILE-ALIST-P . 1))
 (36 36 (:META CANCEL_PLUS-LESSP-CORRECT))
 (35 6 (:REWRITE UNICITY-OF-0))
 (32 8 (:LINEAR NATP-OF-CLUSTER-SIZE))
 (28 28 (:TYPE-PRESCRIPTION MAKE-CLUSTERS))
 (26 26 (:TYPE-PRESCRIPTION GOOD-ROOT-D-E-P))
 (26 26 (:LINEAR LEN-WHEN-FAT32-FILENAME-LIST-PREFIXP))
 (22 22 (:TYPE-PRESCRIPTION ZP))
 (21 3 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-MAKE-LIST-AC))
 (15 15 (:REWRITE CANCEL-COMMON-FACTORS-IN-EQUAL-WITH-0))
 (14 14 (:LINEAR *-WEAKLY-MONOTONIC-NEGATIVE-MULTIPLIER . 2))
 (14 14 (:LINEAR *-WEAKLY-MONOTONIC-NEGATIVE-MULTIPLIER . 1))
 (14 14 (:LINEAR *-WEAKLY-MONOTONIC . 2))
 (14 14 (:LINEAR *-WEAKLY-MONOTONIC . 1))
 (14 14 (:LINEAR *-STRONGLY-MONOTONIC-NEGATIVE-MULTIPLIER . 2))
 (14 14 (:LINEAR *-STRONGLY-MONOTONIC-NEGATIVE-MULTIPLIER . 1))
 (14 14 (:LINEAR *-STRONGLY-MONOTONIC . 2))
 (14 14 (:LINEAR *-STRONGLY-MONOTONIC . 1))
 (13 13 (:TYPE-PRESCRIPTION MOD-NON-POSITIVE-TYPE-PRESCRIPTION))
 (13 13 (:TYPE-PRESCRIPTION M1-FILE-CONTENTS-P))
 (13 13 (:REWRITE EXPT-EXECUTE-REWRITE))
 (13 13 (:LINEAR POSITION-WHEN-MEMBER))
 (13 13 (:LINEAR POSITION-EQUAL-AC-WHEN-MEMBER))
 (13 13 (:LINEAR LENGTH-OF-D-E-CC-CONTENTS . 1))
 (13 1 (:REWRITE STR::EXPLODE-OF-IMPLODE))
 (12 12 (:REWRITE EXPLODE-OF-NATS=>STRING))
 (10 1 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (8 8 (:TYPE-PRESCRIPTION FAT32$C-P))
 (7 7 (:TYPE-PRESCRIPTION NATP))
 (7 7 (:REWRITE DEFAULT-CAR))
 (4 4 (:TYPE-PRESCRIPTION NATS=>CHARS))
 (4 4 (:REWRITE MOD-WHEN-Y-IS-AN-INVERSE))
 (4 2 (:REWRITE MOD-WITH-X-A-NON-ACL2-NUMBER-IS-ZERO))
 (4 1 (:REWRITE APPEND-WHEN-NOT-CONSP))
 (3 3 (:TYPE-PRESCRIPTION MAKE-LIST-AC))
 (3 3 (:REWRITE POWER2-INTEGER))
 (3 1 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-149))
 (2 2 (:REWRITE INTEGERP-PROD))
 (2 2 (:REWRITE INTEGERP-MINUS))
 (2 2 (:REWRITE COLLECT-CONSTANTS-IN-EQUAL-OF-SUMS))
 (1 1 (:TYPE-PRESCRIPTION STRINGP-OF-IMPLODE))
 (1 1 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (1 1 (:REWRITE MOVE-NEGATIVE-CONSTANT-1))
 (1 1 (:REWRITE STR::MAKE-CHARACTER-LIST-IS-IDENTITY-UNDER-CHARLISTEQV))
 (1 1 (:REWRITE FOLD-CONSTS-IN-+))
 (1 1 (:REWRITE COLLECT-CONSTANTS-IN-<-OF-SUMS))
 (1 1 (:REWRITE A4))
 )
(D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-3
 (748 44 (:DEFINITION FIND-D-E))
 (730 1 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-59))
 (413 45 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (362 1 (:LINEAR HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E))
 (294 24 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (252 6 (:REWRITE REMOVE-ASSOC-WHEN-ABSENT-1))
 (238 1 (:LINEAR HIFAT-ENTRY-COUNT-OF-REMOVE-ASSOC-EQUAL))
 (233 45 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (195 3 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-1))
 (189 1 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-3))
 (152 48 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (114 3 (:REWRITE DELETE-D-E-CORRECTNESS-1))
 (112 112 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (111 1 (:DEFINITION DELETE-D-E))
 (90 90 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (90 90 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (85 20 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
 (80 2 (:DEFINITION REMOVE-ASSOC-EQUAL))
 (79 79 (:REWRITE DEFAULT-CAR))
 (75 3 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-23))
 (60 60 (:REWRITE DEFAULT-CDR))
 (60 18 (:TYPE-PRESCRIPTION ASSOC-WHEN-ZP-LEN))
 (48 7 (:DEFINITION ASSOC-EQUAL))
 (46 1 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-6))
 (45 45 (:TYPE-PRESCRIPTION FIND-D-E-CORRECTNESS-1))
 (45 45 (:TYPE-PRESCRIPTION D-E-P))
 (44 44 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (41 14 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (28 28 (:TYPE-PRESCRIPTION ZP))
 (21 5 (:REWRITE NFIX-WHEN-NATP))
 (20 5 (:REWRITE NFIX-WHEN-ZP))
 (19 15 (:REWRITE DEFAULT-<-1))
 (18 18 (:TYPE-PRESCRIPTION LOFAT-TO-HIFAT-HELPER-CORRECTNESS-1 . 2))
 (18 18 (:TYPE-PRESCRIPTION LEN))
 (16 15 (:REWRITE DEFAULT-<-2))
 (14 7 (:REWRITE DEFAULT-+-2))
 (12 4 (:REWRITE USEFUL-D-E-LIST-P-OF-CDR))
 (11 5 (:DEFINITION NATP))
 (10 5 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (9 3 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-2))
 (9 3 (:LINEAR LOFAT-FS-P-CORRECTNESS-1))
 (9 1 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-5))
 (8 7 (:REWRITE DEFAULT-+-1))
 (7 7 (:REWRITE-QUOTED-CONSTANT FAT32-FILENAME-LIST-FIX-UNDER-FAT32-FILENAME-LIST-EQUIV))
 (6 6 (:TYPE-PRESCRIPTION LOFAT-FS-P))
 (6 2 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-26))
 (5 5 (:TYPE-PRESCRIPTION NATP))
 (5 5 (:REWRITE ZP-OPEN))
 (5 5 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (3 3 (:TYPE-PRESCRIPTION DELETE-D-E))
 (3 1 (:REWRITE M1-FILE-ALIST-P-OF-LOFAT-TO-HIFAT-HELPER))
 (2 1 (:REWRITE DEFAULT-UNARY-MINUS))
 (1 1 (:TYPE-PRESCRIPTION HIFAT-NO-DUPS-P))
 (1 1 (:REWRITE HIFAT-NO-DUPS-P-OF-LOFAT-TO-HIFAT-HELPER))
 )
(LOFAT-REMOVE-FILE-HELPER
 (104 6 (:DEFINITION FIND-D-E))
 (92 52 (:REWRITE DEFAULT-<-1))
 (75 75 (:TYPE-PRESCRIPTION FAT32-FILENAME-FIX))
 (71 39 (:REWRITE DEFAULT-+-2))
 (56 8 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-8))
 (56 6 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (54 52 (:REWRITE DEFAULT-<-2))
 (49 4 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (46 39 (:REWRITE DEFAULT-+-1))
 (32 6 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (28 3 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (24 3 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
 (22 22 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (18 18 (:REWRITE DEFAULT-CDR))
 (16 16 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (16 8 (:LINEAR LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-1-LEMMA-1))
 (13 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (12 12 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (11 2 (:REWRITE UPDATE-BPB_SECPERCLUS-CORRECTNESS-2 . 3))
 (9 9 (:REWRITE DEFAULT-CAR))
 (8 4 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (6 6 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (5 1 (:REWRITE UNSIGNED-BYTE-LISTP-WHEN-D-E-P))
 (4 4 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-SUBSETP-EQUAL))
 (3 1 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-23))
 (3 1 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-13))
 (2 2 (:TYPE-PRESCRIPTION GOOD-ROOT-D-E-P))
 (2 2 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-NOT-CONSP))
 )
(LOFAT-REMOVE-FILE
 (228 12 (:DEFINITION FIND-D-E))
 (146 6 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (116 12 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (101 69 (:REWRITE DEFAULT-<-2))
 (93 69 (:REWRITE DEFAULT-<-1))
 (68 12 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (50 26 (:REWRITE DEFAULT-+-2))
 (38 38 (:REWRITE DEFAULT-CDR))
 (30 30 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (30 4 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (28 26 (:REWRITE DEFAULT-+-1))
 (24 24 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (19 19 (:TYPE-PRESCRIPTION FAT32-FILENAME-FIX))
 (18 18 (:REWRITE DEFAULT-CAR))
 (15 5 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (12 12 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (10 4 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-8))
 (8 4 (:LINEAR LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-1-LEMMA-1))
 (6 6 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (4 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (3 1 (:REWRITE UPDATE-BPB_SECPERCLUS-CORRECTNESS-2 . 3))
 (1 1 (:REWRITE SUBSETP-WHEN-ATOM-RIGHT))
 (1 1 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (1 1 (:REWRITE SUBSETP-TRANS2))
 (1 1 (:REWRITE SUBSETP-TRANS))
 (1 1 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-NOT-CONSP))
 )
(LOFAT-REMOVE-FILE-ALT
 (237 13 (:DEFINITION FIND-D-E))
 (122 71 (:REWRITE DEFAULT-<-1))
 (119 13 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (92 49 (:REWRITE DEFAULT-+-2))
 (89 89 (:TYPE-PRESCRIPTION FAT32-FILENAME-FIX))
 (81 8 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (76 6 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
 (75 71 (:REWRITE DEFAULT-<-2))
 (67 13 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (58 6 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (56 56 (:REWRITE DEFAULT-CDR))
 (55 49 (:REWRITE DEFAULT-+-1))
 (47 5 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-8))
 (36 36 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (26 26 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (20 20 (:REWRITE DEFAULT-CAR))
 (17 6 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (13 13 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (13 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (11 11 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (11 2 (:REWRITE UPDATE-BPB_SECPERCLUS-CORRECTNESS-2 . 3))
 (9 5 (:LINEAR LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-1-LEMMA-1))
 (5 1 (:REWRITE UNSIGNED-BYTE-LISTP-WHEN-D-E-P))
 (3 1 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-23))
 (3 1 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-13))
 (2 2 (:TYPE-PRESCRIPTION GOOD-ROOT-D-E-P))
 (2 2 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-NOT-CONSP))
 (1 1 (:REWRITE SUBSETP-WHEN-ATOM-RIGHT))
 (1 1 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (1 1 (:REWRITE SUBSETP-TRANS2))
 (1 1 (:REWRITE SUBSETP-TRANS))
 )
(MAX-ENTRY-COUNT-OF-LOFAT-REMOVE-FILE-HELPER
 (420 21 (:DEFINITION FIND-D-E))
 (210 21 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (180 12 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (126 21 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (68 16 (:REWRITE FAT32-FILENAME-FIX-WHEN-FAT32-FILENAME-P))
 (63 63 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (63 21 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (62 6 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (42 42 (:TYPE-PRESCRIPTION FAT32-FILENAME-FIX))
 (42 42 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (42 42 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (37 37 (:REWRITE DEFAULT-CAR))
 (28 28 (:TYPE-PRESCRIPTION USEFUL-D-E-LIST-P))
 (28 28 (:REWRITE USEFUL-D-E-LIST-P-OF-MAKE-D-E-LIST))
 (28 28 (:REWRITE DEFAULT-CDR))
 (26 26 (:TYPE-PRESCRIPTION FAT32-FILENAME-P))
 (26 26 (:REWRITE FAT32-FILENAME-P-WHEN-MEMBER-EQUAL-OF-FAT32-FILENAME-LIST-P))
 (24 24 (:TYPE-PRESCRIPTION LOFAT-FS-P))
 (21 21 (:TYPE-PRESCRIPTION D-E-P))
 (21 21 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (18 6 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-23))
 (18 6 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-13))
 (18 6 (:LINEAR LOFAT-FS-P-CORRECTNESS-1))
 (16 11 (:REWRITE DEFAULT-<-2))
 (15 11 (:REWRITE DEFAULT-<-1))
 (14 7 (:REWRITE DEFAULT-+-2))
 (14 6 (:LINEAR LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-1-LEMMA-1))
 (12 12 (:TYPE-PRESCRIPTION GOOD-ROOT-D-E-P))
 (12 6 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-8))
 (7 7 (:REWRITE DEFAULT-+-1))
 (6 6 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 )
(MAX-ENTRY-COUNT-OF-LOFAT-REMOVE-FILE
 (816 42 (:DEFINITION FIND-D-E))
 (396 42 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (228 42 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (126 42 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (102 102 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (84 84 (:TYPE-PRESCRIPTION FAT32-FILENAME-FIX))
 (84 84 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (84 84 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (80 16 (:REWRITE FAT32-FILENAME-FIX-WHEN-FAT32-FILENAME-P))
 (58 58 (:REWRITE DEFAULT-CAR))
 (53 53 (:REWRITE DEFAULT-CDR))
 (47 47 (:TYPE-PRESCRIPTION USEFUL-D-E-LIST-P))
 (47 47 (:REWRITE USEFUL-D-E-LIST-P-OF-MAKE-D-E-LIST))
 (42 42 (:TYPE-PRESCRIPTION D-E-P))
 (32 32 (:TYPE-PRESCRIPTION FAT32-FILENAME-P))
 (32 32 (:REWRITE FAT32-FILENAME-P-WHEN-MEMBER-EQUAL-OF-FAT32-FILENAME-LIST-P))
 (32 20 (:REWRITE DEFAULT-<-2))
 (26 20 (:REWRITE DEFAULT-<-1))
 (12 6 (:REWRITE DEFAULT-+-2))
 (9 3 (:LINEAR LOFAT-FS-P-CORRECTNESS-1))
 (9 3 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-8))
 (7 3 (:LINEAR LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-1-LEMMA-1))
 (6 6 (:TYPE-PRESCRIPTION LOFAT-FS-P))
 (6 6 (:REWRITE DEFAULT-+-1))
 (3 3 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 )
(PSEUDO-ROOT-D-E-OF-LOFAT-REMOVE-FILE-HELPER
 (420 21 (:DEFINITION FIND-D-E))
 (210 21 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (180 12 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (126 21 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (68 16 (:REWRITE FAT32-FILENAME-FIX-WHEN-FAT32-FILENAME-P))
 (63 63 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (63 21 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (62 6 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (42 42 (:TYPE-PRESCRIPTION FAT32-FILENAME-FIX))
 (42 42 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (42 42 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (41 39 (:REWRITE DEFAULT-CAR))
 (32 30 (:REWRITE DEFAULT-CDR))
 (28 28 (:TYPE-PRESCRIPTION USEFUL-D-E-LIST-P))
 (28 28 (:REWRITE USEFUL-D-E-LIST-P-OF-MAKE-D-E-LIST))
 (26 26 (:TYPE-PRESCRIPTION FAT32-FILENAME-P))
 (26 26 (:REWRITE FAT32-FILENAME-P-WHEN-MEMBER-EQUAL-OF-FAT32-FILENAME-LIST-P))
 (24 24 (:TYPE-PRESCRIPTION LOFAT-FS-P))
 (21 21 (:TYPE-PRESCRIPTION D-E-P))
 (21 21 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (18 6 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-23))
 (18 6 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-13))
 (18 6 (:LINEAR LOFAT-FS-P-CORRECTNESS-1))
 (16 11 (:REWRITE DEFAULT-<-2))
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 (14 7 (:REWRITE DEFAULT-+-2))
 (14 6 (:LINEAR LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-1-LEMMA-1))
 (12 12 (:TYPE-PRESCRIPTION GOOD-ROOT-D-E-P))
 (12 6 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-8))
 (7 7 (:REWRITE DEFAULT-+-1))
 (6 6 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 )
(PSEUDO-ROOT-D-E-OF-LOFAT-REMOVE-FILE
 (816 42 (:DEFINITION FIND-D-E))
 (396 42 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (228 42 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (126 42 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (102 102 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (84 84 (:TYPE-PRESCRIPTION FAT32-FILENAME-FIX))
 (84 84 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (84 84 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (80 16 (:REWRITE FAT32-FILENAME-FIX-WHEN-FAT32-FILENAME-P))
 (70 64 (:REWRITE DEFAULT-CAR))
 (65 59 (:REWRITE DEFAULT-CDR))
 (47 47 (:TYPE-PRESCRIPTION USEFUL-D-E-LIST-P))
 (47 47 (:REWRITE USEFUL-D-E-LIST-P-OF-MAKE-D-E-LIST))
 (42 42 (:TYPE-PRESCRIPTION D-E-P))
 (32 32 (:TYPE-PRESCRIPTION FAT32-FILENAME-P))
 (32 32 (:REWRITE FAT32-FILENAME-P-WHEN-MEMBER-EQUAL-OF-FAT32-FILENAME-LIST-P))
 (32 20 (:REWRITE DEFAULT-<-2))
 (26 20 (:REWRITE DEFAULT-<-1))
 (12 6 (:REWRITE DEFAULT-+-2))
 (9 3 (:LINEAR LOFAT-FS-P-CORRECTNESS-1))
 (9 3 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-8))
 (7 3 (:LINEAR LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-1-LEMMA-1))
 (6 6 (:TYPE-PRESCRIPTION LOFAT-FS-P))
 (6 6 (:REWRITE DEFAULT-+-1))
 (3 3 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 )
(COUNT-OF-CLUSTERS-OF-LOFAT-REMOVE-FILE-HELPER
 (420 21 (:DEFINITION FIND-D-E))
 (210 21 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (180 12 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (126 21 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (72 24 (:LINEAR LOFAT-FS-P-CORRECTNESS-1))
 (68 16 (:REWRITE FAT32-FILENAME-FIX-WHEN-FAT32-FILENAME-P))
 (63 63 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (63 21 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (62 6 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (60 60 (:TYPE-PRESCRIPTION LOFAT-FS-P))
 (42 42 (:TYPE-PRESCRIPTION FAT32-FILENAME-FIX))
 (42 42 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (42 42 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (37 37 (:REWRITE DEFAULT-CAR))
 (30 30 (:TYPE-PRESCRIPTION USEFUL-D-E-LIST-P))
 (30 30 (:REWRITE USEFUL-D-E-LIST-P-OF-MAKE-D-E-LIST))
 (28 28 (:REWRITE DEFAULT-CDR))
 (26 26 (:TYPE-PRESCRIPTION FAT32-FILENAME-P))
 (26 26 (:REWRITE FAT32-FILENAME-P-WHEN-MEMBER-EQUAL-OF-FAT32-FILENAME-LIST-P))
 (22 12 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-8))
 (21 21 (:TYPE-PRESCRIPTION D-E-P))
 (21 21 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (20 12 (:LINEAR LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-1-LEMMA-1))
 (18 6 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-23))
 (18 6 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-13))
 (16 11 (:REWRITE DEFAULT-<-2))
 (15 11 (:REWRITE DEFAULT-<-1))
 (14 7 (:REWRITE DEFAULT-+-2))
 (12 12 (:TYPE-PRESCRIPTION GOOD-ROOT-D-E-P))
 (12 12 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (7 7 (:REWRITE DEFAULT-+-1))
 )
(COUNT-OF-CLUSTERS-OF-LOFAT-REMOVE-FILE
 (816 42 (:DEFINITION FIND-D-E))
 (396 42 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (228 42 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (126 42 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (108 36 (:LINEAR LOFAT-FS-P-CORRECTNESS-1))
 (102 102 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (84 84 (:TYPE-PRESCRIPTION FAT32-FILENAME-FIX))
 (84 84 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (84 84 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (80 16 (:REWRITE FAT32-FILENAME-FIX-WHEN-FAT32-FILENAME-P))
 (72 72 (:TYPE-PRESCRIPTION LOFAT-FS-P))
 (58 58 (:REWRITE DEFAULT-CAR))
 (53 53 (:REWRITE DEFAULT-CDR))
 (50 50 (:TYPE-PRESCRIPTION USEFUL-D-E-LIST-P))
 (50 50 (:REWRITE USEFUL-D-E-LIST-P-OF-MAKE-D-E-LIST))
 (42 42 (:TYPE-PRESCRIPTION D-E-P))
 (32 32 (:TYPE-PRESCRIPTION FAT32-FILENAME-P))
 (32 32 (:REWRITE FAT32-FILENAME-P-WHEN-MEMBER-EQUAL-OF-FAT32-FILENAME-LIST-P))
 (32 20 (:REWRITE DEFAULT-<-2))
 (26 20 (:REWRITE DEFAULT-<-1))
 (26 14 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-8))
 (18 14 (:LINEAR LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-1-LEMMA-1))
 (14 14 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (12 6 (:REWRITE DEFAULT-+-2))
 (6 6 (:REWRITE DEFAULT-+-1))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-3
 (1935 99 (:DEFINITION FIND-D-E))
 (945 99 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (549 99 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (297 99 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (261 53 (:REWRITE FAT32-FILENAME-FIX-WHEN-FAT32-FILENAME-P))
 (252 252 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (198 198 (:TYPE-PRESCRIPTION FAT32-FILENAME-FIX))
 (198 198 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (198 198 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (166 166 (:REWRITE DEFAULT-CDR))
 (152 152 (:REWRITE DEFAULT-CAR))
 (112 77 (:REWRITE DEFAULT-<-2))
 (104 104 (:TYPE-PRESCRIPTION USEFUL-D-E-LIST-P))
 (104 104 (:TYPE-PRESCRIPTION FAT32-FILENAME-P))
 (104 104 (:REWRITE USEFUL-D-E-LIST-P-OF-MAKE-D-E-LIST))
 (104 104 (:REWRITE FAT32-FILENAME-P-WHEN-MEMBER-EQUAL-OF-FAT32-FILENAME-LIST-P))
 (101 77 (:REWRITE DEFAULT-<-1))
 (99 99 (:TYPE-PRESCRIPTION D-E-P))
 (66 33 (:REWRITE DEFAULT-+-2))
 (63 21 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-23))
 (63 21 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-13))
 (48 48 (:TYPE-PRESCRIPTION LOFAT-FS-P))
 (42 42 (:TYPE-PRESCRIPTION GOOD-ROOT-D-E-P))
 (33 33 (:REWRITE DEFAULT-+-1))
 (9 3 (:LINEAR LOFAT-FS-P-CORRECTNESS-1))
 (9 3 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-8))
 (7 3 (:LINEAR LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-1-LEMMA-1))
 (3 3 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-35
 (2158 21 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-RIGHT))
 (2076 3 (:REWRITE CONSP-OF-FIND-N-FREE-CLUSTERS))
 (1760 89 (:DEFINITION FIND-D-E))
 (1733 351 (:TYPE-PRESCRIPTION PAINFUL-DEBUGGING-LEMMA-10))
 (1258 79 (:DEFINITION LEN))
 (1200 5 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (1065 5 (:REWRITE CONSP-OF-MAKE-LIST-AC))
 (1031 351 (:TYPE-PRESCRIPTION PAINFUL-DEBUGGING-LEMMA-9))
 (980 94 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (664 135 (:REWRITE DEFAULT-<-2))
 (635 8 (:DEFINITION MAKE-LIST-AC))
 (610 5 (:DEFINITION DELETE-D-E))
 (606 3 (:REWRITE COUNT-FREE-CLUSTERS-OF-UPDATE-NTH))
 (604 94 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (559 15 (:REWRITE DELETE-D-E-CORRECTNESS-1))
 (547 158 (:REWRITE STR::CONSP-OF-EXPLODE))
 (545 199 (:REWRITE DEFAULT-CDR))
 (531 3 (:REWRITE FIND-N-FREE-CLUSTERS-WHEN-ZP))
 (462 6 (:REWRITE COUNT-FREE-CLUSTERS-OF-SET-INDICES-IN-FA-TABLE-1))
 (460 171 (:REWRITE DEFAULT-+-2))
 (459 55 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (380 60 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (351 351 (:TYPE-PRESCRIPTION CEILING))
 (324 6 (:LINEAR PAINFUL-DEBUGGING-LEMMA-10))
 (272 26 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-56))
 (250 106 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (243 79 (:REWRITE FAT32-FILENAME-P-CORRECTNESS-1))
 (237 237 (:TYPE-PRESCRIPTION STR::TRUE-LISTP-OF-EXPLODE))
 (200 171 (:REWRITE DEFAULT-+-1))
 (188 188 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (188 188 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (182 182 (:TYPE-PRESCRIPTION D-E-FILE-SIZE))
 (180 12 (:REWRITE NOT-INTERSECTP-LIST-OF-LOFAT-TO-HIFAT-HELPER))
 (177 26 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (174 50 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-8))
 (168 168 (:TYPE-PRESCRIPTION FAT32-FILENAME-FIX))
 (166 136 (:REWRITE DEFAULT-CAR))
 (158 79 (:REWRITE STR::EXPLODE-WHEN-NOT-STRINGP))
 (156 6 (:LINEAR PAINFUL-DEBUGGING-LEMMA-9))
 (156 6 (:DEFINITION FREE-INDEX-LISTP))
 (144 135 (:REWRITE DEFAULT-<-1))
 (128 128 (:TYPE-PRESCRIPTION FAT32-FILENAME-P))
 (128 128 (:REWRITE FAT32-FILENAME-P-WHEN-MEMBER-EQUAL-OF-FAT32-FILENAME-LIST-P))
 (128 36 (:REWRITE FAT32-FILENAME-FIX-WHEN-FAT32-FILENAME-P))
 (126 126 (:TYPE-PRESCRIPTION FAT32-ENTRY-MASK))
 (120 10 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-MAKE-LIST-AC))
 (94 5 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-3))
 (93 93 (:TYPE-PRESCRIPTION COUNT-FREE-CLUSTERS))
 (91 6 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-UPDATE-DIR-CONTENTS))
 (89 89 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-D-E-CC))
 (89 89 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (82 28 (:LINEAR D-E-FILE-SIZE-CORRECTNESS-1))
 (80 21 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-LEFT))
 (79 3 (:REWRITE NON-FREE-INDEX-LISTP-CORRECTNESS-2 . 2))
 (68 1 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-CLEAR-CC))
 (63 27 (:REWRITE NFIX-WHEN-ZP))
 (60 20 (:REWRITE USEFUL-D-E-LIST-P-OF-CDR))
 (50 5 (:REWRITE DEFAULT-*-2))
 (42 12 (:REWRITE NOT-INTERSECTP-LIST-WHEN-ATOM))
 (40 20 (:LINEAR HIFAT-TO-LOFAT-INVERSION-LEMMA-19))
 (40 9 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-18))
 (36 12 (:DEFINITION NATP))
 (30 30 (:TYPE-PRESCRIPTION FREE-INDEX-LISTP))
 (28 28 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (27 6 (:REWRITE SET-INDICES-IN-FA-TABLE-CORRECTNESS-3))
 (25 5 (:REWRITE INTERSECTP-OF-SELF))
 (20 5 (:REWRITE APPEND-WHEN-NOT-CONSP))
 (18 3 (:REWRITE SET-INDICES-IN-FA-TABLE-WHEN-ATOM))
 (15 15 (:TYPE-PRESCRIPTION NATS=>CHARS))
 (15 15 (:TYPE-PRESCRIPTION DELETE-D-E))
 (12 12 (:TYPE-PRESCRIPTION NATP))
 (12 12 (:REWRITE NOT-INTERSECTP-LIST-WHEN-SUBSETP-1))
 (12 12 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-2 . 2))
 (12 6 (:REWRITE FAT32-ENTRY-MASK-OF-FAT32-UPDATE-LOWER-28))
 (10 10 (:TYPE-PRESCRIPTION MAKE-LIST-AC))
 (10 5 (:REWRITE DEFAULT-UNARY-MINUS))
 (10 5 (:REWRITE DEFAULT-*-1))
 (9 3 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-11))
 (8 8 (:REWRITE FOLD-CONSTS-IN-+))
 (6 6 (:TYPE-PRESCRIPTION FIND-N-FREE-CLUSTERS))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-67
 (2158 21 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-RIGHT))
 (2076 3 (:REWRITE CONSP-OF-FIND-N-FREE-CLUSTERS))
 (1760 89 (:DEFINITION FIND-D-E))
 (1733 351 (:TYPE-PRESCRIPTION PAINFUL-DEBUGGING-LEMMA-10))
 (1258 79 (:DEFINITION LEN))
 (1200 5 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (1065 5 (:REWRITE CONSP-OF-MAKE-LIST-AC))
 (1031 351 (:TYPE-PRESCRIPTION PAINFUL-DEBUGGING-LEMMA-9))
 (980 94 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (722 44 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-56))
 (664 135 (:REWRITE DEFAULT-<-2))
 (635 8 (:DEFINITION MAKE-LIST-AC))
 (610 5 (:DEFINITION DELETE-D-E))
 (606 3 (:REWRITE COUNT-FREE-CLUSTERS-OF-UPDATE-NTH))
 (604 94 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (559 15 (:REWRITE DELETE-D-E-CORRECTNESS-1))
 (551 205 (:REWRITE DEFAULT-CDR))
 (547 158 (:REWRITE STR::CONSP-OF-EXPLODE))
 (531 3 (:REWRITE FIND-N-FREE-CLUSTERS-WHEN-ZP))
 (462 6 (:REWRITE COUNT-FREE-CLUSTERS-OF-SET-INDICES-IN-FA-TABLE-1))
 (459 55 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (456 169 (:REWRITE DEFAULT-+-2))
 (380 60 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (351 351 (:TYPE-PRESCRIPTION CEILING))
 (325 25 (:REWRITE NOT-INTERSECTP-LIST-WHEN-SUBSETP-1))
 (324 6 (:LINEAR PAINFUL-DEBUGGING-LEMMA-10))
 (292 25 (:REWRITE NOT-INTERSECTP-LIST-OF-LOFAT-TO-HIFAT-HELPER))
 (246 74 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-8))
 (243 79 (:REWRITE FAT32-FILENAME-P-CORRECTNESS-1))
 (237 237 (:TYPE-PRESCRIPTION STR::TRUE-LISTP-OF-EXPLODE))
 (228 12 (:DEFINITION FREE-INDEX-LISTP))
 (201 90 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (198 169 (:REWRITE DEFAULT-+-1))
 (188 188 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (188 188 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (186 28 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (182 182 (:TYPE-PRESCRIPTION D-E-FILE-SIZE))
 (177 26 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (172 142 (:REWRITE DEFAULT-CAR))
 (168 168 (:TYPE-PRESCRIPTION FAT32-FILENAME-FIX))
 (162 162 (:TYPE-PRESCRIPTION FAT32-ENTRY-MASK))
 (158 79 (:REWRITE STR::EXPLODE-WHEN-NOT-STRINGP))
 (156 6 (:LINEAR PAINFUL-DEBUGGING-LEMMA-9))
 (144 135 (:REWRITE DEFAULT-<-1))
 (137 137 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-D-E-CC))
 (128 128 (:TYPE-PRESCRIPTION FAT32-FILENAME-P))
 (128 128 (:REWRITE FAT32-FILENAME-P-WHEN-MEMBER-EQUAL-OF-FAT32-FILENAME-LIST-P))
 (128 36 (:REWRITE FAT32-FILENAME-FIX-WHEN-FAT32-FILENAME-P))
 (120 10 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-MAKE-LIST-AC))
 (94 5 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-3))
 (93 93 (:TYPE-PRESCRIPTION COUNT-FREE-CLUSTERS))
 (89 89 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (88 28 (:REWRITE SUBSETP-WHEN-ATOM-RIGHT))
 (88 28 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (82 28 (:LINEAR D-E-FILE-SIZE-CORRECTNESS-1))
 (80 21 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-LEFT))
 (79 3 (:REWRITE NON-FREE-INDEX-LISTP-CORRECTNESS-2 . 2))
 (70 70 (:TYPE-PRESCRIPTION SUBSETP-EQUAL))
 (63 27 (:REWRITE NFIX-WHEN-ZP))
 (60 60 (:TYPE-PRESCRIPTION FREE-INDEX-LISTP))
 (60 20 (:REWRITE USEFUL-D-E-LIST-P-OF-CDR))
 (56 25 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-2 . 2))
 (55 25 (:REWRITE NOT-INTERSECTP-LIST-WHEN-ATOM))
 (50 5 (:REWRITE DEFAULT-*-2))
 (40 20 (:LINEAR HIFAT-TO-LOFAT-INVERSION-LEMMA-19))
 (40 9 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-18))
 (36 12 (:DEFINITION NATP))
 (28 28 (:REWRITE SUBSETP-TRANS2))
 (28 28 (:REWRITE SUBSETP-TRANS))
 (28 28 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (27 6 (:REWRITE SET-INDICES-IN-FA-TABLE-CORRECTNESS-3))
 (25 5 (:REWRITE INTERSECTP-OF-SELF))
 (20 5 (:REWRITE APPEND-WHEN-NOT-CONSP))
 (18 3 (:REWRITE SET-INDICES-IN-FA-TABLE-WHEN-ATOM))
 (16 1 (:REWRITE SUBSETP-CONS-2))
 (15 15 (:TYPE-PRESCRIPTION NATS=>CHARS))
 (15 15 (:TYPE-PRESCRIPTION DELETE-D-E))
 (12 12 (:TYPE-PRESCRIPTION NATP))
 (12 6 (:REWRITE FAT32-ENTRY-MASK-OF-FAT32-UPDATE-LOWER-28))
 (10 10 (:TYPE-PRESCRIPTION MAKE-LIST-AC))
 (10 5 (:REWRITE DEFAULT-UNARY-MINUS))
 (10 5 (:REWRITE DEFAULT-*-1))
 (9 3 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-11))
 (8 8 (:REWRITE FOLD-CONSTS-IN-+))
 (6 6 (:TYPE-PRESCRIPTION FIND-N-FREE-CLUSTERS))
 )
(D-E-CC-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-4
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 (1408 32 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-56))
 (1154 64 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (959 65 (:REWRITE ZP-OPEN))
 (760 76 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (672 32 (:REWRITE NOT-INTERSECTP-LIST-WHEN-SUBSETP-1))
 (637 637 (:TYPE-PRESCRIPTION D-E-FILE-SIZE))
 (632 164 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-8))
 (576 32 (:REWRITE NOT-INTERSECTP-LIST-OF-LOFAT-TO-HIFAT-HELPER))
 (516 49 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (512 16 (:DEFINITION FREE-INDEX-LISTP))
 (456 76 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (436 42 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (312 312 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-D-E-CC))
 (265 163 (:REWRITE DEFAULT-<-2))
 (257 98 (:LINEAR D-E-FILE-SIZE-CORRECTNESS-1))
 (243 105 (:REWRITE DEFAULT-CDR))
 (232 32 (:REWRITE SUBSETP-WHEN-ATOM-RIGHT))
 (232 32 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (216 73 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-5))
 (198 132 (:REWRITE DEFAULT-CAR))
 (196 24 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-RIGHT))
 (192 72 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (184 184 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (179 163 (:REWRITE DEFAULT-<-1))
 (174 38 (:REWRITE FAT32-FILENAME-FIX-WHEN-FAT32-FILENAME-P))
 (170 24 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-LEFT))
 (159 17 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (158 79 (:REWRITE D-E-CC-UNDER-IFF . 2))
 (152 152 (:TYPE-PRESCRIPTION FAT32-FILENAME-FIX))
 (152 152 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (150 83 (:REWRITE DEFAULT-+-2))
 (99 83 (:REWRITE DEFAULT-+-1))
 (99 9 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-13))
 (96 96 (:TYPE-PRESCRIPTION FAT32-ENTRY-MASK))
 (96 32 (:REWRITE NOT-INTERSECTP-LIST-WHEN-ATOM))
 (88 13 (:REWRITE D-E-CC-OF-UPDATE-DIR-CONTENTS-COINCIDENT))
 (81 81 (:TYPE-PRESCRIPTION ZP))
 (80 80 (:TYPE-PRESCRIPTION FREE-INDEX-LISTP))
 (80 16 (:REWRITE NFIX-WHEN-NATP))
 (76 76 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (68 68 (:TYPE-PRESCRIPTION FAT32-FILENAME-P))
 (68 68 (:REWRITE FAT32-FILENAME-P-WHEN-MEMBER-EQUAL-OF-FAT32-FILENAME-LIST-P))
 (64 16 (:REWRITE NFIX-WHEN-ZP))
 (48 16 (:DEFINITION NATP))
 (32 32 (:REWRITE SUBSETP-TRANS2))
 (32 32 (:REWRITE SUBSETP-TRANS))
 (32 32 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-2 . 2))
 (27 9 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-23))
 (18 18 (:REWRITE INTERSECT-WITH-SUBSET . 12))
 (18 18 (:REWRITE FLATTEN-SUBSET-NO-DUPLICATESP-LEMMA-1))
 (16 16 (:TYPE-PRESCRIPTION NATP))
 (9 3 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-26))
 )
(D-E-CC-OF-LOFAT-REMOVE-FILE-DISJOINT
 (1403 37 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-56))
 (1212 64 (:DEFINITION FIND-D-E))
 (831 35 (:REWRITE NOT-INTERSECTP-LIST-WHEN-SUBSETP-1))
 (696 32 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (686 1 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-59))
 (595 35 (:REWRITE NOT-INTERSECTP-LIST-OF-LOFAT-TO-HIFAT-HELPER))
 (593 65 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (560 164 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-8))
 (524 18 (:DEFINITION FREE-INDEX-LISTP))
 (512 44 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (390 390 (:TYPE-PRESCRIPTION D-E-FILE-SIZE))
 (359 2 (:REWRITE LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-2-LEMMA-2))
 (338 1 (:LINEAR HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E))
 (333 65 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (313 313 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-D-E-CC))
 (313 3 (:DEFINITION MEMBER-INTERSECTP-EQUAL))
 (295 44 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (259 44 (:REWRITE SUBSETP-WHEN-ATOM-RIGHT))
 (241 107 (:REWRITE DEFAULT-CDR))
 (234 6 (:REWRITE REMOVE-ASSOC-WHEN-ABSENT-1))
 (212 1 (:LINEAR HIFAT-ENTRY-COUNT-OF-REMOVE-ASSOC-EQUAL))
 (203 137 (:REWRITE DEFAULT-CAR))
 (184 67 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (179 107 (:REWRITE DEFAULT-<-2))
 (162 162 (:TYPE-PRESCRIPTION FAT32-FILENAME-FIX))
 (160 160 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (156 78 (:REWRITE D-E-CC-UNDER-IFF . 2))
 (155 53 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-5))
 (154 60 (:LINEAR D-E-FILE-SIZE-CORRECTNESS-1))
 (147 15 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-LEFT))
 (134 1 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-3))
 (130 130 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (125 2 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-1 . 1))
 (120 3 (:REWRITE DELETE-D-E-CORRECTNESS-1))
 (118 107 (:REWRITE DEFAULT-<-1))
 (117 1 (:DEFINITION DELETE-D-E))
 (110 110 (:TYPE-PRESCRIPTION SUBSETP-EQUAL))
 (108 108 (:TYPE-PRESCRIPTION FAT32-ENTRY-MASK))
 (104 2 (:DEFINITION REMOVE-ASSOC-EQUAL))
 (99 35 (:REWRITE NOT-INTERSECTP-LIST-WHEN-ATOM))
 (90 90 (:TYPE-PRESCRIPTION FREE-INDEX-LISTP))
 (82 22 (:REWRITE FAT32-FILENAME-FIX-WHEN-FAT32-FILENAME-P))
 (81 3 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-23))
 (78 18 (:TYPE-PRESCRIPTION ASSOC-WHEN-ZP-LEN))
 (74 15 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-RIGHT))
 (72 3 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-1))
 (68 37 (:REWRITE DEFAULT-+-2))
 (62 7 (:DEFINITION ASSOC-EQUAL))
 (50 1 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-6))
 (44 44 (:REWRITE SUBSETP-TRANS2))
 (44 44 (:REWRITE SUBSETP-TRANS))
 (44 37 (:REWRITE DEFAULT-+-1))
 (41 9 (:REWRITE NFIX-WHEN-NATP))
 (36 9 (:REWRITE NFIX-WHEN-ZP))
 (35 35 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-2 . 2))
 (30 30 (:TYPE-PRESCRIPTION FAT32-FILENAME-P))
 (30 30 (:REWRITE FAT32-FILENAME-P-WHEN-MEMBER-EQUAL-OF-FAT32-FILENAME-LIST-P))
 (23 9 (:DEFINITION NATP))
 (21 21 (:TYPE-PRESCRIPTION MEMBER-INTERSECTP-EQUAL))
 (21 7 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-4))
 (18 18 (:TYPE-PRESCRIPTION LOFAT-TO-HIFAT-HELPER-CORRECTNESS-1 . 2))
 (18 18 (:TYPE-PRESCRIPTION LEN))
 (14 14 (:REWRITE INTERSECT-WITH-SUBSET . 12))
 (14 14 (:REWRITE INTERSECT-WITH-SUBSET . 11))
 (14 14 (:REWRITE FLATTEN-SUBSET-NO-DUPLICATESP-LEMMA-1))
 (12 4 (:REWRITE USEFUL-D-E-LIST-P-OF-CDR))
 (10 10 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 2))
 (10 10 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 1))
 (9 9 (:TYPE-PRESCRIPTION NATP))
 (9 3 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-2))
 (7 7 (:REWRITE-QUOTED-CONSTANT FAT32-FILENAME-LIST-FIX-UNDER-FAT32-FILENAME-LIST-EQUIV))
 (7 7 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-3))
 (7 7 (:REWRITE MEMBER-INTERSECTP-WITH-SUBSET))
 (7 7 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-46))
 (6 3 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-93))
 (6 2 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-26))
 (3 3 (:TYPE-PRESCRIPTION DELETE-D-E))
 (3 1 (:REWRITE M1-FILE-ALIST-P-OF-LOFAT-TO-HIFAT-HELPER))
 (2 1 (:REWRITE DEFAULT-UNARY-MINUS))
 (1 1 (:TYPE-PRESCRIPTION HIFAT-NO-DUPS-P))
 (1 1 (:REWRITE HIFAT-NO-DUPS-P-OF-LOFAT-TO-HIFAT-HELPER))
 )
(D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-8
 (1520 76 (:DEFINITION FIND-D-E))
 (1408 32 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-56))
 (1154 64 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (959 65 (:REWRITE ZP-OPEN))
 (760 76 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (672 32 (:REWRITE NOT-INTERSECTP-LIST-WHEN-SUBSETP-1))
 (637 637 (:TYPE-PRESCRIPTION D-E-FILE-SIZE))
 (632 164 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-8))
 (576 32 (:REWRITE NOT-INTERSECTP-LIST-OF-LOFAT-TO-HIFAT-HELPER))
 (516 49 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (512 16 (:DEFINITION FREE-INDEX-LISTP))
 (456 76 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (436 42 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (312 312 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-D-E-CC))
 (265 163 (:REWRITE DEFAULT-<-2))
 (257 98 (:LINEAR D-E-FILE-SIZE-CORRECTNESS-1))
 (243 105 (:REWRITE DEFAULT-CDR))
 (232 32 (:REWRITE SUBSETP-WHEN-ATOM-RIGHT))
 (232 32 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (216 73 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-5))
 (198 132 (:REWRITE DEFAULT-CAR))
 (196 24 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-RIGHT))
 (192 72 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (184 184 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (179 163 (:REWRITE DEFAULT-<-1))
 (174 38 (:REWRITE FAT32-FILENAME-FIX-WHEN-FAT32-FILENAME-P))
 (170 24 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-LEFT))
 (159 17 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (158 79 (:REWRITE D-E-CC-UNDER-IFF . 2))
 (152 152 (:TYPE-PRESCRIPTION FAT32-FILENAME-FIX))
 (152 152 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (150 83 (:REWRITE DEFAULT-+-2))
 (99 83 (:REWRITE DEFAULT-+-1))
 (99 9 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-13))
 (96 96 (:TYPE-PRESCRIPTION FAT32-ENTRY-MASK))
 (96 32 (:REWRITE NOT-INTERSECTP-LIST-WHEN-ATOM))
 (81 81 (:TYPE-PRESCRIPTION ZP))
 (80 80 (:TYPE-PRESCRIPTION FREE-INDEX-LISTP))
 (80 16 (:REWRITE NFIX-WHEN-NATP))
 (76 76 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (68 68 (:TYPE-PRESCRIPTION FAT32-FILENAME-P))
 (68 68 (:REWRITE FAT32-FILENAME-P-WHEN-MEMBER-EQUAL-OF-FAT32-FILENAME-LIST-P))
 (64 16 (:REWRITE NFIX-WHEN-ZP))
 (48 16 (:DEFINITION NATP))
 (45 6 (:REWRITE D-E-CC-OF-UPDATE-DIR-CONTENTS-COINCIDENT))
 (32 32 (:REWRITE SUBSETP-TRANS2))
 (32 32 (:REWRITE SUBSETP-TRANS))
 (32 32 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-2 . 2))
 (27 9 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-23))
 (18 18 (:REWRITE INTERSECT-WITH-SUBSET . 12))
 (18 18 (:REWRITE FLATTEN-SUBSET-NO-DUPLICATESP-LEMMA-1))
 (16 16 (:TYPE-PRESCRIPTION NATP))
 (9 3 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-26))
 )
(D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT
 (1403 37 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-56))
 (1212 64 (:DEFINITION FIND-D-E))
 (831 35 (:REWRITE NOT-INTERSECTP-LIST-WHEN-SUBSETP-1))
 (696 32 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (686 1 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-59))
 (595 35 (:REWRITE NOT-INTERSECTP-LIST-OF-LOFAT-TO-HIFAT-HELPER))
 (593 65 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (560 164 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-8))
 (524 18 (:DEFINITION FREE-INDEX-LISTP))
 (512 44 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (390 390 (:TYPE-PRESCRIPTION D-E-FILE-SIZE))
 (359 2 (:REWRITE LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-2-LEMMA-2))
 (338 1 (:LINEAR HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E))
 (333 65 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (313 313 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-D-E-CC))
 (313 3 (:DEFINITION MEMBER-INTERSECTP-EQUAL))
 (295 44 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (259 44 (:REWRITE SUBSETP-WHEN-ATOM-RIGHT))
 (241 107 (:REWRITE DEFAULT-CDR))
 (234 6 (:REWRITE REMOVE-ASSOC-WHEN-ABSENT-1))
 (212 1 (:LINEAR HIFAT-ENTRY-COUNT-OF-REMOVE-ASSOC-EQUAL))
 (203 137 (:REWRITE DEFAULT-CAR))
 (184 67 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (179 107 (:REWRITE DEFAULT-<-2))
 (162 162 (:TYPE-PRESCRIPTION FAT32-FILENAME-FIX))
 (160 160 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (156 78 (:REWRITE D-E-CC-UNDER-IFF . 2))
 (155 53 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-5))
 (154 60 (:LINEAR D-E-FILE-SIZE-CORRECTNESS-1))
 (147 15 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-LEFT))
 (134 1 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-3))
 (130 130 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (125 2 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-1 . 1))
 (120 3 (:REWRITE DELETE-D-E-CORRECTNESS-1))
 (118 107 (:REWRITE DEFAULT-<-1))
 (117 1 (:DEFINITION DELETE-D-E))
 (110 110 (:TYPE-PRESCRIPTION SUBSETP-EQUAL))
 (108 108 (:TYPE-PRESCRIPTION FAT32-ENTRY-MASK))
 (104 2 (:DEFINITION REMOVE-ASSOC-EQUAL))
 (99 35 (:REWRITE NOT-INTERSECTP-LIST-WHEN-ATOM))
 (90 90 (:TYPE-PRESCRIPTION FREE-INDEX-LISTP))
 (82 22 (:REWRITE FAT32-FILENAME-FIX-WHEN-FAT32-FILENAME-P))
 (81 3 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-23))
 (78 18 (:TYPE-PRESCRIPTION ASSOC-WHEN-ZP-LEN))
 (74 15 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-RIGHT))
 (72 3 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-1))
 (68 37 (:REWRITE DEFAULT-+-2))
 (62 7 (:DEFINITION ASSOC-EQUAL))
 (50 1 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-6))
 (44 44 (:REWRITE SUBSETP-TRANS2))
 (44 44 (:REWRITE SUBSETP-TRANS))
 (44 37 (:REWRITE DEFAULT-+-1))
 (41 9 (:REWRITE NFIX-WHEN-NATP))
 (36 9 (:REWRITE NFIX-WHEN-ZP))
 (35 35 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-2 . 2))
 (30 30 (:TYPE-PRESCRIPTION FAT32-FILENAME-P))
 (30 30 (:REWRITE FAT32-FILENAME-P-WHEN-MEMBER-EQUAL-OF-FAT32-FILENAME-LIST-P))
 (23 9 (:DEFINITION NATP))
 (21 21 (:TYPE-PRESCRIPTION MEMBER-INTERSECTP-EQUAL))
 (21 7 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-4))
 (18 18 (:TYPE-PRESCRIPTION LOFAT-TO-HIFAT-HELPER-CORRECTNESS-1 . 2))
 (18 18 (:TYPE-PRESCRIPTION LEN))
 (14 14 (:REWRITE INTERSECT-WITH-SUBSET . 12))
 (14 14 (:REWRITE INTERSECT-WITH-SUBSET . 11))
 (14 14 (:REWRITE FLATTEN-SUBSET-NO-DUPLICATESP-LEMMA-1))
 (12 4 (:REWRITE USEFUL-D-E-LIST-P-OF-CDR))
 (10 10 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 2))
 (10 10 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 1))
 (9 9 (:TYPE-PRESCRIPTION NATP))
 (9 3 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-2))
 (7 7 (:REWRITE-QUOTED-CONSTANT FAT32-FILENAME-LIST-FIX-UNDER-FAT32-FILENAME-LIST-EQUIV))
 (7 7 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-3))
 (7 7 (:REWRITE MEMBER-INTERSECTP-WITH-SUBSET))
 (7 7 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-46))
 (6 3 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-93))
 (6 2 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-26))
 (3 3 (:TYPE-PRESCRIPTION DELETE-D-E))
 (3 1 (:REWRITE M1-FILE-ALIST-P-OF-LOFAT-TO-HIFAT-HELPER))
 (2 1 (:REWRITE DEFAULT-UNARY-MINUS))
 (1 1 (:TYPE-PRESCRIPTION HIFAT-NO-DUPS-P))
 (1 1 (:REWRITE HIFAT-NO-DUPS-P-OF-LOFAT-TO-HIFAT-HELPER))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-16)
(D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-10)
(D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-11
 (1180 14 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-13))
 (1160 58 (:DEFINITION FIND-D-E))
 (580 58 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (490 14 (:DEFINITION NO-DUPLICATESP-EQUAL))
 (348 58 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (326 18 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (266 14 (:REWRITE ZP-OPEN))
 (223 129 (:REWRITE DEFAULT-CDR))
 (194 102 (:REWRITE DEFAULT-+-2))
 (182 182 (:TYPE-PRESCRIPTION D-E-FILE-SIZE))
 (174 174 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (174 58 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (167 113 (:REWRITE DEFAULT-CAR))
 (160 10 (:DEFINITION LEN))
 (145 29 (:REWRITE FAT32-FILENAME-FIX-WHEN-FAT32-FILENAME-P))
 (130 130 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (126 14 (:REWRITE SUBSETP-CAR-MEMBER))
 (116 116 (:TYPE-PRESCRIPTION FAT32-FILENAME-FIX))
 (116 116 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (114 114 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-D-E-CC))
 (112 102 (:REWRITE DEFAULT-+-1))
 (98 28 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (97 58 (:REWRITE DEFAULT-<-2))
 (90 2 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-3))
 (77 77 (:TYPE-PRESCRIPTION USEFUL-D-E-LIST-P))
 (77 77 (:REWRITE USEFUL-D-E-LIST-P-OF-MAKE-D-E-LIST))
 (74 74 (:TYPE-PRESCRIPTION FAT32-FILENAME-P))
 (74 74 (:REWRITE FAT32-FILENAME-P-WHEN-MEMBER-EQUAL-OF-FAT32-FILENAME-LIST-P))
 (70 70 (:TYPE-PRESCRIPTION NO-DUPLICATESP-EQUAL))
 (70 28 (:LINEAR D-E-FILE-SIZE-CORRECTNESS-1))
 (70 20 (:REWRITE STR::CONSP-OF-EXPLODE))
 (69 58 (:REWRITE DEFAULT-<-1))
 (63 21 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-5))
 (56 14 (:REWRITE MEMBER-WHEN-ATOM))
 (44 44 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-8))
 (42 42 (:TYPE-PRESCRIPTION SUBSETP-EQUAL))
 (42 14 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-23))
 (42 10 (:REWRITE FAT32-FILENAME-P-CORRECTNESS-1))
 (35 15 (:LINEAR LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-1-LEMMA-1))
 (33 15 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-8))
 (30 30 (:TYPE-PRESCRIPTION STR::TRUE-LISTP-OF-EXPLODE))
 (28 28 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (28 14 (:REWRITE SET-EQUIV-ASYM))
 (20 10 (:REWRITE STR::EXPLODE-WHEN-NOT-STRINGP))
 (16 16 (:TYPE-PRESCRIPTION NATS=>STRING))
 (14 14 (:TYPE-PRESCRIPTION ZP))
 (14 14 (:TYPE-PRESCRIPTION SET-EQUIV))
 (14 14 (:REWRITE SUBSETP-OF-CDR))
 (14 14 (:REWRITE SUBSETP-MEMBER . 3))
 (14 14 (:REWRITE SUBSETP-MEMBER . 1))
 (14 14 (:REWRITE NON-FREE-INDEX-LISTP-CORRECTNESS-2 . 1))
 (14 14 (:REWRITE INTERSECTP-MEMBER . 3))
 (14 14 (:REWRITE INTERSECTP-MEMBER . 2))
 (6 2 (:REWRITE INTERSECTP-OF-SELF))
 (2 2 (:TYPE-PRESCRIPTION INTERSECTP-EQUAL))
 )
(D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-12
 (5878 19 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (5769 9 (:REWRITE CONSP-OF-MAKE-LIST-AC))
 (3919 262 (:DEFINITION LEN))
 (3048 12 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-RIGHT))
 (3045 129 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-8))
 (2502 36 (:LINEAR MAKE-CLUSTERS-CORRECTNESS-2))
 (2039 28 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-13))
 (1625 128 (:REWRITE ZP-OPEN))
 (1341 414 (:REWRITE STR::CONSP-OF-EXPLODE))
 (1331 402 (:REWRITE DEFAULT-CDR))
 (1110 207 (:REWRITE FAT32-FILENAME-P-CORRECTNESS-1))
 (1008 18 (:LINEAR LEN-OF-EXPLODE-WHEN-M1-FILE-CONTENTS-P-1))
 (980 28 (:DEFINITION NO-DUPLICATESP-EQUAL))
 (972 54 (:DEFINITION FIND-D-E))
 (948 6 (:REWRITE D-E-CC-OF-UPDATE-DIR-CONTENTS-COINCIDENT))
 (926 467 (:REWRITE DEFAULT-+-2))
 (809 71 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (630 18 (:REWRITE M1-FILE-CONTENTS-P-WHEN-STRINGP))
 (621 621 (:TYPE-PRESCRIPTION STR::TRUE-LISTP-OF-EXPLODE))
 (551 19 (:DEFINITION MAKE-LIST-AC))
 (540 54 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (512 467 (:REWRITE DEFAULT-+-1))
 (496 220 (:REWRITE DEFAULT-<-2))
 (429 429 (:TYPE-PRESCRIPTION D-E-FILE-SIZE))
 (414 207 (:REWRITE STR::EXPLODE-WHEN-NOT-STRINGP))
 (330 110 (:TYPE-PRESCRIPTION MAKE-CLUSTERS-OF-NIL))
 (324 54 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (299 299 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-D-E-CC))
 (288 18 (:LINEAR MAKE-CLUSTERS-CORRECTNESS-3))
 (283 10 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-3))
 (241 140 (:REWRITE DEFAULT-CAR))
 (230 220 (:REWRITE DEFAULT-<-1))
 (208 62 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (195 41 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (177 66 (:LINEAR D-E-FILE-SIZE-CORRECTNESS-1))
 (175 10 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-56))
 (164 3 (:REWRITE D-E-CC-OF-UPDATE-DIR-CONTENTS))
 (157 157 (:REWRITE SUBSETP-MEMBER . 1))
 (140 140 (:TYPE-PRESCRIPTION NO-DUPLICATESP-EQUAL))
 (135 57 (:LINEAR HIFAT-TO-LOFAT-INVERSION-LEMMA-19))
 (120 45 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-5))
 (120 10 (:REWRITE NOT-INTERSECTP-LIST-OF-LOFAT-TO-HIFAT-HELPER))
 (118 118 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (115 13 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (112 28 (:REWRITE MEMBER-WHEN-ATOM))
 (110 110 (:TYPE-PRESCRIPTION MAKE-CLUSTERS))
 (110 55 (:REWRITE DEFAULT-*-2))
 (110 55 (:REWRITE DEFAULT-*-1))
 (108 108 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (107 107 (:TYPE-PRESCRIPTION ZP))
 (100 5 (:DEFINITION FREE-INDEX-LISTP))
 (95 35 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (90 18 (:DEFINITION UNSIGNED-BYTE-P))
 (90 3 (:REWRITE CONSP-OF-FAT32-BUILD-INDEX-LIST))
 (84 21 (:LINEAR NATP-OF-CLUSTER-SIZE))
 (78 28 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-23))
 (72 72 (:TYPE-PRESCRIPTION HIFAT-BOUNDED-FILE-ALIST-P))
 (72 18 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-MAKE-LIST-AC))
 (72 18 (:DEFINITION INTEGER-RANGE-P))
 (56 28 (:REWRITE SET-EQUIV-ASYM))
 (54 54 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (54 18 (:LINEAR LEN-WHEN-HIFAT-BOUNDED-FILE-ALIST-P . 2))
 (54 18 (:LINEAR LEN-WHEN-HIFAT-BOUNDED-FILE-ALIST-P . 1))
 (50 10 (:REWRITE NFIX-WHEN-NATP))
 (46 19 (:REWRITE APPEND-WHEN-NOT-CONSP))
 (45 12 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-LEFT))
 (40 10 (:REWRITE NFIX-WHEN-ZP))
 (38 19 (:REWRITE DEFAULT-UNARY-MINUS))
 (36 36 (:LINEAR LEN-WHEN-FAT32-FILENAME-LIST-PREFIXP))
 (30 30 (:TYPE-PRESCRIPTION FAT32-ENTRY-MASK))
 (30 10 (:REWRITE INTERSECTP-OF-SELF))
 (30 10 (:DEFINITION NATP))
 (28 28 (:TYPE-PRESCRIPTION SET-EQUIV))
 (28 28 (:REWRITE SUBSETP-OF-CDR))
 (28 28 (:REWRITE SUBSETP-MEMBER . 3))
 (28 28 (:REWRITE NON-FREE-INDEX-LISTP-CORRECTNESS-2 . 1))
 (28 28 (:REWRITE INTERSECTP-MEMBER . 3))
 (28 28 (:REWRITE INTERSECTP-MEMBER . 2))
 (27 27 (:TYPE-PRESCRIPTION NATS=>CHARS))
 (25 25 (:TYPE-PRESCRIPTION FREE-INDEX-LISTP))
 (25 10 (:REWRITE NOT-INTERSECTP-LIST-WHEN-ATOM))
 (21 21 (:TYPE-PRESCRIPTION FAT32$C-P))
 (21 21 (:REWRITE LOFAT-FS-P-CORRECTNESS-1))
 (19 19 (:REWRITE FOLD-CONSTS-IN-+))
 (18 18 (:TYPE-PRESCRIPTION MAKE-LIST-AC))
 (18 18 (:TYPE-PRESCRIPTION M1-FILE-CONTENTS-P))
 (18 18 (:LINEAR POSITION-WHEN-MEMBER))
 (18 18 (:LINEAR POSITION-EQUAL-AC-WHEN-MEMBER))
 (18 18 (:LINEAR LENGTH-OF-D-E-CC-CONTENTS . 1))
 (10 10 (:TYPE-PRESCRIPTION NATP))
 (10 10 (:REWRITE NOT-INTERSECTP-LIST-WHEN-SUBSETP-1))
 (10 10 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-2 . 2))
 (10 10 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-SUBSETP-EQUAL))
 (9 3 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-26))
 (6 6 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-FAT32-BUILD-INDEX-LIST))
 (5 5 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-NOT-CONSP))
 (3 3 (:REWRITE INTERSECT-WITH-SUBSET . 12))
 (3 3 (:REWRITE INTERSECT-WITH-SUBSET . 11))
 (3 3 (:REWRITE FLATTEN-SUBSET-NO-DUPLICATESP-LEMMA-1))
 )
(D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-13
 (198 11 (:DEFINITION FIND-D-E))
 (154 6 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (110 11 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (98 2 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-8))
 (66 11 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (52 6 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
 (35 6 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (33 33 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (33 11 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (22 22 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (22 22 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (19 17 (:REWRITE DEFAULT-CDR))
 (17 15 (:REWRITE DEFAULT-CAR))
 (13 13 (:TYPE-PRESCRIPTION USEFUL-D-E-LIST-P))
 (13 13 (:REWRITE USEFUL-D-E-LIST-P-OF-MAKE-D-E-LIST))
 (11 11 (:TYPE-PRESCRIPTION D-E-P))
 (11 11 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (6 2 (:LINEAR LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-1-LEMMA-1))
 (5 3 (:REWRITE DEFAULT-<-2))
 (5 3 (:REWRITE DEFAULT-<-1))
 (4 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-SUBSETP-EQUAL))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (2 1 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (1 1 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-NOT-CONSP))
 )
(D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-5
 (108 6 (:DEFINITION FIND-D-E))
 (76 3 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (60 6 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (36 6 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (31 4 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (26 4 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
 (18 18 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (18 6 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (12 12 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (12 12 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (12 10 (:REWRITE DEFAULT-CDR))
 (12 10 (:REWRITE DEFAULT-CAR))
 (6 6 (:TYPE-PRESCRIPTION USEFUL-D-E-LIST-P))
 (6 6 (:TYPE-PRESCRIPTION D-E-P))
 (6 6 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (6 6 (:REWRITE USEFUL-D-E-LIST-P-OF-MAKE-D-E-LIST))
 (2 2 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-SUBSETP-EQUAL))
 (2 1 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (1 1 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-NOT-CONSP))
 )
(D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-14
 (198 11 (:DEFINITION FIND-D-E))
 (154 6 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (110 11 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (98 2 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-8))
 (66 11 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (52 6 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
 (35 6 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (33 33 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (33 11 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (22 22 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (22 22 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (18 16 (:REWRITE DEFAULT-CDR))
 (17 15 (:REWRITE DEFAULT-CAR))
 (13 13 (:TYPE-PRESCRIPTION USEFUL-D-E-LIST-P))
 (13 13 (:REWRITE USEFUL-D-E-LIST-P-OF-MAKE-D-E-LIST))
 (11 11 (:TYPE-PRESCRIPTION D-E-P))
 (11 11 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (6 2 (:LINEAR LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-1-LEMMA-1))
 (4 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-SUBSETP-EQUAL))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (2 1 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (1 1 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-NOT-CONSP))
 )
(D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT
 (1492 84 (:DEFINITION FIND-D-E))
 (1305 3 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (1282 2 (:REWRITE CONSP-OF-MAKE-LIST-AC))
 (820 84 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (556 8 (:LINEAR MAKE-CLUSTERS-CORRECTNESS-2))
 (551 38 (:DEFINITION LEN))
 (484 84 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (453 29 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-56))
 (372 20 (:REWRITE LENGTH-WHEN-STRINGP))
 (336 27 (:REWRITE NOT-INTERSECTP-LIST-OF-LOFAT-TO-HIFAT-HELPER))
 (330 14 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (319 165 (:REWRITE DEFAULT-CDR))
 (281 14 (:DEFINITION FREE-INDEX-LISTP))
 (257 2 (:REWRITE LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-2-LEMMA-2))
 (240 240 (:TYPE-PRESCRIPTION LEN))
 (231 84 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (228 8 (:REWRITE LEN-OF-NATS=>CHARS))
 (226 35 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (224 4 (:LINEAR LEN-OF-EXPLODE-WHEN-M1-FILE-CONTENTS-P-1))
 (220 8 (:REWRITE LEN-OF-CLEAR-D-E))
 (212 8 (:REWRITE LEN-OF-STRING=>NATS))
 (211 3 (:DEFINITION MEMBER-INTERSECTP-EQUAL))
 (194 114 (:REWRITE DEFAULT-<-2))
 (188 188 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (182 182 (:TYPE-PRESCRIPTION D-E-FILE-SIZE))
 (174 174 (:TYPE-PRESCRIPTION STRINGP-OF-D-E-CC-CONTENTS))
 (171 130 (:REWRITE DEFAULT-CAR))
 (168 168 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (165 54 (:REWRITE STR::CONSP-OF-EXPLODE))
 (153 27 (:REWRITE FAT32-FILENAME-P-CORRECTNESS-1))
 (144 74 (:REWRITE DEFAULT-+-2))
 (140 4 (:REWRITE M1-FILE-CONTENTS-P-WHEN-STRINGP))
 (132 27 (:REWRITE NOT-INTERSECTP-LIST-WHEN-SUBSETP-1))
 (123 114 (:REWRITE DEFAULT-<-1))
 (112 4 (:LINEAR LENGTH-OF-D-E-CC-CONTENTS . 3))
 (112 4 (:LINEAR LENGTH-OF-D-E-CC-CONTENTS . 2))
 (111 56 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-8))
 (110 22 (:REWRITE NFIX-WHEN-NATP))
 (101 101 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-D-E-CC))
 (91 2 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-1 . 1))
 (88 22 (:REWRITE NFIX-WHEN-ZP))
 (87 3 (:DEFINITION MAKE-LIST-AC))
 (85 74 (:REWRITE DEFAULT-+-1))
 (84 84 (:TYPE-PRESCRIPTION FAT32-ENTRY-MASK))
 (81 81 (:TYPE-PRESCRIPTION STR::TRUE-LISTP-OF-EXPLODE))
 (78 28 (:LINEAR D-E-FILE-SIZE-CORRECTNESS-1))
 (71 13 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (70 70 (:TYPE-PRESCRIPTION ZP))
 (70 70 (:TYPE-PRESCRIPTION FREE-INDEX-LISTP))
 (66 22 (:TYPE-PRESCRIPTION MAKE-CLUSTERS-OF-NIL))
 (66 22 (:DEFINITION NATP))
 (65 27 (:REWRITE NOT-INTERSECTP-LIST-WHEN-ATOM))
 (64 4 (:LINEAR MAKE-CLUSTERS-CORRECTNESS-3))
 (57 17 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-5))
 (54 27 (:REWRITE STR::EXPLODE-WHEN-NOT-STRINGP))
 (52 20 (:REWRITE STR::COERCE-TO-LIST-REMOVAL))
 (34 34 (:TYPE-PRESCRIPTION NATS=>STRING))
 (33 8 (:REWRITE SUBSETP-WHEN-ATOM-RIGHT))
 (28 12 (:LINEAR HIFAT-TO-LOFAT-INVERSION-LEMMA-19))
 (28 8 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (27 27 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-2 . 2))
 (22 22 (:TYPE-PRESCRIPTION NATP))
 (22 22 (:TYPE-PRESCRIPTION MAKE-CLUSTERS))
 (22 11 (:REWRITE DEFAULT-*-2))
 (22 11 (:REWRITE DEFAULT-*-1))
 (21 21 (:TYPE-PRESCRIPTION MEMBER-INTERSECTP-EQUAL))
 (21 7 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-4))
 (20 20 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-SUBSETP-EQUAL))
 (20 4 (:DEFINITION UNSIGNED-BYTE-P))
 (18 18 (:REWRITE SUBSETP-MEMBER . 1))
 (16 16 (:TYPE-PRESCRIPTION HIFAT-BOUNDED-FILE-ALIST-P))
 (16 4 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-MAKE-LIST-AC))
 (16 4 (:LINEAR NATP-OF-CLUSTER-SIZE))
 (16 4 (:DEFINITION INTEGER-RANGE-P))
 (14 1 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-LEFT))
 (12 4 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-26))
 (12 4 (:LINEAR LEN-WHEN-HIFAT-BOUNDED-FILE-ALIST-P . 2))
 (12 4 (:LINEAR LEN-WHEN-HIFAT-BOUNDED-FILE-ALIST-P . 1))
 (10 10 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 2))
 (10 10 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 1))
 (9 3 (:REWRITE APPEND-WHEN-NOT-CONSP))
 (8 8 (:REWRITE SUBSETP-TRANS2))
 (8 8 (:REWRITE SUBSETP-TRANS))
 (8 8 (:REWRITE EXPLODE-OF-NATS=>STRING))
 (8 8 (:LINEAR LEN-WHEN-FAT32-FILENAME-LIST-PREFIXP))
 (7 7 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-3))
 (7 7 (:REWRITE MEMBER-INTERSECTP-WITH-SUBSET))
 (7 7 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-46))
 (6 6 (:TYPE-PRESCRIPTION NATS=>CHARS))
 (6 3 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-93))
 (6 3 (:REWRITE DEFAULT-UNARY-MINUS))
 (4 4 (:TYPE-PRESCRIPTION MAKE-LIST-AC))
 (4 4 (:TYPE-PRESCRIPTION M1-FILE-CONTENTS-P))
 (4 4 (:TYPE-PRESCRIPTION FAT32$C-P))
 (4 4 (:REWRITE LOFAT-FS-P-CORRECTNESS-1))
 (4 4 (:REWRITE FIND-D-E-CORRECTNESS-1))
 (4 4 (:LINEAR POSITION-WHEN-MEMBER))
 (4 4 (:LINEAR POSITION-EQUAL-AC-WHEN-MEMBER))
 (4 4 (:LINEAR LENGTH-OF-D-E-CC-CONTENTS . 1))
 (4 1 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-RIGHT))
 (3 3 (:REWRITE FOLD-CONSTS-IN-+))
 )
(LOFAT-FS-P-OF-LOFAT-REMOVE-FILE-LEMMA-2
 (120 6 (:DEFINITION FIND-D-E))
 (78 4 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
 (60 6 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (36 6 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (18 18 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (18 6 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (12 12 (:TYPE-PRESCRIPTION FAT32-FILENAME-FIX))
 (12 12 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (12 12 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (10 2 (:REWRITE FAT32-FILENAME-FIX-WHEN-FAT32-FILENAME-P))
 (8 8 (:REWRITE DEFAULT-CAR))
 (6 6 (:TYPE-PRESCRIPTION USEFUL-D-E-LIST-P))
 (6 6 (:TYPE-PRESCRIPTION D-E-P))
 (6 6 (:TYPE-PRESCRIPTION D-E-LIST-P))
 (6 6 (:REWRITE USEFUL-D-E-LIST-P-OF-MAKE-D-E-LIST))
 (6 6 (:REWRITE DEFAULT-CDR))
 (4 4 (:TYPE-PRESCRIPTION FAT32-FILENAME-P))
 (4 4 (:TYPE-PRESCRIPTION D-E-DIRECTORY-P))
 (4 4 (:REWRITE FAT32-FILENAME-P-WHEN-MEMBER-EQUAL-OF-FAT32-FILENAME-LIST-P))
 (2 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 )
(LOFAT-FS-P-OF-LOFAT-REMOVE-FILE-LEMMA-4
 (1140 57 (:DEFINITION FIND-D-E))
 (570 57 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (497 30 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (342 57 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (174 38 (:REWRITE FAT32-FILENAME-FIX-WHEN-FAT32-FILENAME-P))
 (171 171 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (171 57 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (159 17 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (130 130 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (130 20 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-8))
 (114 114 (:TYPE-PRESCRIPTION FAT32-FILENAME-FIX))
 (114 114 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (100 58 (:REWRITE DEFAULT-+-2))
 (95 95 (:REWRITE DEFAULT-CAR))
 (78 78 (:TYPE-PRESCRIPTION USEFUL-D-E-LIST-P))
 (78 78 (:REWRITE USEFUL-D-E-LIST-P-OF-MAKE-D-E-LIST))
 (74 58 (:REWRITE DEFAULT-+-1))
 (68 68 (:TYPE-PRESCRIPTION FAT32-FILENAME-P))
 (68 68 (:REWRITE FAT32-FILENAME-P-WHEN-MEMBER-EQUAL-OF-FAT32-FILENAME-LIST-P))
 (68 68 (:REWRITE DEFAULT-CDR))
 (57 57 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (49 33 (:REWRITE DEFAULT-<-1))
 (44 20 (:LINEAR LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-1-LEMMA-1))
 (37 33 (:REWRITE DEFAULT-<-2))
 (36 36 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (27 9 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-23))
 (27 9 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-13))
 (18 18 (:TYPE-PRESCRIPTION GOOD-ROOT-D-E-P))
 )
(LOFAT-FS-P-OF-LOFAT-REMOVE-FILE
 (816 42 (:DEFINITION FIND-D-E))
 (396 42 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (228 42 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (126 42 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (102 102 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (102 102 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (84 84 (:TYPE-PRESCRIPTION FAT32-FILENAME-FIX))
 (84 84 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (80 16 (:REWRITE FAT32-FILENAME-FIX-WHEN-FAT32-FILENAME-P))
 (70 40 (:REWRITE DEFAULT-+-2))
 (58 58 (:REWRITE DEFAULT-CAR))
 (53 53 (:REWRITE DEFAULT-CDR))
 (53 38 (:REWRITE DEFAULT-<-2))
 (53 38 (:REWRITE DEFAULT-<-1))
 (50 40 (:REWRITE DEFAULT-+-1))
 (47 47 (:TYPE-PRESCRIPTION USEFUL-D-E-LIST-P))
 (47 47 (:REWRITE USEFUL-D-E-LIST-P-OF-MAKE-D-E-LIST))
 (32 32 (:TYPE-PRESCRIPTION FAT32-FILENAME-P))
 (32 32 (:REWRITE FAT32-FILENAME-P-WHEN-MEMBER-EQUAL-OF-FAT32-FILENAME-LIST-P))
 (17 17 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (13 7 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-8))
 (11 7 (:LINEAR LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-1-LEMMA-1))
 )
(LOFAT-TO-HIFAT-HELPER-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-7
 (1520 76 (:DEFINITION FIND-D-E))
 (1216 16 (:DEFINITION MEMBER-INTERSECTP-EQUAL))
 (1024 64 (:REWRITE NOT-INTERSECTP-LIST-OF-LOFAT-TO-HIFAT-HELPER))
 (896 32 (:DEFINITION FREE-INDEX-LISTP))
 (760 76 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (735 102 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-8))
 (734 19 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-93))
 (683 102 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (608 64 (:REWRITE NOT-INTERSECTP-LIST-WHEN-SUBSETP-1))
 (560 64 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-2 . 2))
 (521 25 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (516 49 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (486 78 (:REWRITE ZP-OPEN))
 (456 76 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (402 216 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (363 137 (:REWRITE DEFAULT-CDR))
 (323 99 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (288 64 (:REWRITE NOT-INTERSECTP-LIST-WHEN-ATOM))
 (286 286 (:TYPE-PRESCRIPTION D-E-FILE-SIZE))
 (280 56 (:REWRITE NFIX-WHEN-NATP))
 (249 82 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-5))
 (246 164 (:REWRITE DEFAULT-CAR))
 (237 189 (:REWRITE DEFAULT-<-2))
 (224 56 (:REWRITE NFIX-WHEN-ZP))
 (205 189 (:REWRITE DEFAULT-<-1))
 (198 99 (:REWRITE D-E-CC-UNDER-IFF . 2))
 (192 192 (:TYPE-PRESCRIPTION FAT32-ENTRY-MASK))
 (188 188 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-D-E-CC))
 (179 99 (:REWRITE SUBSETP-WHEN-ATOM-RIGHT))
 (174 38 (:REWRITE FAT32-FILENAME-FIX-WHEN-FAT32-FILENAME-P))
 (168 168 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (168 56 (:DEFINITION NATP))
 (160 160 (:TYPE-PRESCRIPTION FREE-INDEX-LISTP))
 (159 17 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (152 152 (:TYPE-PRESCRIPTION FAT32-FILENAME-FIX))
 (152 152 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (134 134 (:TYPE-PRESCRIPTION ZP))
 (124 70 (:REWRITE DEFAULT-+-2))
 (122 44 (:LINEAR D-E-FILE-SIZE-CORRECTNESS-1))
 (99 99 (:REWRITE SUBSETP-TRANS2))
 (99 99 (:REWRITE SUBSETP-TRANS))
 (99 9 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-13))
 (86 70 (:REWRITE DEFAULT-+-1))
 (76 76 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (68 68 (:TYPE-PRESCRIPTION FAT32-FILENAME-P))
 (68 68 (:REWRITE FAT32-FILENAME-P-WHEN-MEMBER-EQUAL-OF-FAT32-FILENAME-LIST-P))
 (56 56 (:TYPE-PRESCRIPTION NATP))
 (48 48 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 1))
 (45 3 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-LEFT))
 (42 3 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-RIGHT))
 (36 36 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (35 35 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-46))
 (32 32 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-3))
 (32 32 (:REWRITE MEMBER-INTERSECTP-WITH-SUBSET))
 (27 9 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-23))
 (15 3 (:REWRITE D-E-CC-OF-UPDATE-DIR-CONTENTS-COINCIDENT))
 (9 3 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-26))
 )
(LOFAT-TO-HIFAT-HELPER-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-9
 (360 18 (:DEFINITION FIND-D-E))
 (199 10 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (180 18 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (154 4 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-8))
 (140 4 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-56))
 (110 9 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
 (108 18 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (96 4 (:REWRITE NOT-INTERSECTP-LIST-OF-LOFAT-TO-HIFAT-HELPER))
 (88 2 (:DEFINITION FREE-INDEX-LISTP))
 (68 9 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (62 8 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-8))
 (56 26 (:REWRITE DEFAULT-CDR))
 (54 54 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (54 18 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (46 2 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (42 6 (:REWRITE ZP-OPEN))
 (40 40 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (39 27 (:REWRITE DEFAULT-CAR))
 (36 36 (:TYPE-PRESCRIPTION FAT32-FILENAME-FIX))
 (36 36 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (32 4 (:REWRITE NOT-INTERSECTP-LIST-WHEN-ATOM))
 (26 26 (:TYPE-PRESCRIPTION D-E-FILE-SIZE))
 (25 19 (:REWRITE DEFAULT-<-1))
 (25 5 (:REWRITE FAT32-FILENAME-FIX-WHEN-FAT32-FILENAME-P))
 (24 19 (:REWRITE DEFAULT-<-2))
 (22 22 (:REWRITE USEFUL-D-E-LIST-P-OF-MAKE-D-E-LIST))
 (20 4 (:REWRITE NFIX-WHEN-NATP))
 (18 18 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (18 18 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (18 6 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-5))
 (16 8 (:REWRITE D-E-CC-UNDER-IFF . 2))
 (16 4 (:REWRITE NFIX-WHEN-ZP))
 (14 14 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-D-E-CC))
 (12 12 (:TYPE-PRESCRIPTION FAT32-ENTRY-MASK))
 (12 4 (:LINEAR LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-1-LEMMA-1))
 (12 4 (:DEFINITION NATP))
 (11 1 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-13))
 (10 10 (:TYPE-PRESCRIPTION ZP))
 (10 10 (:TYPE-PRESCRIPTION FREE-INDEX-LISTP))
 (10 10 (:TYPE-PRESCRIPTION FAT32-FILENAME-P))
 (10 10 (:REWRITE FAT32-FILENAME-P-WHEN-MEMBER-EQUAL-OF-FAT32-FILENAME-LIST-P))
 (10 4 (:LINEAR D-E-FILE-SIZE-CORRECTNESS-1))
 (8 8 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (4 4 (:TYPE-PRESCRIPTION NATP))
 (4 4 (:REWRITE NOT-INTERSECTP-LIST-WHEN-SUBSETP-1))
 (4 4 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-2 . 2))
 (3 1 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-23))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE DEFAULT-+-1))
 )
(LOFAT-TO-HIFAT-HELPER-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-5
 (360 18 (:DEFINITION FIND-D-E))
 (199 10 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (180 18 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (154 4 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-8))
 (140 4 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-56))
 (110 9 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
 (108 18 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (96 4 (:REWRITE NOT-INTERSECTP-LIST-OF-LOFAT-TO-HIFAT-HELPER))
 (88 2 (:DEFINITION FREE-INDEX-LISTP))
 (68 9 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (62 8 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-8))
 (58 28 (:REWRITE DEFAULT-CDR))
 (54 54 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (54 18 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (46 2 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (42 6 (:REWRITE ZP-OPEN))
 (40 40 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (39 27 (:REWRITE DEFAULT-CAR))
 (36 36 (:TYPE-PRESCRIPTION FAT32-FILENAME-FIX))
 (36 36 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (34 23 (:REWRITE DEFAULT-<-2))
 (32 4 (:REWRITE NOT-INTERSECTP-LIST-WHEN-ATOM))
 (29 23 (:REWRITE DEFAULT-<-1))
 (26 26 (:TYPE-PRESCRIPTION D-E-FILE-SIZE))
 (25 5 (:REWRITE FAT32-FILENAME-FIX-WHEN-FAT32-FILENAME-P))
 (22 22 (:REWRITE USEFUL-D-E-LIST-P-OF-MAKE-D-E-LIST))
 (22 2 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-13))
 (20 4 (:REWRITE NFIX-WHEN-NATP))
 (18 18 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (18 18 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (18 6 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-5))
 (16 8 (:REWRITE D-E-CC-UNDER-IFF . 2))
 (16 4 (:REWRITE NFIX-WHEN-ZP))
 (14 14 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-D-E-CC))
 (14 7 (:REWRITE DEFAULT-+-2))
 (12 12 (:TYPE-PRESCRIPTION FAT32-ENTRY-MASK))
 (12 4 (:LINEAR LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-1-LEMMA-1))
 (12 4 (:DEFINITION NATP))
 (10 10 (:TYPE-PRESCRIPTION ZP))
 (10 10 (:TYPE-PRESCRIPTION FREE-INDEX-LISTP))
 (10 10 (:TYPE-PRESCRIPTION FAT32-FILENAME-P))
 (10 10 (:REWRITE FAT32-FILENAME-P-WHEN-MEMBER-EQUAL-OF-FAT32-FILENAME-LIST-P))
 (10 4 (:LINEAR D-E-FILE-SIZE-CORRECTNESS-1))
 (8 8 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (7 7 (:REWRITE DEFAULT-+-1))
 (6 2 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-23))
 (4 4 (:TYPE-PRESCRIPTION NATP))
 (4 4 (:REWRITE NOT-INTERSECTP-LIST-WHEN-SUBSETP-1))
 (4 4 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-2 . 2))
 )
(LOFAT-TO-HIFAT-HELPER-OF-LOFAT-REMOVE-FILE-DISJOINT
 (2256 120 (:DEFINITION FIND-D-E))
 (1953 24 (:DEFINITION MEMBER-INTERSECTP-EQUAL))
 (1344 39 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-93))
 (1117 121 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (1104 77 (:REWRITE NOT-INTERSECTP-LIST-OF-LOFAT-TO-HIFAT-HELPER))
 (949 39 (:DEFINITION FREE-INDEX-LISTP))
 (948 77 (:REWRITE NOT-INTERSECTP-LIST-WHEN-SUBSETP-1))
 (942 131 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (760 112 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-8))
 (686 1 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-59))
 (633 121 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (511 77 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-2 . 2))
 (488 130 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (437 437 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (416 205 (:REWRITE DEFAULT-CDR))
 (380 124 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (350 16 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (340 160 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (338 1 (:LINEAR HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E))
 (322 242 (:REWRITE DEFAULT-CAR))
 (309 2 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-2))
 (281 77 (:REWRITE NOT-INTERSECTP-LIST-WHEN-ATOM))
 (268 130 (:REWRITE SUBSETP-WHEN-ATOM-RIGHT))
 (264 101 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 1))
 (256 256 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (242 242 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (234 234 (:TYPE-PRESCRIPTION FAT32-FILENAME-FIX))
 (234 234 (:TYPE-PRESCRIPTION FAT32-ENTRY-MASK))
 (234 6 (:REWRITE REMOVE-ASSOC-WHEN-ABSENT-1))
 (222 73 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-5))
 (213 2 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-1 . 1))
 (212 106 (:REWRITE D-E-CC-UNDER-IFF . 2))
 (212 1 (:LINEAR HIFAT-ENTRY-COUNT-OF-REMOVE-ASSOC-EQUAL))
 (209 209 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-D-E-CC))
 (195 195 (:TYPE-PRESCRIPTION FREE-INDEX-LISTP))
 (195 195 (:TYPE-PRESCRIPTION D-E-FILE-SIZE))
 (147 105 (:REWRITE DEFAULT-<-2))
 (134 1 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-3))
 (130 130 (:REWRITE SUBSETP-TRANS2))
 (130 130 (:REWRITE SUBSETP-TRANS))
 (123 105 (:REWRITE DEFAULT-<-1))
 (120 3 (:REWRITE DELETE-D-E-CORRECTNESS-1))
 (117 1 (:DEFINITION DELETE-D-E))
 (105 29 (:REWRITE FAT32-FILENAME-FIX-WHEN-FAT32-FILENAME-P))
 (104 2 (:DEFINITION REMOVE-ASSOC-EQUAL))
 (91 19 (:REWRITE NFIX-WHEN-NATP))
 (81 3 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-23))
 (79 63 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-3))
 (79 30 (:LINEAR D-E-FILE-SIZE-CORRECTNESS-1))
 (78 18 (:TYPE-PRESCRIPTION ASSOC-WHEN-ZP-LEN))
 (76 19 (:REWRITE NFIX-WHEN-ZP))
 (72 3 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-1))
 (66 36 (:REWRITE DEFAULT-+-2))
 (64 64 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-46))
 (62 7 (:DEFINITION ASSOC-EQUAL))
 (53 19 (:DEFINITION NATP))
 (50 1 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-6))
 (49 49 (:REWRITE MEMBER-INTERSECTP-WITH-SUBSET))
 (43 36 (:REWRITE DEFAULT-+-1))
 (38 38 (:TYPE-PRESCRIPTION FAT32-FILENAME-P))
 (38 38 (:REWRITE FAT32-FILENAME-P-WHEN-MEMBER-EQUAL-OF-FAT32-FILENAME-LIST-P))
 (25 25 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (19 19 (:TYPE-PRESCRIPTION NATP))
 (18 18 (:TYPE-PRESCRIPTION LOFAT-TO-HIFAT-HELPER-CORRECTNESS-1 . 2))
 (18 18 (:TYPE-PRESCRIPTION LEN))
 (18 6 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-4))
 (12 4 (:REWRITE USEFUL-D-E-LIST-P-OF-CDR))
 (9 3 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-26))
 (9 3 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-2))
 (7 7 (:REWRITE-QUOTED-CONSTANT FAT32-FILENAME-LIST-FIX-UNDER-FAT32-FILENAME-LIST-EQUIV))
 (3 3 (:TYPE-PRESCRIPTION DELETE-D-E))
 (3 1 (:REWRITE M1-FILE-ALIST-P-OF-LOFAT-TO-HIFAT-HELPER))
 (2 1 (:REWRITE DEFAULT-UNARY-MINUS))
 (1 1 (:TYPE-PRESCRIPTION HIFAT-NO-DUPS-P))
 (1 1 (:REWRITE HIFAT-NO-DUPS-P-OF-LOFAT-TO-HIFAT-HELPER))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-18
 (198 11 (:DEFINITION FIND-D-E))
 (154 6 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (110 11 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (98 2 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-8))
 (66 11 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (52 6 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
 (35 6 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (33 33 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (33 11 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (22 22 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (22 22 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (18 16 (:REWRITE DEFAULT-CDR))
 (17 15 (:REWRITE DEFAULT-CAR))
 (13 13 (:TYPE-PRESCRIPTION USEFUL-D-E-LIST-P))
 (13 13 (:REWRITE USEFUL-D-E-LIST-P-OF-MAKE-D-E-LIST))
 (11 11 (:TYPE-PRESCRIPTION D-E-P))
 (11 11 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (6 2 (:LINEAR LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-1-LEMMA-1))
 (4 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-SUBSETP-EQUAL))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (2 1 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (1 1 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-NOT-CONSP))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-19
 (108 6 (:DEFINITION FIND-D-E))
 (76 3 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (60 6 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (36 6 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (31 4 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (26 4 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
 (18 18 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (18 6 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (12 12 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (12 12 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (12 10 (:REWRITE DEFAULT-CDR))
 (12 10 (:REWRITE DEFAULT-CAR))
 (6 6 (:TYPE-PRESCRIPTION USEFUL-D-E-LIST-P))
 (6 6 (:TYPE-PRESCRIPTION D-E-P))
 (6 6 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (6 6 (:REWRITE USEFUL-D-E-LIST-P-OF-MAKE-D-E-LIST))
 (2 2 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-SUBSETP-EQUAL))
 (2 1 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (1 1 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-NOT-CONSP))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-20
 (198 11 (:DEFINITION FIND-D-E))
 (154 6 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (110 11 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (98 2 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-8))
 (66 11 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (52 6 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
 (35 6 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (33 33 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (33 11 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (22 22 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (22 22 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (19 17 (:REWRITE DEFAULT-CDR))
 (17 15 (:REWRITE DEFAULT-CAR))
 (13 13 (:TYPE-PRESCRIPTION USEFUL-D-E-LIST-P))
 (13 13 (:REWRITE USEFUL-D-E-LIST-P-OF-MAKE-D-E-LIST))
 (11 11 (:TYPE-PRESCRIPTION D-E-P))
 (11 11 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (6 2 (:LINEAR LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-1-LEMMA-1))
 (5 3 (:REWRITE DEFAULT-<-2))
 (5 3 (:REWRITE DEFAULT-<-1))
 (4 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-SUBSETP-EQUAL))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (2 1 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (1 1 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-NOT-CONSP))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-21
 (2185 124 (:DEFINITION FIND-D-E))
 (1210 125 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (710 125 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (620 1 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-59))
 (510 59 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
 (488 31 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-56))
 (425 17 (:LINEAR LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-1-LEMMA-1))
 (401 17 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-8))
 (355 29 (:REWRITE NOT-INTERSECTP-LIST-OF-LOFAT-TO-HIFAT-HELPER))
 (306 1 (:LINEAR HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E))
 (305 15 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (296 15 (:DEFINITION FREE-INDEX-LISTP))
 (279 220 (:REWRITE DEFAULT-CAR))
 (274 274 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (258 194 (:REWRITE DEFAULT-CDR))
 (257 2 (:REWRITE LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-2-LEMMA-2))
 (250 250 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (235 85 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (211 3 (:DEFINITION MEMBER-INTERSECTP-EQUAL))
 (209 49 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (198 6 (:REWRITE REMOVE-ASSOC-WHEN-ABSENT-1))
 (184 1 (:LINEAR HIFAT-ENTRY-COUNT-OF-REMOVE-ASSOC-EQUAL))
 (169 169 (:TYPE-PRESCRIPTION D-E-FILE-SIZE))
 (165 25 (:LINEAR LOFAT-FS-P-CORRECTNESS-1))
 (129 29 (:REWRITE NOT-INTERSECTP-LIST-WHEN-SUBSETP-1))
 (126 84 (:REWRITE DEFAULT-<-2))
 (114 3 (:REWRITE DELETE-D-E-CORRECTNESS-1))
 (114 1 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-3))
 (111 1 (:DEFINITION DELETE-D-E))
 (108 108 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-D-E-CC))
 (105 60 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-8))
 (96 84 (:REWRITE DEFAULT-<-1))
 (92 27 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (91 19 (:REWRITE NFIX-WHEN-NATP))
 (91 2 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-1 . 1))
 (90 90 (:TYPE-PRESCRIPTION FAT32-ENTRY-MASK))
 (82 46 (:REWRITE DEFAULT-+-2))
 (80 2 (:DEFINITION REMOVE-ASSOC-EQUAL))
 (76 19 (:REWRITE NFIX-WHEN-ZP))
 (75 75 (:TYPE-PRESCRIPTION FREE-INDEX-LISTP))
 (75 3 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-23))
 (70 29 (:REWRITE NOT-INTERSECTP-LIST-WHEN-ATOM))
 (69 69 (:TYPE-PRESCRIPTION ZP))
 (69 26 (:LINEAR D-E-FILE-SIZE-CORRECTNESS-1))
 (66 3 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-1))
 (64 12 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (60 18 (:TYPE-PRESCRIPTION ASSOC-WHEN-ZP-LEN))
 (57 46 (:REWRITE DEFAULT-+-1))
 (53 19 (:DEFINITION NATP))
 (50 18 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-5))
 (48 7 (:DEFINITION ASSOC-EQUAL))
 (46 1 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-6))
 (40 10 (:REWRITE COMMUTATIVITY-OF-+))
 (29 29 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-2 . 2))
 (28 8 (:REWRITE SUBSETP-WHEN-ATOM-RIGHT))
 (28 8 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (25 25 (:TYPE-PRESCRIPTION FAT-ENTRY-COUNT))
 (22 22 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-SUBSETP-EQUAL))
 (21 21 (:TYPE-PRESCRIPTION MEMBER-INTERSECTP-EQUAL))
 (21 7 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-4))
 (19 19 (:TYPE-PRESCRIPTION NATP))
 (18 18 (:TYPE-PRESCRIPTION LOFAT-TO-HIFAT-HELPER-CORRECTNESS-1 . 2))
 (18 18 (:TYPE-PRESCRIPTION LEN))
 (14 1 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-LEFT))
 (12 4 (:REWRITE USEFUL-D-E-LIST-P-OF-CDR))
 (11 11 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-NOT-CONSP))
 (10 10 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 2))
 (10 10 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 1))
 (9 3 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-2))
 (8 8 (:REWRITE SUBSETP-TRANS2))
 (8 8 (:REWRITE SUBSETP-TRANS))
 (7 7 (:REWRITE-QUOTED-CONSTANT FAT32-FILENAME-LIST-FIX-UNDER-FAT32-FILENAME-LIST-EQUIV))
 (7 7 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-3))
 (7 7 (:REWRITE MEMBER-INTERSECTP-WITH-SUBSET))
 (7 7 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-46))
 (6 3 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-93))
 (6 2 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-26))
 (4 1 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-RIGHT))
 (3 3 (:TYPE-PRESCRIPTION DELETE-D-E))
 (3 1 (:REWRITE M1-FILE-ALIST-P-OF-LOFAT-TO-HIFAT-HELPER))
 (2 1 (:REWRITE DEFAULT-UNARY-MINUS))
 (1 1 (:TYPE-PRESCRIPTION HIFAT-NO-DUPS-P))
 (1 1 (:REWRITE HIFAT-NO-DUPS-P-OF-LOFAT-TO-HIFAT-HELPER))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-25)
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-30)
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-33
 (920 46 (:DEFINITION FIND-D-E))
 (748 3 (:REWRITE CLEAR-CC-CORRECTNESS-3))
 (733 3 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-3))
 (460 46 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (366 3 (:REWRITE D-E-CC-CONTENTS-OF-UPDATE-DIR-CONTENTS-COINCIDENT))
 (328 3 (:REWRITE D-E-CC-CONTENTS-OF-UPDATE-DIR-CONTENTS-DISJOINT))
 (276 46 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (165 3 (:LINEAR LEN-OF-EXPLODE-WHEN-M1-FILE-CONTENTS-P-1))
 (156 6 (:REWRITE LENGTH-WHEN-STRINGP))
 (147 49 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (144 144 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (144 9 (:DEFINITION LEN))
 (111 75 (:REWRITE DEFAULT-CDR))
 (102 102 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (101 7 (:REWRITE ZP-OPEN))
 (100 55 (:REWRITE DEFAULT-+-2))
 (100 20 (:REWRITE FAT32-FILENAME-FIX-WHEN-FAT32-FILENAME-P))
 (99 3 (:REWRITE M1-FILE-CONTENTS-P-WHEN-STRINGP))
 (99 3 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-LEFT))
 (92 92 (:TYPE-PRESCRIPTION FAT32-FILENAME-FIX))
 (92 92 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (91 3 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-RIGHT))
 (90 3 (:REWRITE LEN-OF-NATS=>CHARS))
 (90 3 (:REWRITE CONSP-OF-FAT32-BUILD-INDEX-LIST))
 (87 3 (:REWRITE LEN-OF-CLEAR-D-E))
 (84 3 (:REWRITE LEN-OF-STRING=>NATS))
 (81 3 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (73 55 (:REWRITE DEFAULT-<-2))
 (69 69 (:TYPE-PRESCRIPTION USEFUL-D-E-LIST-P))
 (69 69 (:REWRITE USEFUL-D-E-LIST-P-OF-MAKE-D-E-LIST))
 (69 55 (:REWRITE DEFAULT-<-1))
 (66 66 (:TYPE-PRESCRIPTION STRINGP-OF-D-E-CC-CONTENTS))
 (66 66 (:REWRITE DEFAULT-CAR))
 (65 55 (:REWRITE DEFAULT-+-1))
 (63 18 (:REWRITE STR::CONSP-OF-EXPLODE))
 (54 54 (:TYPE-PRESCRIPTION D-E-FILE-SIZE))
 (52 52 (:TYPE-PRESCRIPTION FAT32-FILENAME-P))
 (52 52 (:REWRITE FAT32-FILENAME-P-WHEN-MEMBER-EQUAL-OF-FAT32-FILENAME-LIST-P))
 (48 48 (:TYPE-PRESCRIPTION INTEGERP-OF-D-E-CC-CONTENTS))
 (48 3 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-8))
 (44 44 (:TYPE-PRESCRIPTION GOOD-ROOT-D-E-P))
 (36 36 (:TYPE-PRESCRIPTION LEN))
 (36 16 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-23))
 (36 16 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-13))
 (36 9 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-5))
 (36 8 (:LINEAR D-E-FILE-SIZE-CORRECTNESS-1))
 (34 3 (:REWRITE D-E-CC-UNDER-IFF . 2))
 (33 9 (:REWRITE FAT32-FILENAME-P-CORRECTNESS-1))
 (30 3 (:LINEAR LENGTH-OF-D-E-CC-CONTENTS . 3))
 (29 13 (:LINEAR LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-1-LEMMA-1))
 (27 27 (:TYPE-PRESCRIPTION STR::TRUE-LISTP-OF-EXPLODE))
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 (23 23 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (21 3 (:REWRITE GET-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-5 . 1))
 (18 9 (:REWRITE STR::EXPLODE-WHEN-NOT-STRINGP))
 (18 6 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-4))
 (18 6 (:REWRITE STR::COERCE-TO-LIST-REMOVAL))
 (18 3 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-3))
 (15 3 (:DEFINITION UNSIGNED-BYTE-P))
 (14 14 (:REWRITE FIND-D-E-CORRECTNESS-1))
 (12 12 (:TYPE-PRESCRIPTION HIFAT-BOUNDED-FILE-ALIST-P))
 (12 3 (:LINEAR NATP-OF-CLUSTER-SIZE))
 (12 3 (:DEFINITION INTEGER-RANGE-P))
 (9 3 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-26))
 (9 3 (:LINEAR LENGTH-OF-D-E-CC-CONTENTS . 2))
 (9 3 (:LINEAR LENGTH-OF-D-E-CC-CONTENTS . 1))
 (9 3 (:LINEAR LEN-WHEN-HIFAT-BOUNDED-FILE-ALIST-P . 2))
 (9 3 (:LINEAR LEN-WHEN-HIFAT-BOUNDED-FILE-ALIST-P . 1))
 (9 3 (:LINEAR HIFAT-TO-LOFAT-INVERSION-LEMMA-19))
 (6 6 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-FAT32-BUILD-INDEX-LIST))
 (6 6 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-D-E-CC))
 (6 6 (:TYPE-PRESCRIPTION NATS=>STRING))
 (6 6 (:TYPE-PRESCRIPTION INTERSECTP-EQUAL))
 (6 6 (:LINEAR LEN-WHEN-FAT32-FILENAME-LIST-PREFIXP))
 (3 3 (:TYPE-PRESCRIPTION ZP))
 (3 3 (:TYPE-PRESCRIPTION M1-FILE-CONTENTS-P))
 (3 3 (:TYPE-PRESCRIPTION FAT32$C-P))
 (3 3 (:REWRITE LOFAT-FS-P-CORRECTNESS-1))
 (3 3 (:REWRITE INTERSECT-WITH-SUBSET . 12))
 (3 3 (:REWRITE INTERSECT-WITH-SUBSET . 11))
 (3 3 (:REWRITE FLATTEN-SUBSET-NO-DUPLICATESP-LEMMA-1))
 (3 3 (:REWRITE EXPLODE-OF-NATS=>STRING))
 (3 3 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-7 . 1))
 (3 3 (:LINEAR POSITION-WHEN-MEMBER))
 (3 3 (:LINEAR POSITION-EQUAL-AC-WHEN-MEMBER))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-2
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 (433 79 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (237 79 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (196 196 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (178 178 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (158 158 (:TYPE-PRESCRIPTION FAT32-FILENAME-FIX))
 (158 158 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (145 29 (:REWRITE FAT32-FILENAME-FIX-WHEN-FAT32-FILENAME-P))
 (108 108 (:REWRITE DEFAULT-CAR))
 (101 101 (:REWRITE DEFAULT-CDR))
 (100 57 (:REWRITE DEFAULT-+-2))
 (89 89 (:TYPE-PRESCRIPTION USEFUL-D-E-LIST-P))
 (89 89 (:REWRITE USEFUL-D-E-LIST-P-OF-MAKE-D-E-LIST))
 (80 59 (:REWRITE DEFAULT-<-2))
 (80 59 (:REWRITE DEFAULT-<-1))
 (71 57 (:REWRITE DEFAULT-+-1))
 (58 58 (:TYPE-PRESCRIPTION FAT32-FILENAME-P))
 (58 58 (:REWRITE FAT32-FILENAME-P-WHEN-MEMBER-EQUAL-OF-FAT32-FILENAME-LIST-P))
 (25 25 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (23 11 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-8))
 (19 11 (:LINEAR LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-1-LEMMA-1))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-28
 (108 6 (:DEFINITION FIND-D-E))
 (76 3 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (60 6 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (36 6 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (31 4 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (26 4 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
 (21 21 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
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 (12 12 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (12 12 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (8 8 (:REWRITE DEFAULT-CDR))
 (8 8 (:REWRITE DEFAULT-CAR))
 (6 6 (:TYPE-PRESCRIPTION USEFUL-D-E-LIST-P))
 (6 6 (:TYPE-PRESCRIPTION D-E-P))
 (6 6 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (6 6 (:REWRITE USEFUL-D-E-LIST-P-OF-MAKE-D-E-LIST))
 (5 2 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (2 2 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-SUBSETP-EQUAL))
 (2 1 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (1 1 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-NOT-CONSP))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-34)
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-36
 (108 6 (:DEFINITION FIND-D-E))
 (72 4 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
 (60 6 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (36 6 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (18 18 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
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 (12 12 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (12 12 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (8 8 (:REWRITE DEFAULT-CAR))
 (6 6 (:TYPE-PRESCRIPTION USEFUL-D-E-LIST-P))
 (6 6 (:TYPE-PRESCRIPTION D-E-P))
 (6 6 (:TYPE-PRESCRIPTION D-E-LIST-P))
 (6 6 (:REWRITE USEFUL-D-E-LIST-P-OF-MAKE-D-E-LIST))
 (6 6 (:REWRITE DEFAULT-CDR))
 (4 4 (:TYPE-PRESCRIPTION D-E-DIRECTORY-P))
 (2 2 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-SUBSETP-EQUAL))
 (2 1 (:REWRITE SUBSETP-WHEN-SUBSETP))
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 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-37
 (3041 170 (:DEFINITION FIND-D-E))
 (1876 180 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (1856 57 (:REWRITE REMOVE-ASSOC-WHEN-ABSENT-1))
 (1156 180 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (1107 10 (:DEFINITION DELETE-D-E))
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 (760 19 (:DEFINITION REMOVE-ASSOC-EQUAL))
 (719 9 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-1))
 (504 110 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (477 427 (:REWRITE DEFAULT-CAR))
 (444 34 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-56))
 (438 30 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (402 129 (:TYPE-PRESCRIPTION ASSOC-WHEN-ZP-LEN))
 (374 38 (:REWRITE ZP-OPEN))
 (360 360 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (343 293 (:REWRITE DEFAULT-CDR))
 (340 340 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (312 129 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (300 20 (:REWRITE NOT-INTERSECTP-LIST-OF-LOFAT-TO-HIFAT-HELPER))
 (273 47 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (268 43 (:DEFINITION ASSOC-EQUAL))
 (260 10 (:DEFINITION FREE-INDEX-LISTP))
 (234 234 (:TYPE-PRESCRIPTION D-E-FILE-SIZE))
 (232 10 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-2))
 (187 187 (:TYPE-PRESCRIPTION ZP))
 (173 5 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-23))
 (170 170 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (148 46 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-8))
 (139 103 (:REWRITE DEFAULT-<-2))
 (129 129 (:TYPE-PRESCRIPTION LEN))
 (124 72 (:REWRITE DEFAULT-+-2))
 (116 103 (:REWRITE DEFAULT-<-1))
 (114 38 (:REWRITE USEFUL-D-E-LIST-P-OF-CDR))
 (102 36 (:LINEAR D-E-FILE-SIZE-CORRECTNESS-1))
 (100 20 (:REWRITE NFIX-WHEN-NATP))
 (92 72 (:REWRITE DEFAULT-+-1))
 (82 82 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-D-E-CC))
 (80 20 (:REWRITE NFIX-WHEN-ZP))
 (70 20 (:REWRITE NOT-INTERSECTP-LIST-WHEN-ATOM))
 (60 60 (:TYPE-PRESCRIPTION FAT32-ENTRY-MASK))
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 (58 58 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (50 50 (:TYPE-PRESCRIPTION FREE-INDEX-LISTP))
 (43 43 (:REWRITE-QUOTED-CONSTANT FAT32-FILENAME-LIST-FIX-UNDER-FAT32-FILENAME-LIST-EQUIV))
 (30 30 (:TYPE-PRESCRIPTION DELETE-D-E))
 (28 3 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-RIGHT))
 (20 20 (:TYPE-PRESCRIPTION NATP))
 (20 20 (:REWRITE NOT-INTERSECTP-LIST-WHEN-SUBSETP-1))
 (20 20 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-2 . 2))
 (20 20 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-SUBSETP-EQUAL))
 (18 3 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-LEFT))
 (11 5 (:REWRITE M1-FILE-HIFAT-FILE-ALIST-FIX-NORMALISATION))
 (9 3 (:REWRITE D-E-CC-OF-UPDATE-DIR-CONTENTS-COINCIDENT))
 (5 5 (:TYPE-PRESCRIPTION M1-FILE))
 (5 5 (:TYPE-PRESCRIPTION HIFAT-FILE-ALIST-FIX))
 (4 4 (:REWRITE-QUOTED-CONSTANT M1-FILE-CONTENTS-FIX-UNDER-M1-FILE-CONTENTS-EQUIV))
 (2 1 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (1 1 (:TYPE-PRESCRIPTION STRINGP-OF-D-E-CC-CONTENTS))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-38
 (216 12 (:DEFINITION FIND-D-E))
 (120 12 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (72 12 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (72 4 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
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 (44 2 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-8))
 (36 12 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (36 9 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (30 4 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (24 24 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (24 24 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
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 (14 5 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (12 12 (:TYPE-PRESCRIPTION D-E-P))
 (12 12 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
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 (2 2 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-SUBSETP-EQUAL))
 (2 2 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (2 1 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (1 1 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-NOT-CONSP))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-39
 (72 4 (:DEFINITION FIND-D-E))
 (40 4 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (28 3 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (24 4 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (12 12 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (12 4 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (8 8 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (8 8 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (7 7 (:REWRITE DEFAULT-CAR))
 (6 6 (:REWRITE DEFAULT-CDR))
 (4 4 (:TYPE-PRESCRIPTION USEFUL-D-E-LIST-P))
 (4 4 (:TYPE-PRESCRIPTION D-E-P))
 (4 4 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (4 4 (:REWRITE USEFUL-D-E-LIST-P-OF-MAKE-D-E-LIST))
 (3 3 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
 (2 2 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-SUBSETP-EQUAL))
 (2 2 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (2 1 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (1 1 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-NOT-CONSP))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-40
 (342 19 (:DEFINITION FIND-D-E))
 (190 19 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (124 10 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (114 19 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (59 7 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (57 57 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (57 19 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (38 38 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (38 38 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (34 20 (:REWRITE DEFAULT-+-2))
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 (26 26 (:REWRITE USEFUL-D-E-LIST-P-OF-MAKE-D-E-LIST))
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 (19 19 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (15 7 (:LINEAR LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-1-LEMMA-1))
 (13 13 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (13 7 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-8))
 (11 8 (:REWRITE DEFAULT-<-1))
 (8 8 (:REWRITE DEFAULT-<-2))
 (6 6 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-SUBSETP-EQUAL))
 (3 3 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-NOT-CONSP))
 (2 1 (:REWRITE SUBSETP-WHEN-SUBSETP))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-17)
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-15
 (147 12 (:REWRITE PUT-ASSOC-EQUAL-WITHOUT-CHANGE . 2))
 (132 6 (:DEFINITION PUT-ASSOC-EQUAL))
 (81 27 (:TYPE-PRESCRIPTION ASSOC-WHEN-ZP-LEN))
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 (27 27 (:TYPE-PRESCRIPTION LEN))
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 (15 12 (:REWRITE DEFAULT-<-2))
 (12 12 (:TYPE-PRESCRIPTION USEFUL-D-E-LIST-P))
 (12 12 (:REWRITE DEFAULT-<-1))
 (9 9 (:REWRITE-QUOTED-CONSTANT FAT32-FILENAME-LIST-FIX-UNDER-FAT32-FILENAME-LIST-EQUIV))
 (9 3 (:DEFINITION NATP))
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 (3 3 (:TYPE-PRESCRIPTION NATP))
 (1 1 (:LINEAR POSITION-WHEN-MEMBER-OF-TAKE))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-72
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 (109061 82094 (:REWRITE DEFAULT-+-2))
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 (96306 96306 (:TYPE-PRESCRIPTION FAT32-ENTRY-MASK))
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 (40860 36 (:REWRITE SUBSETP-OF-APPEND-WHEN-SUBSET-OF-EITHER))
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 (32594 4920 (:REWRITE SUBDIR-CONTENTS-P-WHEN-ZERO-LENGTH))
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 (29331 29331 (:REWRITE SUBSETP-TRANS2))
 (29331 29331 (:REWRITE SUBSETP-TRANS))
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 (16877 16829 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-3))
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 (9956 9956 (:TYPE-PRESCRIPTION FAT32-FILENAME-P))
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 (9847 9847 (:REWRITE INTERSECTP-MEMBER . 3))
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 (854 854 (:REWRITE TAKE-WHEN-ATOM))
 (848 848 (:REWRITE-QUOTED-CONSTANT FAT32-FILENAME-LIST-FIX-UNDER-FAT32-FILENAME-LIST-EQUIV))
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 (754 29 (:REWRITE LENGTH-WHEN-STRINGP))
 (725 29 (:LINEAR LENGTH-OF-D-E-CC-CONTENTS . 3))
 (641 641 (:TYPE-PRESCRIPTION STRINGP-OF-D-E-CC-CONTENTS))
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 (290 29 (:DEFINITION UNSIGNED-BYTE-P))
 (261 261 (:TYPE-PRESCRIPTION STR::TRUE-LISTP-OF-EXPLODE))
 (261 29 (:DEFINITION INTEGER-RANGE-P))
 (255 85 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (176 176 (:REWRITE D-E-FILENAME-OF-D-E-FIX))
 (174 87 (:REWRITE STR::EXPLODE-WHEN-NOT-STRINGP))
 (116 116 (:TYPE-PRESCRIPTION HIFAT-BOUNDED-FILE-ALIST-P))
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 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-22
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 (53 53 (:TYPE-PRESCRIPTION ZP))
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 (18 18 (:TYPE-PRESCRIPTION D-E-LIST-P))
 (18 18 (:REWRITE D-E-LIST-P-WHEN-SUBSETP-EQUAL))
 (18 6 (:REWRITE LOFAT-TO-HIFAT-HELPER-CORRECTNESS-3))
 (15 15 (:REWRITE-QUOTED-CONSTANT FAT32-FILENAME-LIST-FIX-UNDER-FAT32-FILENAME-LIST-EQUIV))
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 (12 12 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (12 12 (:REWRITE DEFAULT-<-1))
 (12 12 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (9 9 (:TYPE-PRESCRIPTION FIND-D-E-CORRECTNESS-1))
 (9 9 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (9 9 (:REWRITE D-E-LIST-P-WHEN-NOT-CONSP))
 (9 3 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-2))
 (9 3 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (9 3 (:DEFINITION NATP))
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 (6 3 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (4 4 (:REWRITE ZP-OPEN))
 (3 3 (:TYPE-PRESCRIPTION NATP))
 (3 3 (:TYPE-PRESCRIPTION D-E-DIRECTORY-P))
 (1 1 (:LINEAR POSITION-WHEN-MEMBER-OF-TAKE))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-2
 (2333 169 (:DEFINITION FIND-D-E))
 (1852 6 (:LINEAR HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E))
 (1317 175 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (1294 36 (:REWRITE REMOVE-ASSOC-WHEN-ABSENT-1))
 (1253 2 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-59))
 (1198 6 (:LINEAR HIFAT-ENTRY-COUNT-OF-REMOVE-ASSOC-EQUAL))
 (974 18 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-1))
 (946 6 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-3))
 (865 82 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (629 5 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-56))
 (617 175 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (612 18 (:REWRITE DELETE-D-E-CORRECTNESS-1))
 (594 6 (:DEFINITION DELETE-D-E))
 (593 1 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-38))
 (480 12 (:DEFINITION REMOVE-ASSOC-EQUAL))
 (420 87 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
 (360 108 (:TYPE-PRESCRIPTION ASSOC-WHEN-ZP-LEN))
 (350 350 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (350 350 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (339 339 (:REWRITE DEFAULT-CAR))
 (306 18 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-23))
 (288 42 (:DEFINITION ASSOC-EQUAL))
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 (216 6 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-6))
 (191 191 (:TYPE-PRESCRIPTION FIND-D-E-CORRECTNESS-1))
 (175 175 (:TYPE-PRESCRIPTION D-E-P))
 (169 169 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
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 (140 140 (:TYPE-PRESCRIPTION ZP))
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 (48 24 (:REWRITE DEFAULT-+-2))
 (42 42 (:REWRITE-QUOTED-CONSTANT FAT32-FILENAME-LIST-FIX-UNDER-FAT32-FILENAME-LIST-EQUIV))
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 (16 16 (:TYPE-PRESCRIPTION NATP))
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 (12 12 (:TYPE-PRESCRIPTION FAT32-ENTRY-MASK))
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 (12 2 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-5))
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 (6 6 (:TYPE-PRESCRIPTION M1-FILE-ALIST-P))
 (6 6 (:TYPE-PRESCRIPTION HIFAT-NO-DUPS-P))
 (6 6 (:REWRITE M1-FILE-ALIST-P-OF-LOFAT-TO-HIFAT-HELPER))
 (6 6 (:REWRITE HIFAT-NO-DUPS-P-OF-LOFAT-TO-HIFAT-HELPER))
 (6 2 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-26))
 (6 2 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (6 2 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-4))
 (5 5 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (4 4 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-D-E-CC))
 (4 4 (:REWRITE NOT-INTERSECTP-LIST-WHEN-SUBSETP-1))
 (4 4 (:REWRITE NOT-INTERSECTP-LIST-WHEN-ATOM))
 (3 3 (:REWRITE SUBSETP-WHEN-ATOM-RIGHT))
 (3 3 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (3 3 (:REWRITE SUBSETP-TRANS2))
 (3 3 (:REWRITE SUBSETP-TRANS))
 (2 2 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-LEFT))
 (2 1 (:REWRITE SET-EQUIV-ASYM))
 (1 1 (:TYPE-PRESCRIPTION SET-EQUIV))
 (1 1 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-61))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-9
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 (1517 2 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-59))
 (1148 152 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (1080 30 (:REWRITE REMOVE-ASSOC-WHEN-ABSENT-1))
 (1000 5 (:LINEAR HIFAT-ENTRY-COUNT-OF-REMOVE-ASSOC-EQUAL))
 (815 15 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-1))
 (793 72 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (790 5 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-3))
 (746 9 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-93))
 (540 152 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (510 15 (:REWRITE DELETE-D-E-CORRECTNESS-1))
 (495 5 (:DEFINITION DELETE-D-E))
 (400 10 (:DEFINITION REMOVE-ASSOC-EQUAL))
 (370 75 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
 (313 30 (:REWRITE NFIX-WHEN-ZP))
 (304 304 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (304 304 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (300 90 (:TYPE-PRESCRIPTION ASSOC-WHEN-ZP-LEN))
 (289 289 (:REWRITE DEFAULT-CAR))
 (282 30 (:REWRITE NFIX-WHEN-NATP))
 (255 15 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-23))
 (251 167 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (240 35 (:DEFINITION ASSOC-EQUAL))
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 (227 27 (:REWRITE ZP-OPEN))
 (214 214 (:REWRITE DEFAULT-CDR))
 (205 23 (:DEFINITION NATP))
 (190 5 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-6))
 (187 19 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 1))
 (170 170 (:TYPE-PRESCRIPTION FIND-D-E-CORRECTNESS-1))
 (167 167 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (167 167 (:TYPE-PRESCRIPTION D-E-LIST-P))
 (152 152 (:TYPE-PRESCRIPTION D-E-P))
 (147 147 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (130 130 (:TYPE-PRESCRIPTION ZP))
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 (90 90 (:TYPE-PRESCRIPTION LOFAT-TO-HIFAT-HELPER-CORRECTNESS-1 . 2))
 (90 90 (:TYPE-PRESCRIPTION LEN))
 (55 55 (:REWRITE REDUCE-INTEGERP-+-CONSTANT))
 (54 12 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (50 25 (:REWRITE DEFAULT-+-2))
 (38 19 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (37 1 (:DEFINITION MEMBER-INTERSECTP-EQUAL))
 (35 35 (:TYPE-PRESCRIPTION NATP))
 (35 35 (:REWRITE-QUOTED-CONSTANT FAT32-FILENAME-LIST-FIX-UNDER-FAT32-FILENAME-LIST-EQUIV))
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 (15 15 (:TYPE-PRESCRIPTION DELETE-D-E))
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 (12 1 (:DEFINITION FREE-INDEX-LISTP))
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 (10 10 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-46))
 (9 3 (:LINEAR LOFAT-FS-P-CORRECTNESS-1))
 (6 6 (:TYPE-PRESCRIPTION FAT32-ENTRY-MASK))
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 (6 2 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (5 5 (:TYPE-PRESCRIPTION M1-FILE-ALIST-P))
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 (5 5 (:TYPE-PRESCRIPTION FREE-INDEX-LISTP))
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 (5 5 (:REWRITE HIFAT-NO-DUPS-P-OF-LOFAT-TO-HIFAT-HELPER))
 (5 5 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (3 3 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
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 (2 2 (:REWRITE NOT-INTERSECTP-LIST-WHEN-ATOM))
 (2 2 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-2 . 2))
 (2 2 (:REWRITE MEMBER-INTERSECTP-WITH-SUBSET))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-7
 (1566053 620685 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (1391565 774262 (:REWRITE DEFAULT-+-2))
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 (949968 949968 (:TYPE-PRESCRIPTION FAT32-ENTRY-MASK))
 (925116 774262 (:REWRITE DEFAULT-+-1))
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 (583280 1718 (:REWRITE GET-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-5 . 1))
 (508871 413960 (:REWRITE DEFAULT-<-1))
 (493733 271656 (:REWRITE FOLD-CONSTS-IN-+))
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 (424415 11233 (:REWRITE D-E-CC-UNDER-IFF . 2))
 (294315 39378 (:LINEAR D-E-FILE-SIZE-CORRECTNESS-1))
 (281271 281271 (:TYPE-PRESCRIPTION D-E-FILE-SIZE))
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 (229042 228426 (:REWRITE INTERSECT-WITH-SUBSET . 12))
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 (228426 228426 (:REWRITE FLATTEN-SUBSET-NO-DUPLICATESP-LEMMA-1))
 (211239 1705 (:REWRITE D-E-CC-CONTENTS-OF-UPDATE-DIR-CONTENTS-DISJOINT))
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 (175616 87808 (:REWRITE DEFAULT-UNARY-MINUS))
 (167433 167433 (:REWRITE MEMBER-INTERSECTP-WITH-SUBSET))
 (98310 3277 (:REWRITE CONSP-OF-FAT32-BUILD-INDEX-LIST))
 (97370 85730 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (92470 85549 (:REWRITE MEMBER-WHEN-ATOM))
 (86234 86234 (:REWRITE SUBSETP-MEMBER . 1))
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 (55005 14389 (:REWRITE FAT32-FILENAME-P-CORRECTNESS-1))
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 (33993 1879 (:REWRITE SUBSETP-OF-APPEND-WHEN-SUBSET-OF-EITHER))
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 (28098 630 (:REWRITE REMOVE-ASSOC-WHEN-ABSENT-1))
 (20392 20392 (:TYPE-PRESCRIPTION FAT32-FILENAME-P))
 (20392 20392 (:REWRITE FAT32-FILENAME-P-WHEN-MEMBER-EQUAL-OF-FAT32-FILENAME-LIST-P))
 (13108 3277 (:LINEAR NATP-OF-CLUSTER-SIZE))
 (12894 1134 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-2))
 (9831 3277 (:LINEAR HIFAT-TO-LOFAT-INVERSION-LEMMA-19))
 (9312 2328 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-MAKE-LIST-AC))
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 (6554 6554 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-FAT32-BUILD-INDEX-LIST))
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 (3277 3277 (:TYPE-PRESCRIPTION FAT32$C-P))
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 (3201 1067 (:LINEAR LEN-WHEN-HIFAT-BOUNDED-FILE-ALIST-P . 1))
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 (2328 2328 (:TYPE-PRESCRIPTION MAKE-LIST-AC))
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 (2177 941 (:LINEAR LENGTH-OF-D-E-CC-CONTENTS . 1))
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 (168 168 (:TYPE-PRESCRIPTION REMOVE-ASSOC-EQUAL))
 (153 153 (:REWRITE-QUOTED-CONSTANT M1-FILE-CONTENTS-FIX-UNDER-M1-FILE-CONTENTS-EQUIV))
 (126 42 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-149))
 (104 4 (:REWRITE LOFAT-FS-P-OF-UPDATE-DIR-CONTENTS))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-3
 (447 18 (:REWRITE REMOVE-ASSOC-WHEN-ABSENT-1))
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 (150 24 (:DEFINITION ASSOC-EQUAL))
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 (132 6 (:DEFINITION PUT-ASSOC-EQUAL))
 (126 6 (:DEFINITION FIND-D-E))
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 (80 80 (:TYPE-PRESCRIPTION ZP))
 (78 3 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
 (72 72 (:TYPE-PRESCRIPTION LEN))
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 (54 6 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (39 6 (:REWRITE M1-FILE-HIFAT-FILE-ALIST-FIX-NORMALISATION))
 (36 36 (:TYPE-PRESCRIPTION USEFUL-D-E-LIST-P))
 (30 5 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-58))
 (27 27 (:TYPE-PRESCRIPTION LOFAT-TO-HIFAT-HELPER-CORRECTNESS-1 . 2))
 (27 9 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (27 3 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-23))
 (24 24 (:REWRITE-QUOTED-CONSTANT FAT32-FILENAME-LIST-FIX-UNDER-FAT32-FILENAME-LIST-EQUIV))
 (19 19 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (18 18 (:TYPE-PRESCRIPTION D-E-LIST-P))
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 (12 12 (:TYPE-PRESCRIPTION D-E-FILENAME))
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 (12 12 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
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 (9 3 (:REWRITE HIFAT-FILE-ALIST-FIX-WHEN-HIFAT-NO-DUPS-P))
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 (9 3 (:DEFINITION NATP))
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 (1 1 (:LINEAR POSITION-WHEN-MEMBER-OF-TAKE))
 )
(LOFAT-REMOVE-FILE-SPEC-1)
(INDUCTION-SCHEME
 (25 16 (:TYPE-PRESCRIPTION BINARY-APPEND))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-1-LEMMA-2
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 (1398 274 (:REWRITE SET-EQUIV-OF-CONS-SELF))
 (1378 1378 (:LINEAR LEN-WHEN-FAT32-FILENAME-LIST-PREFIXP))
 (1042 1042 (:TYPE-PRESCRIPTION DELETE-D-E))
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 (627 627 (:TYPE-PRESCRIPTION UNSIGNED-BYTE-P))
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 (408 130 (:REWRITE SET-EQUIV-WITH-APPEND-OTHER-LEFT))
 (333 9 (:REWRITE HIFAT-FIND-FILE-CORRECTNESS-1-LEMMA-1))
 (290 290 (:REWRITE FAT32-FILENAME-P-WHEN-MEMBER-EQUAL-OF-FAT32-FILENAME-LIST-P))
 (282 282 (:REWRITE SUBSETP-MEMBER . 1))
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 (152 76 (:REWRITE SET-EQUIV-ASYM))
 (144 72 (:REWRITE DEFAULT-*-2))
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 (76 76 (:REWRITE-QUOTED-CONSTANT M1-FILE-CONTENTS-FIX-UNDER-M1-FILE-CONTENTS-EQUIV))
 (64 10 (:REWRITE CAR-OF-APPEND))
 (63 9 (:REWRITE HIFAT-FIND-FILE-CORRECTNESS-LEMMA-6))
 (36 36 (:TYPE-PRESCRIPTION M1-FILE->D-E$INLINE))
 (24 4 (:REWRITE MEMBER-OF-BINARY-APPEND))
 (20 8 (:REWRITE CDR-OF-APPEND-WHEN-CONSP))
 (16 4 (:REWRITE FLATTEN-EQUIV-OF-CONS-WHEN-ATOM))
 (3 3 (:REWRITE FLATTEN-WHEN-NOT-CONSP))
 (2 2 (:REWRITE-QUOTED-CONSTANT FAT32-FILENAME-LIST-FIX-UNDER-FAT32-FILENAME-LIST-EQUIV))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-1-LEMMA-4
 (26043 50 (:DEFINITION LOFAT-TO-HIFAT-HELPER))
 (10687 925 (:DEFINITION FIND-D-E))
 (6007 211 (:LINEAR LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-1-LEMMA-1))
 (5582 438 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (5203 929 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (4809 7 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-2))
 (4540 1 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-59))
 (4158 2 (:LINEAR HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E))
 (3832 100 (:REWRITE NOT-INTERSECTP-LIST-OF-APPEND-1))
 (3524 96 (:DEFINITION MEMBER-INTERSECTP-EQUAL))
 (3385 941 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (3100 4 (:REWRITE LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-2-LEMMA-2))
 (2948 9 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-1))
 (2883 7 (:REWRITE D-E-CC-OF-UPDATE-DIR-CONTENTS-COINCIDENT))
 (2683 487 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
 (2462 562 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-2 . 2))
 (2386 7 (:REWRITE D-E-CC-CONTENTS-OF-UPDATE-DIR-CONTENTS-COINCIDENT))
 (2254 2254 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (2184 79 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-8))
 (2106 14 (:REWRITE INTERSECTP-IS-COMMUTATIVE))
 (2078 14 (:LINEAR LENGTH-OF-D-E-CC-CONTENTS . 3))
 (1966 14 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-4))
 (1910 14 (:REWRITE GET-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-5 . 1))
 (1863 7 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-3))
 (1863 7 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-11))
 (1754 2 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-3))
 (1623 5 (:REWRITE REMOVE-ASSOC-WHEN-ABSENT-1))
 (1527 963 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (1444 947 (:REWRITE DEFAULT-+-2))
 (1345 1343 (:REWRITE DEFAULT-CDR))
 (1339 155 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (1294 1292 (:REWRITE DEFAULT-CAR))
 (1247 1247 (:TYPE-PRESCRIPTION COUNT-OF-CLUSTERS))
 (1200 400 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (1149 947 (:REWRITE DEFAULT-+-1))
 (1124 2 (:LINEAR HIFAT-ENTRY-COUNT-OF-REMOVE-ASSOC-EQUAL))
 (1000 1000 (:TYPE-PRESCRIPTION SUBSETP-EQUAL))
 (1000 100 (:REWRITE SUBSETP-CONS-2))
 (986 986 (:TYPE-PRESCRIPTION D-E-FIRST-CLUSTER))
 (986 2 (:REWRITE PUT-ASSOC-EQUAL-WITHOUT-CHANGE . 2))
 (968 968 (:TYPE-PRESCRIPTION D-E-P))
 (963 963 (:TYPE-PRESCRIPTION D-E-LIST-P))
 (809 143 (:REWRITE ZP-OPEN))
 (783 125 (:LINEAR LOFAT-FS-P-CORRECTNESS-1))
 (782 2 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-6))
 (681 503 (:REWRITE DEFAULT-<-2))
 (609 503 (:REWRITE DEFAULT-<-1))
 (600 150 (:REWRITE COMMUTATIVITY-OF-+))
 (576 32 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (538 358 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (449 449 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (445 62 (:REWRITE NFIX-WHEN-ZP))
 (424 52 (:REWRITE M1-FILE-HIFAT-FILE-ALIST-FIX-NORMALISATION))
 (408 258 (:REWRITE USEFUL-D-E-LIST-P-OF-CDR))
 (400 400 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (397 1 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-7))
 (320 320 (:TYPE-PRESCRIPTION D-E-FILE-SIZE))
 (300 50 (:REWRITE COMMUTATIVITY-2-OF-+))
 (298 62 (:REWRITE NFIX-WHEN-NATP))
 (228 228 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (222 222 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-D-E-CC))
 (205 205 (:TYPE-PRESCRIPTION HIFAT-FILE-ALIST-FIX))
 (204 204 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 2))
 (204 204 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 1))
 (200 200 (:REWRITE MEMBER-INTERSECTP-WITH-SUBSET))
 (200 200 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-46))
 (200 200 (:REWRITE APPEND-WHEN-NOT-CONSP))
 (200 50 (:REWRITE DISTRIBUTIVITY-OF-MINUS-OVER-+))
 (184 6 (:REWRITE DELETE-D-E-CORRECTNESS-1))
 (178 2 (:DEFINITION DELETE-D-E))
 (175 61 (:DEFINITION NATP))
 (171 53 (:REWRITE HIFAT-FILE-ALIST-FIX-WHEN-HIFAT-NO-DUPS-P))
 (150 150 (:REWRITE FOLD-CONSTS-IN-+))
 (147 8 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-23))
 (126 14 (:REWRITE LEN-OF-NATS=>CHARS))
 (125 125 (:TYPE-PRESCRIPTION FAT-ENTRY-COUNT))
 (124 124 (:TYPE-PRESCRIPTION ZP))
 (124 124 (:TYPE-PRESCRIPTION MEMBER-INTERSECTP-EQUAL))
 (112 28 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-RIGHT))
 (112 28 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-LEFT))
 (112 14 (:REWRITE LEN-OF-CLEAR-D-E))
 (107 107 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (104 102 (:REWRITE DEFAULT-UNARY-MINUS))
 (100 100 (:TYPE-PRESCRIPTION NO-DUPLICATESP-EQUAL))
 (100 100 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (100 50 (:REWRITE APPEND-OF-CONS))
 (98 14 (:REWRITE LEN-OF-STRING=>NATS))
 (92 92 (:REWRITE USEFUL-D-E-LIST-P-OF-MAKE-D-E-LIST))
 (90 90 (:REWRITE COUNT-OF-CLUSTERS-OF-UPDATE-DIR-CONTENTS))
 (83 83 (:TYPE-PRESCRIPTION LEN))
 (77 20 (:TYPE-PRESCRIPTION ASSOC-WHEN-ZP-LEN))
 (70 35 (:REWRITE STR::EXPLODE-WHEN-NOT-STRINGP))
 (70 14 (:REWRITE LENGTH-WHEN-STRINGP))
 (63 63 (:TYPE-PRESCRIPTION STRINGP-OF-D-E-CC-CONTENTS))
 (63 21 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-5))
 (61 61 (:TYPE-PRESCRIPTION NATP))
 (56 56 (:TYPE-PRESCRIPTION INTEGERP-OF-D-E-CC-CONTENTS))
 (50 50 (:TYPE-PRESCRIPTION SUBDIR-CONTENTS-P))
 (50 50 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (42 42 (:TYPE-PRESCRIPTION GOOD-ROOT-D-E-P))
 (42 14 (:REWRITE STR::COERCE-TO-LIST-REMOVAL))
 (41 1 (:REWRITE EQUAL-OF-M1-FILE))
 (29 9 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-2))
 (28 28 (:TYPE-PRESCRIPTION INTERSECTP-EQUAL))
 (28 28 (:REWRITE INTERSECT-WITH-SUBSET . 12))
 (28 28 (:REWRITE INTERSECT-WITH-SUBSET . 11))
 (28 28 (:REWRITE FLATTEN-SUBSET-NO-DUPLICATESP-LEMMA-1))
 (28 7 (:LINEAR LENGTH-OF-D-E-CC-CONTENTS . 2))
 (27 27 (:REWRITE FIND-D-E-CORRECTNESS-1))
 (21 7 (:REWRITE FAT32-MASKED-ENTRY-P-OF-D-E-FIRST-CLUSTER))
 (19 1 (:DEFINITION PUT-ASSOC-EQUAL))
 (18 18 (:TYPE-PRESCRIPTION NATS=>STRING))
 (15 1 (:REWRITE M1-FILE-CONTENTS-FIX-WHEN-M1-FILE-CONTENTS-P))
 (14 14 (:REWRITE EXPLODE-OF-NATS=>STRING))
 (14 14 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-7 . 4))
 (14 14 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-7 . 1))
 (11 5 (:REWRITE M1-FILE-ALIST-P-OF-LOFAT-TO-HIFAT-HELPER))
 (11 1 (:REWRITE M1-FILE-CONTENTS-P-CORRECTNESS-1))
 (10 10 (:TYPE-PRESCRIPTION REMOVE-ASSOC-EQUAL))
 (10 10 (:TYPE-PRESCRIPTION DELETE-D-E))
 (10 10 (:REWRITE USEFUL-D-E-LIST-P-OF-DELETE-D-E))
 (10 1 (:REWRITE M1-FILE->CONTENTS-OF-M1-FILE-HIFAT-FILE-ALIST-FIX))
 (8 4 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-93))
 (7 7 (:TYPE-PRESCRIPTION M1-FILE-HIFAT-FILE-ALIST-FIX))
 (7 7 (:TYPE-PRESCRIPTION M1-FILE))
 (7 7 (:TYPE-PRESCRIPTION FAT32-MASKED-ENTRY-P))
 (7 1 (:REWRITE M1-FILE-ALIST-P-OF-REMOVE-ASSOC))
 (6 6 (:TYPE-PRESCRIPTION M1-FILE-ALIST-P))
 (4 4 (:REWRITE HIFAT-NO-DUPS-P-OF-LOFAT-TO-HIFAT-HELPER))
 (4 4 (:REWRITE FAT32-FILENAME-P-WHEN-MEMBER-EQUAL-OF-FAT32-FILENAME-LIST-P))
 (4 1 (:REWRITE M1-FILE->D-E-OF-M1-FILE-HIFAT-FILE-ALIST-FIX))
 (2 2 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-3))
 (2 1 (:REWRITE M1-FILE-CONTENTS-P-WHEN-STRINGP))
 (1 1 (:TYPE-PRESCRIPTION M1-FILE-CONTENTS-P))
 (1 1 (:REWRITE M1-FILE-P-OF-M1-FILE-HIFAT-FILE-ALIST-FIX))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-29
 (48558 134 (:DEFINITION LOFAT-TO-HIFAT-HELPER))
 (14044 819 (:DEFINITION FIND-D-E))
 (13476 3 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-9))
 (9977 767 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-56))
 (9828 251 (:DEFINITION MEMBER-INTERSECTP-EQUAL))
 (9676 268 (:REWRITE NOT-INTERSECTP-LIST-OF-APPEND-1))
 (8581 14 (:REWRITE LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-2-LEMMA-2))
 (7624 819 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (6411 1300 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-2 . 2))
 (6118 841 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (5943 764 (:REWRITE NOT-INTERSECTP-LIST-OF-LOFAT-TO-HIFAT-HELPER))
 (5430 331 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (5392 11 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-2))
 (4008 421 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (3784 350 (:REWRITE ZP-OPEN))
 (3661 863 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (3420 555 (:DEFINITION FREE-INDEX-LISTP))
 (3322 1111 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (3244 170 (:REWRITE NFIX-WHEN-ZP))
 (2910 6 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-1 . 1))
 (2878 170 (:REWRITE NFIX-WHEN-NATP))
 (2775 2775 (:TYPE-PRESCRIPTION FREE-INDEX-LISTP))
 (2710 2710 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (2690 269 (:REWRITE SUBSETP-CONS-2))
 (2550 158 (:DEFINITION NATP))
 (2348 1716 (:REWRITE DEFAULT-+-2))
 (2218 2218 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (2145 1716 (:REWRITE DEFAULT-+-1))
 (2010 670 (:REWRITE USEFUL-D-E-LIST-P-OF-CDR))
 (1968 6 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-2))
 (1939 1939 (:REWRITE DEFAULT-CDR))
 (1822 1822 (:REWRITE DEFAULT-CAR))
 (1606 22 (:REWRITE INTERSECTP-IS-COMMUTATIVE))
 (1584 11 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-3))
 (1538 1257 (:REWRITE DEFAULT-<-1))
 (1373 1257 (:REWRITE DEFAULT-<-2))
 (1355 746 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (1298 22 (:REWRITE GET-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-5 . 1))
 (1088 1088 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (942 58 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (864 134 (:REWRITE COMMUTATIVITY-2-OF-+))
 (775 775 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (754 134 (:REWRITE M1-FILE-HIFAT-FILE-ALIST-FIX-NORMALISATION))
 (638 11 (:REWRITE D-E-CC-CONTENTS-OF-UPDATE-DIR-CONTENTS-COINCIDENT))
 (544 544 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 2))
 (544 544 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 1))
 (536 536 (:REWRITE APPEND-WHEN-NOT-CONSP))
 (536 134 (:REWRITE DISTRIBUTIVITY-OF-MINUS-OVER-+))
 (533 533 (:REWRITE MEMBER-INTERSECTP-WITH-SUBSET))
 (533 533 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-46))
 (520 520 (:TYPE-PRESCRIPTION D-E-FILE-SIZE))
 (414 414 (:REWRITE FOLD-CONSTS-IN-+))
 (377 377 (:TYPE-PRESCRIPTION HIFAT-FILE-ALIST-FIX))
 (354 354 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-D-E-CC))
 (343 343 (:TYPE-PRESCRIPTION MEMBER-INTERSECTP-EQUAL))
 (274 271 (:REWRITE DEFAULT-UNARY-MINUS))
 (268 268 (:TYPE-PRESCRIPTION NO-DUPLICATESP-EQUAL))
 (268 268 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (268 134 (:REWRITE APPEND-OF-CONS))
 (252 252 (:TYPE-PRESCRIPTION ZP))
 (243 81 (:REWRITE HIFAT-FILE-ALIST-FIX-WHEN-HIFAT-NO-DUPS-P))
 (198 22 (:REWRITE LEN-OF-NATS=>CHARS))
 (182 182 (:TYPE-PRESCRIPTION NATP))
 (176 44 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-RIGHT))
 (176 44 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-LEFT))
 (176 22 (:REWRITE LEN-OF-CLEAR-D-E))
 (176 22 (:LINEAR LENGTH-OF-D-E-CC-CONTENTS . 3))
 (171 14 (:REWRITE D-E-CC-OF-UPDATE-DIR-CONTENTS-COINCIDENT))
 (162 162 (:TYPE-PRESCRIPTION HIFAT-NO-DUPS-P))
 (154 22 (:REWRITE LEN-OF-STRING=>NATS))
 (143 143 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (134 134 (:TYPE-PRESCRIPTION SUBDIR-CONTENTS-P))
 (110 55 (:REWRITE STR::EXPLODE-WHEN-NOT-STRINGP))
 (110 44 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-5))
 (110 22 (:REWRITE LENGTH-WHEN-STRINGP))
 (99 99 (:TYPE-PRESCRIPTION STRINGP-OF-D-E-CC-CONTENTS))
 (99 99 (:TYPE-PRESCRIPTION LEN))
 (84 84 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (66 22 (:REWRITE STR::COERCE-TO-LIST-REMOVAL))
 (54 6 (:REWRITE ASSOCIATIVITY-OF-+))
 (44 44 (:REWRITE INTERSECT-WITH-SUBSET . 12))
 (44 44 (:REWRITE INTERSECT-WITH-SUBSET . 11))
 (44 44 (:REWRITE FLATTEN-SUBSET-NO-DUPLICATESP-LEMMA-1))
 (44 11 (:LINEAR LENGTH-OF-D-E-CC-CONTENTS . 2))
 (24 24 (:REWRITE REDUCE-INTEGERP-+-CONSTANT))
 (22 22 (:REWRITE EXPLODE-OF-NATS=>STRING))
 (22 22 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-7 . 4))
 (22 22 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-7 . 1))
 (22 11 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-93))
 (12 12 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-SUBSETP-EQUAL))
 (9 3 (:REWRITE NON-FREE-INDEX-LISTP-OF-D-E-CC))
 (6 6 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-NOT-CONSP))
 (6 3 (:REWRITE D-E-CC-CORRECTNESS-1))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-42
 (502220 3100 (:DEFINITION LOFAT-TO-HIFAT-HELPER))
 (65554 45760 (:REWRITE DEFAULT-+-2))
 (56503 45760 (:REWRITE DEFAULT-+-1))
 (48318 8883 (:REWRITE ZP-OPEN))
 (43722 6322 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (37612 30550 (:REWRITE DEFAULT-<-1))
 (37124 30550 (:REWRITE DEFAULT-<-2))
 (36428 117 (:REWRITE CONSP-OF-MAKE-LIST-AC))
 (29807 3801 (:REWRITE NFIX-WHEN-ZP))
 (28752 285 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-2))
 (25659 56 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-33))
 (24316 12571 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (21129 131 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-6))
 (20676 56 (:REWRITE FAT32-BUILD-INDEX-LIST-OF-EFFECTIVE-FAT-OF-UPDATE-DIR-CONTENTS))
 (18620 3100 (:REWRITE COMMUTATIVITY-2-OF-+))
 (17841 474 (:LINEAR MAKE-CLUSTERS-CORRECTNESS-2))
 (15300 15300 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (14381 1546 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (12873 12522 (:REWRITE APPEND-WHEN-NOT-CONSP))
 (12400 3100 (:REWRITE DISTRIBUTIVITY-OF-MINUS-OVER-+))
 (11848 560 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-1))
 (9748 334 (:REWRITE CONSP-OF-FAT32-BUILD-INDEX-LIST))
 (9713 95 (:REWRITE GET-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-5 . 2))
 (8328 7636 (:REWRITE DEFAULT-CDR))
 (7848 7848 (:TYPE-PRESCRIPTION D-E-FILE-SIZE))
 (7235 39 (:REWRITE LOFAT-PLACE-FILE-GUARD-LEMMA-9))
 (6754 6754 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-2 . 2))
 (6662 3100 (:REWRITE USEFUL-D-E-LIST-P-OF-CDR))
 (6338 6284 (:REWRITE DEFAULT-UNARY-MINUS))
 (6200 6200 (:TYPE-PRESCRIPTION MEMBER-INTERSECTP-EQUAL))
 (6200 6200 (:REWRITE MEMBER-INTERSECTP-WITH-SUBSET))
 (6200 6200 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-46))
 (6200 6200 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 2))
 (6200 6200 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 1))
 (6200 3100 (:REWRITE APPEND-OF-CONS))
 (5943 5251 (:REWRITE DEFAULT-CAR))
 (4334 2167 (:REWRITE STR::EXPLODE-WHEN-NOT-STRINGP))
 (4139 17 (:REWRITE LOFAT-PLACE-FILE-GUARD-LEMMA-11))
 (3862 209 (:DEFINITION PUT-ASSOC-EQUAL))
 (3792 237 (:LINEAR MAKE-CLUSTERS-CORRECTNESS-3))
 (3745 107 (:REWRITE EQUAL-OF-M1-FILE))
 (3672 12 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-1-LEMMA-2))
 (3100 3100 (:TYPE-PRESCRIPTION SUBDIR-CONTENTS-P))
 (3096 3096 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2960 1202 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-5))
 (2958 176 (:REWRITE REMOVE-ASSOC-WHEN-ABSENT-1))
 (2904 129 (:DEFINITION MAKE-LIST-AC))
 (2487 992 (:LINEAR HIFAT-TO-LOFAT-INVERSION-LEMMA-19))
 (2428 12 (:REWRITE CONSP-OF-FIND-N-FREE-CLUSTERS))
 (2345 1 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-9))
 (2339 17 (:REWRITE GET-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-5 . 3))
 (2293 76 (:REWRITE GET-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-5 . 1))
 (2214 2214 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (2012 503 (:LINEAR NATP-OF-CLUSTER-SIZE))
 (1948 69 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-9))
 (1605 107 (:REWRITE M1-FILE-CONTENTS-FIX-WHEN-M1-FILE-CONTENTS-P))
 (1582 7 (:REWRITE PUT-ASSOC-EQUAL-WITHOUT-CHANGE . 1))
 (1576 12 (:REWRITE COUNT-FREE-CLUSTERS-OF-UPDATE-NTH))
 (1346 231 (:REWRITE HIFAT-REMOVE-FILE-CORRECTNESS-4))
 (1213 116 (:REWRITE M1-FILE-CONTENTS-P-CORRECTNESS-1))
 (1192 596 (:REWRITE DEFAULT-*-1))
 (1165 594 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-2))
 (1115 1115 (:TYPE-PRESCRIPTION HIFAT-REMOVE-FILE-CORRECTNESS-1 . 1))
 (1070 107 (:REWRITE M1-FILE->CONTENTS-OF-M1-FILE-HIFAT-FILE-ALIST-FIX))
 (1042 596 (:REWRITE DEFAULT-*-2))
 (822 822 (:TYPE-PRESCRIPTION M1-FILE))
 (768 66 (:REWRITE DELETE-D-E-CORRECTNESS-1))
 (749 107 (:REWRITE M1-FILE-ALIST-P-OF-REMOVE-ASSOC))
 (748 22 (:DEFINITION DELETE-D-E))
 (668 668 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-FAT32-BUILD-INDEX-LIST))
 (662 662 (:LINEAR LEN-WHEN-FAT32-FILENAME-LIST-PREFIXP))
 (651 245 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-23))
 (503 503 (:TYPE-PRESCRIPTION FAT32$C-P))
 (466 23 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-1))
 (409 7 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-5))
 (331 331 (:REWRITE INTERSECT-WITH-SUBSET . 12))
 (331 331 (:REWRITE INTERSECT-WITH-SUBSET . 11))
 (331 331 (:REWRITE FLATTEN-SUBSET-NO-DUPLICATESP-LEMMA-1))
 (331 331 (:LINEAR POSITION-WHEN-MEMBER))
 (331 331 (:LINEAR POSITION-EQUAL-AC-WHEN-MEMBER))
 (312 156 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (258 86 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-26))
 (241 12 (:REWRITE FIND-N-FREE-CLUSTERS-WHEN-ZP))
 (232 232 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-SUBSETP-EQUAL))
 (200 200 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-3))
 (180 180 (:LINEAR LENGTH-OF-D-E-CC-CONTENTS . 1))
 (170 10 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-2))
 (144 144 (:TYPE-PRESCRIPTION DELETE-D-E))
 (144 144 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-7 . 4))
 (136 136 (:TYPE-PRESCRIPTION LENGTH))
 (132 66 (:REWRITE COUNT-OF-CLUSTERS-OF-CLEAR-CC))
 (130 130 (:REWRITE SUBSETP-MEMBER . 1))
 (107 107 (:REWRITE M1-FILE-P-OF-M1-FILE-HIFAT-FILE-ALIST-FIX))
 (107 107 (:REWRITE M1-FILE->D-E-OF-M1-FILE-HIFAT-FILE-ALIST-FIX))
 (95 95 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-7 . 3))
 (91 31 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-18))
 (76 76 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-7 . 1))
 (56 56 (:REWRITE CLUSTER-SIZE-OF-UPDATE-DIR-CONTENTS))
 (44 44 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (39 39 (:REWRITE-QUOTED-CONSTANT M1-FILE-CONTENTS-FIX-UNDER-M1-FILE-CONTENTS-EQUIV))
 (24 24 (:TYPE-PRESCRIPTION FIND-N-FREE-CLUSTERS))
 (22 22 (:LINEAR POSITION-WHEN-MEMBER-OF-TAKE))
 (18 18 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-15))
 (18 2 (:REWRITE ASSOCIATIVITY-OF-+))
 (17 17 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-7 . 2))
 (16 16 (:REWRITE-QUOTED-CONSTANT FAT32-FILENAME-LIST-FIX-UNDER-FAT32-FILENAME-LIST-EQUIV))
 (10 10 (:REWRITE REDUCE-INTEGERP-+-CONSTANT))
 (9 9 (:REWRITE M1-FILE-ALIST-P-WHEN-NOT-CONSP))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-43
 (57962 158 (:DEFINITION LOFAT-TO-HIFAT-HELPER))
 (19706 4 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-1-LEMMA-2))
 (17968 4 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-9))
 (16584 968 (:DEFINITION FIND-D-E))
 (12456 292 (:DEFINITION MEMBER-INTERSECTP-EQUAL))
 (12388 20 (:REWRITE LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-2-LEMMA-2))
 (11296 316 (:REWRITE NOT-INTERSECTP-LIST-OF-APPEND-1))
 (9268 860 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-56))
 (9008 968 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (8640 16 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-2))
 (7492 1488 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-2 . 2))
 (7276 1002 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (6305 403 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (6204 856 (:REWRITE NOT-INTERSECTP-LIST-OF-LOFAT-TO-HIFAT-HELPER))
 (4990 428 (:REWRITE ZP-OPEN))
 (4714 498 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (4366 1034 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (4144 202 (:REWRITE NFIX-WHEN-ZP))
 (4044 652 (:DEFINITION FREE-INDEX-LISTP))
 (3932 1316 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (3880 8 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-1 . 1))
 (3714 202 (:REWRITE NFIX-WHEN-NATP))
 (3326 186 (:DEFINITION NATP))
 (3260 3260 (:TYPE-PRESCRIPTION FREE-INDEX-LISTP))
 (3200 3200 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (3160 316 (:REWRITE SUBSETP-CONS-2))
 (2782 2029 (:REWRITE DEFAULT-+-2))
 (2624 8 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-2))
 (2614 2614 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (2535 2029 (:REWRITE DEFAULT-+-1))
 (2370 790 (:REWRITE USEFUL-D-E-LIST-P-OF-CDR))
 (2336 32 (:REWRITE INTERSECTP-IS-COMMUTATIVE))
 (2304 16 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-3))
 (2274 2274 (:REWRITE DEFAULT-CDR))
 (2135 2135 (:REWRITE DEFAULT-CAR))
 (1888 32 (:REWRITE GET-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-5 . 1))
 (1846 1513 (:REWRITE DEFAULT-<-1))
 (1679 1513 (:REWRITE DEFAULT-<-2))
 (1568 848 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (1376 84 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (1282 1282 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (1028 158 (:REWRITE COMMUTATIVITY-2-OF-+))
 (928 16 (:REWRITE D-E-CC-CONTENTS-OF-UPDATE-DIR-CONTENTS-COINCIDENT))
 (904 904 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (856 158 (:REWRITE M1-FILE-HIFAT-FILE-ALIST-FIX-NORMALISATION))
 (760 760 (:TYPE-PRESCRIPTION D-E-FILE-SIZE))
 (644 644 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 2))
 (644 644 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 1))
 (632 632 (:REWRITE APPEND-WHEN-NOT-CONSP))
 (632 158 (:REWRITE DISTRIBUTIVITY-OF-MINUS-OVER-+))
 (628 628 (:REWRITE MEMBER-INTERSECTP-WITH-SUBSET))
 (628 628 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-46))
 (516 516 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-D-E-CC))
 (490 490 (:REWRITE FOLD-CONSTS-IN-+))
 (428 428 (:TYPE-PRESCRIPTION HIFAT-FILE-ALIST-FIX))
 (424 424 (:TYPE-PRESCRIPTION MEMBER-INTERSECTP-EQUAL))
 (324 320 (:REWRITE DEFAULT-UNARY-MINUS))
 (316 316 (:TYPE-PRESCRIPTION NO-DUPLICATESP-EQUAL))
 (316 316 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (316 158 (:REWRITE APPEND-OF-CONS))
 (314 314 (:TYPE-PRESCRIPTION ZP))
 (288 32 (:REWRITE LEN-OF-NATS=>CHARS))
 (270 90 (:REWRITE HIFAT-FILE-ALIST-FIX-WHEN-HIFAT-NO-DUPS-P))
 (256 64 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-RIGHT))
 (256 64 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-LEFT))
 (256 32 (:REWRITE LEN-OF-CLEAR-D-E))
 (256 32 (:LINEAR LENGTH-OF-D-E-CC-CONTENTS . 3))
 (244 20 (:REWRITE D-E-CC-OF-UPDATE-DIR-CONTENTS-COINCIDENT))
 (224 32 (:REWRITE LEN-OF-STRING=>NATS))
 (218 218 (:TYPE-PRESCRIPTION NATP))
 (203 1 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-5))
 (180 180 (:TYPE-PRESCRIPTION HIFAT-NO-DUPS-P))
 (170 170 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (160 80 (:REWRITE STR::EXPLODE-WHEN-NOT-STRINGP))
 (160 64 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-5))
 (160 32 (:REWRITE LENGTH-WHEN-STRINGP))
 (158 158 (:TYPE-PRESCRIPTION SUBDIR-CONTENTS-P))
 (144 144 (:TYPE-PRESCRIPTION STRINGP-OF-D-E-CC-CONTENTS))
 (144 144 (:TYPE-PRESCRIPTION LEN))
 (135 1 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-9))
 (108 108 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (96 32 (:REWRITE STR::COERCE-TO-LIST-REMOVAL))
 (72 8 (:REWRITE ASSOCIATIVITY-OF-+))
 (64 64 (:REWRITE INTERSECT-WITH-SUBSET . 12))
 (64 64 (:REWRITE INTERSECT-WITH-SUBSET . 11))
 (64 64 (:REWRITE FLATTEN-SUBSET-NO-DUPLICATESP-LEMMA-1))
 (64 16 (:LINEAR LENGTH-OF-D-E-CC-CONTENTS . 2))
 (32 32 (:REWRITE REDUCE-INTEGERP-+-CONSTANT))
 (32 32 (:REWRITE EXPLODE-OF-NATS=>STRING))
 (32 32 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-7 . 4))
 (32 32 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-7 . 1))
 (32 16 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-93))
 (24 24 (:TYPE-PRESCRIPTION FAT32-FILENAME-FIX))
 (17 1 (:REWRITE D-E-CC-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-4))
 (17 1 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-8))
 (12 12 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-SUBSETP-EQUAL))
 (12 4 (:REWRITE NON-FREE-INDEX-LISTP-OF-D-E-CC))
 (12 1 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-7))
 (8 4 (:REWRITE D-E-CC-CORRECTNESS-1))
 (6 6 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-NOT-CONSP))
 (4 4 (:TYPE-PRESCRIPTION NON-FREE-INDEX-LISTP))
 (2 2 (:REWRITE COUNT-OF-CLUSTERS-OF-LOFAT-REMOVE-FILE-HELPER))
 (1 1 (:REWRITE SUBSETP-MEMBER . 1))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-46
 (17766 49 (:DEFINITION LOFAT-TO-HIFAT-HELPER))
 (7495 49 (:REWRITE LOFAT-TO-HIFAT-HELPER-CORRECTNESS-4))
 (5183 392 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-56))
 (3840 98 (:REWRITE NOT-INTERSECTP-LIST-OF-APPEND-1))
 (3496 196 (:DEFINITION FIND-D-E))
 (2536 98 (:DEFINITION MEMBER-INTERSECTP-EQUAL))
 (2434 147 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
 (1984 392 (:REWRITE NOT-INTERSECTP-LIST-OF-LOFAT-TO-HIFAT-HELPER))
 (1928 196 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (1536 196 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (1413 147 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (1364 49 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (1194 199 (:DEFINITION FREE-INDEX-LISTP))
 (1134 378 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (995 995 (:TYPE-PRESCRIPTION FREE-INDEX-LISTP))
 (980 196 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (802 606 (:REWRITE DEFAULT-+-2))
 (784 784 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (753 606 (:REWRITE DEFAULT-+-1))
 (735 245 (:REWRITE USEFUL-D-E-LIST-P-OF-CDR))
 (686 686 (:TYPE-PRESCRIPTION FIND-D-E-CORRECTNESS-1))
 (591 591 (:REWRITE DEFAULT-CDR))
 (589 388 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (588 588 (:TYPE-PRESCRIPTION COUNT-OF-CLUSTERS))
 (542 542 (:REWRITE DEFAULT-CAR))
 (524 421 (:REWRITE DEFAULT-<-2))
 (522 421 (:REWRITE DEFAULT-<-1))
 (463 463 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (447 69 (:REWRITE NFIX-WHEN-ZP))
 (392 98 (:REWRITE COMMUTATIVITY-OF-+))
 (392 49 (:REWRITE M1-FILE-HIFAT-FILE-ALIST-FIX-NORMALISATION))
 (382 3 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-31))
 (377 377 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (330 49 (:REWRITE COMMUTATIVITY-2-OF-+))
 (294 294 (:TYPE-PRESCRIPTION D-E-FIRST-CLUSTER))
 (245 245 (:TYPE-PRESCRIPTION D-E-DIRECTORY-P))
 (196 196 (:TYPE-PRESCRIPTION HIFAT-FILE-ALIST-FIX))
 (196 196 (:TYPE-PRESCRIPTION D-E-P))
 (196 196 (:TYPE-PRESCRIPTION D-E-LIST-P))
 (196 196 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (196 196 (:REWRITE MEMBER-INTERSECTP-WITH-SUBSET))
 (196 196 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-46))
 (196 196 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 2))
 (196 196 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 1))
 (196 196 (:REWRITE APPEND-WHEN-NOT-CONSP))
 (196 49 (:REWRITE DISTRIBUTIVITY-OF-MINUS-OVER-+))
 (175 159 (:REWRITE FOLD-CONSTS-IN-+))
 (147 49 (:REWRITE HIFAT-FILE-ALIST-FIX-WHEN-HIFAT-NO-DUPS-P))
 (147 49 (:DEFINITION NFIX))
 (147 49 (:DEFINITION NATP))
 (98 98 (:TYPE-PRESCRIPTION NO-DUPLICATESP-EQUAL))
 (98 98 (:TYPE-PRESCRIPTION MEMBER-INTERSECTP-EQUAL))
 (98 98 (:TYPE-PRESCRIPTION HIFAT-NO-DUPS-P))
 (98 98 (:REWRITE DEFAULT-UNARY-MINUS))
 (98 98 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (98 49 (:REWRITE APPEND-OF-CONS))
 (88 88 (:REWRITE COUNT-OF-CLUSTERS-OF-LOFAT-REMOVE-FILE))
 (49 49 (:TYPE-PRESCRIPTION SUBDIR-CONTENTS-P))
 (49 49 (:TYPE-PRESCRIPTION NATP))
 (49 49 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (24 4 (:REWRITE ASSOCIATIVITY-OF-+))
 (21 7 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-2))
 (14 14 (:TYPE-PRESCRIPTION LOFAT-FS-P))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-47
 (882 35 (:DEFINITION FIND-D-E))
 (585 35 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (525 37 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (507 10 (:REWRITE SUBSETP-CONS-2))
 (484 21 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
 (480 35 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (476 42 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-56))
 (412 2 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-38))
 (366 10 (:REWRITE NOT-INTERSECTP-LIST-OF-APPEND-1))
 (338 14 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (270 35 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (222 222 (:TYPE-PRESCRIPTION USEFUL-D-E-LIST-P))
 (204 68 (:REWRITE USEFUL-D-E-LIST-P-OF-CDR))
 (122 122 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (112 89 (:REWRITE DEFAULT-+-2))
 (104 89 (:REWRITE DEFAULT-+-1))
 (88 88 (:REWRITE DEFAULT-CDR))
 (77 77 (:REWRITE DEFAULT-CAR))
 (75 5 (:REWRITE COMMUTATIVITY-2-OF-+))
 (70 70 (:TYPE-PRESCRIPTION D-E-P))
 (70 70 (:REWRITE D-E-LIST-P-WHEN-SUBSETP-EQUAL))
 (65 52 (:REWRITE DEFAULT-<-1))
 (64 52 (:REWRITE DEFAULT-<-2))
 (63 8 (:REWRITE LOFAT-TO-HIFAT-HELPER-CORRECTNESS-3))
 (60 60 (:TYPE-PRESCRIPTION COUNT-OF-CLUSTERS))
 (52 37 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (50 30 (:REWRITE FOLD-CONSTS-IN-+))
 (48 6 (:REWRITE NFIX-WHEN-ZP))
 (44 7 (:REWRITE M1-FILE-HIFAT-FILE-ALIST-FIX-NORMALISATION))
 (36 36 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (35 35 (:REWRITE D-E-LIST-P-WHEN-NOT-CONSP))
 (35 35 (:REWRITE D-E-FILENAME-OF-D-E-FIX))
 (32 32 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (30 5 (:REWRITE ASSOCIATIVITY-OF-+))
 (26 6 (:REWRITE NFIX-WHEN-NATP))
 (22 22 (:TYPE-PRESCRIPTION HIFAT-FILE-ALIST-FIX))
 (21 21 (:REWRITE MEMBER-INTERSECTP-WITH-SUBSET))
 (21 21 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-46))
 (21 21 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 2))
 (21 21 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 1))
 (20 5 (:REWRITE DISTRIBUTIVITY-OF-MINUS-OVER-+))
 (15 15 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (15 5 (:REWRITE HIFAT-FILE-ALIST-FIX-WHEN-HIFAT-NO-DUPS-P))
 (15 5 (:DEFINITION NFIX))
 (15 5 (:DEFINITION NATP))
 (10 10 (:TYPE-PRESCRIPTION NO-DUPLICATESP-EQUAL))
 (10 10 (:TYPE-PRESCRIPTION MEMBER-INTERSECTP-EQUAL))
 (10 10 (:TYPE-PRESCRIPTION HIFAT-NO-DUPS-P))
 (10 10 (:REWRITE DEFAULT-UNARY-MINUS))
 (10 10 (:REWRITE COUNT-OF-CLUSTERS-OF-LOFAT-REMOVE-FILE))
 (10 10 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (9 5 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-2))
 (7 7 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-58))
 (6 6 (:REWRITE LOFAT-TO-HIFAT-HELPER-CORRECTNESS-4))
 (5 5 (:TYPE-PRESCRIPTION SUBDIR-CONTENTS-P))
 (5 5 (:TYPE-PRESCRIPTION NATP))
 (5 5 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (5 5 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-17))
 (5 5 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-16))
 (5 1 (:REWRITE SET-EQUIV-OF-CONS-SELF))
 (4 4 (:TYPE-PRESCRIPTION LOFAT-FS-P))
 (3 3 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (2 2 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (1 1 (:TYPE-PRESCRIPTION NFIX))
 (1 1 (:REWRITE-QUOTED-CONSTANT M1-FILE-CONTENTS-FIX-UNDER-M1-FILE-CONTENTS-EQUIV))
 (1 1 (:REWRITE SUBSETP-MEMBER . 1))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-48
 (26306 71 (:DEFINITION LOFAT-TO-HIFAT-HELPER))
 (9795 71 (:REWRITE LOFAT-TO-HIFAT-HELPER-CORRECTNESS-4))
 (7988 566 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-56))
 (6801 359 (:DEFINITION FIND-D-E))
 (5644 142 (:REWRITE NOT-INTERSECTP-LIST-OF-APPEND-1))
 (4053 236 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
 (3988 361 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (3967 142 (:DEFINITION MEMBER-INTERSECTP-EQUAL))
 (3548 850 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-2 . 2))
 (3149 361 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (2992 566 (:REWRITE NOT-INTERSECTP-LIST-OF-LOFAT-TO-HIFAT-HELPER))
 (2706 123 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (2165 236 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (1844 291 (:DEFINITION FREE-INDEX-LISTP))
 (1748 364 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (1704 568 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (1455 1455 (:TYPE-PRESCRIPTION FREE-INDEX-LISTP))
 (1420 1420 (:TYPE-PRESCRIPTION SUBSETP-EQUAL))
 (1420 142 (:REWRITE SUBSETP-CONS-2))
 (1290 1290 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (1221 937 (:REWRITE DEFAULT-+-2))
 (1150 937 (:REWRITE DEFAULT-+-1))
 (1135 1135 (:TYPE-PRESCRIPTION FIND-D-E-CORRECTNESS-1))
 (1119 363 (:REWRITE USEFUL-D-E-LIST-P-OF-CDR))
 (984 946 (:REWRITE DEFAULT-CDR))
 (886 879 (:REWRITE DEFAULT-CAR))
 (852 852 (:TYPE-PRESCRIPTION COUNT-OF-CLUSTERS))
 (831 546 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (759 613 (:REWRITE DEFAULT-<-2))
 (758 613 (:REWRITE DEFAULT-<-1))
 (625 93 (:REWRITE NFIX-WHEN-ZP))
 (609 609 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (588 71 (:REWRITE COMMUTATIVITY-2-OF-+))
 (568 568 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (568 142 (:REWRITE COMMUTATIVITY-OF-+))
 (526 71 (:REWRITE M1-FILE-HIFAT-FILE-ALIST-FIX-NORMALISATION))
 (484 484 (:TYPE-PRESCRIPTION D-E-LIST-P))
 (478 478 (:TYPE-PRESCRIPTION D-E-P))
 (426 426 (:TYPE-PRESCRIPTION D-E-FIRST-CLUSTER))
 (384 3 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-31))
 (359 359 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (339 267 (:REWRITE FOLD-CONSTS-IN-+))
 (307 6 (:REWRITE DELETE-D-E-CORRECTNESS-1))
 (289 286 (:REWRITE APPEND-WHEN-NOT-CONSP))
 (288 288 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 2))
 (288 288 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 1))
 (286 286 (:REWRITE MEMBER-INTERSECTP-WITH-SUBSET))
 (286 286 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-46))
 (284 71 (:REWRITE DISTRIBUTIVITY-OF-MINUS-OVER-+))
 (264 2 (:DEFINITION DELETE-D-E))
 (263 263 (:TYPE-PRESCRIPTION HIFAT-FILE-ALIST-FIX))
 (240 240 (:REWRITE D-E-LIST-P-WHEN-SUBSETP-EQUAL))
 (213 71 (:DEFINITION NFIX))
 (213 71 (:DEFINITION NATP))
 (192 64 (:REWRITE HIFAT-FILE-ALIST-FIX-WHEN-HIFAT-NO-DUPS-P))
 (177 6 (:REWRITE PUT-ASSOC-EQUAL-WITHOUT-CHANGE . 2))
 (153 3 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-6))
 (142 142 (:TYPE-PRESCRIPTION NO-DUPLICATESP-EQUAL))
 (142 142 (:REWRITE DEFAULT-UNARY-MINUS))
 (142 142 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (142 71 (:REWRITE APPEND-OF-CONS))
 (128 128 (:TYPE-PRESCRIPTION HIFAT-NO-DUPS-P))
 (120 120 (:REWRITE D-E-LIST-P-WHEN-NOT-CONSP))
 (120 120 (:REWRITE COUNT-OF-CLUSTERS-OF-LOFAT-REMOVE-FILE))
 (115 115 (:REWRITE D-E-FILENAME-OF-D-E-FIX))
 (108 18 (:REWRITE ASSOCIATIVITY-OF-+))
 (72 3 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-1))
 (71 71 (:TYPE-PRESCRIPTION SUBDIR-CONTENTS-P))
 (71 71 (:TYPE-PRESCRIPTION NATP))
 (71 71 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (63 18 (:TYPE-PRESCRIPTION ASSOC-WHEN-ZP-LEN))
 (60 60 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-17))
 (60 60 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-16))
 (57 3 (:DEFINITION PUT-ASSOC-EQUAL))
 (37 15 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-2))
 (34 6 (:REWRITE CONSP-OF-APPEND))
 (30 10 (:REWRITE USEFUL-D-E-LIST-P-OF-DELETE-D-E))
 (27 3 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-23))
 (26 26 (:TYPE-PRESCRIPTION LOFAT-FS-P))
 (22 22 (:TYPE-PRESCRIPTION DELETE-D-E))
 (18 18 (:TYPE-PRESCRIPTION LEN))
 (18 3 (:REWRITE CAR-OF-APPEND))
 (9 3 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-2))
 (9 3 (:LINEAR HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E))
 (7 3 (:REWRITE LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-2-LEMMA-2))
 (6 2 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (5 2 (:REWRITE CDR-OF-APPEND-WHEN-CONSP))
 (2 2 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-93))
 (1 1 (:REWRITE FLATTEN-WHEN-NOT-CONSP))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-50
 (882 35 (:DEFINITION FIND-D-E))
 (585 35 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (525 37 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (507 10 (:REWRITE SUBSETP-CONS-2))
 (484 21 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
 (480 35 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (476 42 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-56))
 (412 2 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-38))
 (366 10 (:REWRITE NOT-INTERSECTP-LIST-OF-APPEND-1))
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 (270 35 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (222 222 (:TYPE-PRESCRIPTION USEFUL-D-E-LIST-P))
 (204 68 (:REWRITE USEFUL-D-E-LIST-P-OF-CDR))
 (122 122 (:TYPE-PRESCRIPTION D-E-FILENAME))
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 (111 94 (:REWRITE DEFAULT-+-1))
 (88 88 (:REWRITE DEFAULT-CDR))
 (77 77 (:REWRITE DEFAULT-CAR))
 (75 5 (:REWRITE COMMUTATIVITY-2-OF-+))
 (70 70 (:TYPE-PRESCRIPTION D-E-P))
 (70 70 (:REWRITE D-E-LIST-P-WHEN-SUBSETP-EQUAL))
 (69 54 (:REWRITE DEFAULT-<-2))
 (67 54 (:REWRITE DEFAULT-<-1))
 (63 8 (:REWRITE LOFAT-TO-HIFAT-HELPER-CORRECTNESS-3))
 (52 37 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (50 30 (:REWRITE FOLD-CONSTS-IN-+))
 (48 6 (:REWRITE NFIX-WHEN-ZP))
 (44 7 (:REWRITE M1-FILE-HIFAT-FILE-ALIST-FIX-NORMALISATION))
 (36 36 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (35 35 (:REWRITE D-E-LIST-P-WHEN-NOT-CONSP))
 (35 35 (:REWRITE D-E-FILENAME-OF-D-E-FIX))
 (32 32 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (30 5 (:REWRITE ASSOCIATIVITY-OF-+))
 (26 6 (:REWRITE NFIX-WHEN-NATP))
 (22 22 (:TYPE-PRESCRIPTION HIFAT-FILE-ALIST-FIX))
 (21 21 (:REWRITE MEMBER-INTERSECTP-WITH-SUBSET))
 (21 21 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-46))
 (21 21 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 2))
 (21 21 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 1))
 (20 5 (:REWRITE DISTRIBUTIVITY-OF-MINUS-OVER-+))
 (15 15 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (15 5 (:REWRITE HIFAT-FILE-ALIST-FIX-WHEN-HIFAT-NO-DUPS-P))
 (15 5 (:DEFINITION NFIX))
 (15 5 (:DEFINITION NATP))
 (10 10 (:TYPE-PRESCRIPTION NO-DUPLICATESP-EQUAL))
 (10 10 (:TYPE-PRESCRIPTION MEMBER-INTERSECTP-EQUAL))
 (10 10 (:TYPE-PRESCRIPTION HIFAT-NO-DUPS-P))
 (10 10 (:REWRITE DEFAULT-UNARY-MINUS))
 (10 10 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (9 5 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-2))
 (7 7 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-58))
 (6 6 (:REWRITE LOFAT-TO-HIFAT-HELPER-CORRECTNESS-4))
 (5 5 (:TYPE-PRESCRIPTION SUBDIR-CONTENTS-P))
 (5 5 (:TYPE-PRESCRIPTION NATP))
 (5 5 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (5 5 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-17))
 (5 5 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-16))
 (5 1 (:REWRITE SET-EQUIV-OF-CONS-SELF))
 (4 4 (:TYPE-PRESCRIPTION LOFAT-FS-P))
 (3 3 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (2 2 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (1 1 (:TYPE-PRESCRIPTION NFIX))
 (1 1 (:REWRITE-QUOTED-CONSTANT M1-FILE-CONTENTS-FIX-UNDER-M1-FILE-CONTENTS-EQUIV))
 (1 1 (:REWRITE SUBSETP-MEMBER . 1))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-52
 (54697 4201 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-56))
 (42032 1052 (:REWRITE NOT-INTERSECTP-LIST-OF-APPEND-1))
 (27304 1052 (:DEFINITION MEMBER-INTERSECTP-EQUAL))
 (26293 6305 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-2 . 2))
 (22716 3108 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (21073 4201 (:REWRITE NOT-INTERSECTP-LIST-OF-LOFAT-TO-HIFAT-HELPER))
 (19384 1018 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (16500 3108 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (14460 1617 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (12654 2109 (:DEFINITION FREE-INDEX-LISTP))
 (12624 4208 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (11838 34 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-1))
 (10545 10545 (:TYPE-PRESCRIPTION FREE-INDEX-LISTP))
 (10520 10520 (:TYPE-PRESCRIPTION SUBSETP-EQUAL))
 (10520 1052 (:REWRITE SUBSETP-CONS-2))
 (10424 10424 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (8919 6564 (:REWRITE DEFAULT-+-2))
 (8848 26 (:REWRITE REMOVE-ASSOC-WHEN-ABSENT-1))
 (8160 6564 (:REWRITE DEFAULT-+-1))
 (8058 8058 (:TYPE-PRESCRIPTION FIND-D-E-CORRECTNESS-1))
 (7339 7339 (:REWRITE DEFAULT-CDR))
 (7014 7014 (:TYPE-PRESCRIPTION COUNT-OF-CLUSTERS))
 (6795 6795 (:REWRITE DEFAULT-CAR))
 (6172 4267 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (5755 4562 (:REWRITE DEFAULT-<-2))
 (5664 4562 (:REWRITE DEFAULT-<-1))
 (5212 2702 (:REWRITE USEFUL-D-E-LIST-P-OF-CDR))
 (4874 802 (:REWRITE NFIX-WHEN-ZP))
 (4602 156 (:LINEAR LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-1-LEMMA-1))
 (4550 156 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-8))
 (4208 4208 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (4208 1052 (:REWRITE COMMUTATIVITY-OF-+))
 (3572 3572 (:TYPE-PRESCRIPTION D-E-FIRST-CLUSTER))
 (3452 526 (:REWRITE M1-FILE-HIFAT-FILE-ALIST-FIX-NORMALISATION))
 (3156 526 (:REWRITE COMMUTATIVITY-2-OF-+))
 (3108 3108 (:TYPE-PRESCRIPTION D-E-P))
 (2104 2104 (:REWRITE MEMBER-INTERSECTP-WITH-SUBSET))
 (2104 2104 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-46))
 (2104 2104 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 2))
 (2104 2104 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 1))
 (2104 2104 (:REWRITE APPEND-WHEN-NOT-CONSP))
 (2104 526 (:REWRITE DISTRIBUTIVITY-OF-MINUS-OVER-+))
 (1726 1726 (:TYPE-PRESCRIPTION HIFAT-FILE-ALIST-FIX))
 (1691 571 (:DEFINITION NATP))
 (1656 54 (:REWRITE DELETE-D-E-CORRECTNESS-1))
 (1602 18 (:DEFINITION DELETE-D-E))
 (1578 1578 (:REWRITE FOLD-CONSTS-IN-+))
 (1200 400 (:REWRITE HIFAT-FILE-ALIST-FIX-WHEN-HIFAT-NO-DUPS-P))
 (1087 1070 (:REWRITE DEFAULT-UNARY-MINUS))
 (1052 1052 (:TYPE-PRESCRIPTION NO-DUPLICATESP-EQUAL))
 (1052 1052 (:TYPE-PRESCRIPTION MEMBER-INTERSECTP-EQUAL))
 (1052 1052 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (1052 526 (:REWRITE APPEND-OF-CONS))
 (750 750 (:TYPE-PRESCRIPTION LOFAT-FS-P))
 (571 571 (:TYPE-PRESCRIPTION NATP))
 (570 570 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (526 526 (:TYPE-PRESCRIPTION SUBDIR-CONTENTS-P))
 (468 156 (:LINEAR LOFAT-FS-P-CORRECTNESS-1))
 (300 100 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-17))
 (300 100 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-16))
 (200 200 (:REWRITE COUNT-OF-CLUSTERS-OF-LOFAT-REMOVE-FILE))
 (156 156 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (142 142 (:TYPE-PRESCRIPTION DELETE-D-E))
 (90 90 (:REWRITE USEFUL-D-E-LIST-P-OF-DELETE-D-E))
 (57 19 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-2))
 (34 34 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-2))
 (1 1 (:LINEAR POSITION-WHEN-MEMBER-OF-TAKE))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-53
 (25437 70 (:DEFINITION LOFAT-TO-HIFAT-HELPER))
 (9800 70 (:REWRITE LOFAT-TO-HIFAT-HELPER-CORRECTNESS-4))
 (7939 565 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-56))
 (6398 346 (:DEFINITION FIND-D-E))
 (5348 140 (:REWRITE NOT-INTERSECTP-LIST-OF-APPEND-1))
 (3945 232 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
 (3903 140 (:DEFINITION MEMBER-INTERSECTP-EQUAL))
 (3720 349 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (3335 565 (:REWRITE NOT-INTERSECTP-LIST-OF-LOFAT-TO-HIFAT-HELPER))
 (2941 349 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (2580 114 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (2176 297 (:DEFINITION FREE-INDEX-LISTP))
 (2091 232 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (1691 349 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (1554 518 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (1485 1485 (:TYPE-PRESCRIPTION FREE-INDEX-LISTP))
 (1258 1258 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (1153 873 (:REWRITE DEFAULT-+-2))
 (1131 362 (:REWRITE USEFUL-D-E-LIST-P-OF-CDR))
 (1128 1128 (:TYPE-PRESCRIPTION FIND-D-E-CORRECTNESS-1))
 (1087 929 (:REWRITE DEFAULT-CDR))
 (1083 873 (:REWRITE DEFAULT-+-1))
 (886 868 (:REWRITE DEFAULT-CAR))
 (840 840 (:TYPE-PRESCRIPTION COUNT-OF-CLUSTERS))
 (835 541 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (746 601 (:REWRITE DEFAULT-<-2))
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 (642 96 (:REWRITE NFIX-WHEN-ZP))
 (631 631 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (560 140 (:REWRITE COMMUTATIVITY-OF-+))
 (560 70 (:REWRITE M1-FILE-HIFAT-FILE-ALIST-FIX-NORMALISATION))
 (515 515 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (483 70 (:REWRITE COMMUTATIVITY-2-OF-+))
 (449 9 (:REWRITE DELETE-D-E-CORRECTNESS-1))
 (430 430 (:TYPE-PRESCRIPTION D-E-P))
 (430 430 (:TYPE-PRESCRIPTION D-E-LIST-P))
 (420 420 (:TYPE-PRESCRIPTION D-E-FIRST-CLUSTER))
 (396 3 (:DEFINITION DELETE-D-E))
 (384 3 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-31))
 (346 346 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (298 286 (:REWRITE APPEND-WHEN-NOT-CONSP))
 (284 284 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 2))
 (284 284 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 1))
 (282 282 (:REWRITE MEMBER-INTERSECTP-WITH-SUBSET))
 (280 280 (:TYPE-PRESCRIPTION HIFAT-FILE-ALIST-FIX))
 (280 70 (:REWRITE DISTRIBUTIVITY-OF-MINUS-OVER-+))
 (259 231 (:REWRITE FOLD-CONSTS-IN-+))
 (210 70 (:REWRITE HIFAT-FILE-ALIST-FIX-WHEN-HIFAT-NO-DUPS-P))
 (210 70 (:DEFINITION NFIX))
 (210 70 (:DEFINITION NATP))
 (162 162 (:REWRITE D-E-LIST-P-WHEN-SUBSETP-EQUAL))
 (160 24 (:REWRITE CONSP-OF-APPEND))
 (153 3 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-6))
 (140 140 (:TYPE-PRESCRIPTION NO-DUPLICATESP-EQUAL))
 (140 140 (:TYPE-PRESCRIPTION HIFAT-NO-DUPS-P))
 (140 140 (:REWRITE DEFAULT-UNARY-MINUS))
 (140 140 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (140 70 (:REWRITE APPEND-OF-CONS))
 (124 124 (:REWRITE COUNT-OF-CLUSTERS-OF-LOFAT-REMOVE-FILE))
 (81 81 (:REWRITE D-E-LIST-P-WHEN-NOT-CONSP))
 (78 78 (:REWRITE D-E-FILENAME-OF-D-E-FIX))
 (70 70 (:TYPE-PRESCRIPTION SUBDIR-CONTENTS-P))
 (70 70 (:TYPE-PRESCRIPTION NATP))
 (70 70 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (66 12 (:REWRITE CAR-OF-APPEND))
 (62 62 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-17))
 (62 62 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-16))
 (45 15 (:REWRITE USEFUL-D-E-LIST-P-OF-DELETE-D-E))
 (42 7 (:REWRITE ASSOCIATIVITY-OF-+))
 (31 31 (:TYPE-PRESCRIPTION DELETE-D-E))
 (30 10 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-2))
 (28 28 (:TYPE-PRESCRIPTION LOFAT-FS-P))
 (18 6 (:REWRITE CDR-OF-APPEND-WHEN-CONSP))
 (14 6 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (10 4 (:REWRITE LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-2-LEMMA-2))
 (9 3 (:LINEAR HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E))
 (3 3 (:LINEAR LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-52))
 (2 2 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-93))
 (2 2 (:REWRITE FLATTEN-WHEN-NOT-CONSP))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-54
 (7754 515 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (5541 323 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-56))
 (5346 56 (:REWRITE NOT-INTERSECTP-LIST-OF-APPEND-1))
 (4585 33 (:REWRITE LOFAT-TO-HIFAT-HELPER-CORRECTNESS-4))
 (4474 314 (:DEFINITION FIND-D-E))
 (2454 314 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (1787 319 (:REWRITE NOT-INTERSECTP-LIST-OF-LOFAT-TO-HIFAT-HELPER))
 (1673 170 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (1660 144 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
 (1136 166 (:DEFINITION FREE-INDEX-LISTP))
 (984 972 (:REWRITE DEFAULT-CDR))
 (940 940 (:REWRITE DEFAULT-CAR))
 (896 896 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (830 830 (:TYPE-PRESCRIPTION FREE-INDEX-LISTP))
 (828 46 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (775 589 (:REWRITE DEFAULT-+-2))
 (689 589 (:REWRITE DEFAULT-+-1))
 (618 6 (:REWRITE LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-2-LEMMA-2))
 (539 335 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (511 508 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (507 413 (:REWRITE DEFAULT-<-2))
 (501 336 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-LEFT))
 (480 32 (:REWRITE COMMUTATIVITY-2-OF-+))
 (478 413 (:REWRITE DEFAULT-<-1))
 (360 333 (:REWRITE INTERSECT-WITH-SUBSET . 11))
 (354 46 (:REWRITE NFIX-WHEN-ZP))
 (348 336 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-RIGHT))
 (334 334 (:REWRITE FLATTEN-SUBSET-NO-DUPLICATESP-LEMMA-1))
 (320 192 (:REWRITE FOLD-CONSTS-IN-+))
 (262 34 (:REWRITE M1-FILE-HIFAT-FILE-ALIST-FIX-NORMALISATION))
 (204 204 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (192 32 (:REWRITE ASSOCIATIVITY-OF-+))
 (183 183 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (151 151 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 2))
 (151 151 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 1))
 (147 147 (:REWRITE MEMBER-INTERSECTP-WITH-SUBSET))
 (143 143 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-46))
 (134 4 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-1 . 1))
 (130 130 (:TYPE-PRESCRIPTION HIFAT-FILE-ALIST-FIX))
 (128 32 (:REWRITE DISTRIBUTIVITY-OF-MINUS-OVER-+))
 (118 118 (:TYPE-PRESCRIPTION MEMBER-INTERSECTP-EQUAL))
 (96 32 (:REWRITE HIFAT-FILE-ALIST-FIX-WHEN-HIFAT-NO-DUPS-P))
 (96 32 (:DEFINITION NFIX))
 (96 32 (:DEFINITION NATP))
 (64 64 (:TYPE-PRESCRIPTION HIFAT-NO-DUPS-P))
 (64 64 (:REWRITE DEFAULT-UNARY-MINUS))
 (64 64 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (33 5 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-2))
 (32 32 (:TYPE-PRESCRIPTION SUBDIR-CONTENTS-P))
 (32 32 (:TYPE-PRESCRIPTION NATP))
 (32 32 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (26 26 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (16 8 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-93))
 (10 10 (:TYPE-PRESCRIPTION LOFAT-REMOVE-FILE-CORRECTNESS-3))
 (10 4 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-5))
 (10 2 (:REWRITE SET-EQUIV-OF-CONS-SELF))
 (8 8 (:REWRITE INTERSECTP-OF-SELF))
 (8 2 (:REWRITE CONSP-OF-APPEND))
 (6 6 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (5 1 (:REWRITE CAR-OF-APPEND))
 (4 1 (:REWRITE CDR-OF-APPEND-WHEN-CONSP))
 (2 2 (:TYPE-PRESCRIPTION STRINGP-OF-D-E-CC-CONTENTS))
 (2 2 (:REWRITE SUBSETP-MEMBER . 1))
 (2 2 (:REWRITE FIND-D-E-CORRECTNESS-1))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-55
 (27896 75 (:DEFINITION LOFAT-TO-HIFAT-HELPER))
 (10547 75 (:REWRITE LOFAT-TO-HIFAT-HELPER-CORRECTNESS-4))
 (8661 598 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-56))
 (7522 379 (:DEFINITION FIND-D-E))
 (5952 150 (:REWRITE NOT-INTERSECTP-LIST-OF-APPEND-1))
 (4559 381 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (4385 249 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
 (4163 150 (:DEFINITION MEMBER-INTERSECTP-EQUAL))
 (3748 898 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-2 . 2))
 (3676 381 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (3285 598 (:REWRITE NOT-INTERSECTP-LIST-OF-LOFAT-TO-HIFAT-HELPER))
 (2978 130 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (2313 249 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (2206 384 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (2067 310 (:DEFINITION FREE-INDEX-LISTP))
 (1800 600 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (1599 525 (:REWRITE USEFUL-D-E-LIST-P-OF-CDR))
 (1550 1550 (:TYPE-PRESCRIPTION FREE-INDEX-LISTP))
 (1500 1500 (:TYPE-PRESCRIPTION SUBSETP-EQUAL))
 (1500 150 (:REWRITE SUBSETP-CONS-2))
 (1362 1362 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (1285 985 (:REWRITE DEFAULT-+-2))
 (1210 985 (:REWRITE DEFAULT-+-1))
 (1198 1198 (:TYPE-PRESCRIPTION FIND-D-E-CORRECTNESS-1))
 (1130 1047 (:REWRITE DEFAULT-CDR))
 (945 935 (:REWRITE DEFAULT-CAR))
 (900 900 (:TYPE-PRESCRIPTION COUNT-OF-CLUSTERS))
 (874 574 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (800 646 (:REWRITE DEFAULT-<-2))
 (799 646 (:REWRITE DEFAULT-<-1))
 (658 98 (:REWRITE NFIX-WHEN-ZP))
 (648 648 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (612 75 (:REWRITE COMMUTATIVITY-2-OF-+))
 (600 600 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (600 150 (:REWRITE COMMUTATIVITY-OF-+))
 (558 75 (:REWRITE M1-FILE-HIFAT-FILE-ALIST-FIX-NORMALISATION))
 (502 502 (:TYPE-PRESCRIPTION D-E-P))
 (450 450 (:TYPE-PRESCRIPTION D-E-FIRST-CLUSTER))
 (384 3 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-31))
 (379 379 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (351 279 (:REWRITE FOLD-CONSTS-IN-+))
 (340 6 (:REWRITE DELETE-D-E-CORRECTNESS-1))
 (309 303 (:REWRITE APPEND-WHEN-NOT-CONSP))
 (304 304 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 2))
 (304 304 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 1))
 (302 302 (:REWRITE MEMBER-INTERSECTP-WITH-SUBSET))
 (302 302 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-46))
 (300 75 (:REWRITE DISTRIBUTIVITY-OF-MINUS-OVER-+))
 (294 2 (:DEFINITION DELETE-D-E))
 (279 279 (:TYPE-PRESCRIPTION HIFAT-FILE-ALIST-FIX))
 (248 248 (:REWRITE D-E-LIST-P-WHEN-SUBSETP-EQUAL))
 (225 75 (:DEFINITION NFIX))
 (225 75 (:DEFINITION NATP))
 (204 68 (:REWRITE HIFAT-FILE-ALIST-FIX-WHEN-HIFAT-NO-DUPS-P))
 (198 6 (:REWRITE PUT-ASSOC-EQUAL-WITHOUT-CHANGE . 2))
 (171 3 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-6))
 (150 150 (:TYPE-PRESCRIPTION NO-DUPLICATESP-EQUAL))
 (150 150 (:REWRITE DEFAULT-UNARY-MINUS))
 (150 150 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (150 75 (:REWRITE APPEND-OF-CONS))
 (136 136 (:TYPE-PRESCRIPTION HIFAT-NO-DUPS-P))
 (128 128 (:REWRITE COUNT-OF-CLUSTERS-OF-LOFAT-REMOVE-FILE))
 (124 124 (:REWRITE D-E-LIST-P-WHEN-NOT-CONSP))
 (119 119 (:REWRITE D-E-FILENAME-OF-D-E-FIX))
 (108 18 (:REWRITE ASSOCIATIVITY-OF-+))
 (84 12 (:REWRITE CONSP-OF-APPEND))
 (81 3 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-1))
 (75 75 (:TYPE-PRESCRIPTION SUBDIR-CONTENTS-P))
 (75 75 (:TYPE-PRESCRIPTION NATP))
 (75 75 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (64 64 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-17))
 (64 64 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-16))
 (63 18 (:TYPE-PRESCRIPTION ASSOC-WHEN-ZP-LEN))
 (60 10 (:REWRITE USEFUL-D-E-LIST-P-OF-DELETE-D-E))
 (57 3 (:DEFINITION PUT-ASSOC-EQUAL))
 (40 16 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-2))
 (34 6 (:REWRITE CAR-OF-APPEND))
 (30 30 (:TYPE-PRESCRIPTION LOFAT-FS-P))
 (30 3 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-23))
 (22 22 (:TYPE-PRESCRIPTION DELETE-D-E))
 (18 18 (:TYPE-PRESCRIPTION LEN))
 (18 3 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-2))
 (18 3 (:LINEAR HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E))
 (13 3 (:REWRITE LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-2-LEMMA-2))
 (10 4 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (9 3 (:REWRITE CDR-OF-APPEND-WHEN-CONSP))
 (4 4 (:LINEAR LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-52))
 (2 2 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-93))
 (1 1 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-48))
 (1 1 (:REWRITE FLATTEN-WHEN-NOT-CONSP))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-57
 (1313775 430754 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (551839 421668 (:REWRITE DEFAULT-+-2))
 (497719 421668 (:REWRITE DEFAULT-+-1))
 (430850 430728 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (258061 157871 (:REWRITE FOLD-CONSTS-IN-+))
 (230422 176939 (:REWRITE DEFAULT-<-1))
 (180629 176939 (:REWRITE DEFAULT-<-2))
 (177636 177633 (:REWRITE DEFAULT-CDR))
 (165454 26526 (:REWRITE ASSOCIATIVITY-OF-+))
 (151388 151385 (:REWRITE DEFAULT-CAR))
 (124576 124576 (:REWRITE FLATTEN-SUBSET-NO-DUPLICATESP-LEMMA-1))
 (59778 53712 (:REWRITE DEFAULT-UNARY-MINUS))
 (56067 55748 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 2))
 (54362 54362 (:REWRITE MEMBER-INTERSECTP-WITH-SUBSET))
 (52987 52987 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (23946 23946 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (22857 9 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-38))
 (21553 16 (:REWRITE SUBSETP-OF-APPEND-WHEN-SUBSET-OF-EITHER))
 (10589 15 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-31))
 (9764 567 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (5410 5410 (:TYPE-PRESCRIPTION D-E-FILE-SIZE))
 (603 78 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-2))
 (60 20 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-5))
 (18 18 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-SUBSETP-EQUAL))
 (14 14 (:LINEAR POSITION-WHEN-MEMBER-OF-TAKE))
 (10 10 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (9 9 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-NOT-CONSP))
 (9 1 (:REWRITE SET-EQUIV-WITH-APPEND-OTHER-RIGHT))
 (8 8 (:LINEAR LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-1-LEMMA-1))
 (8 8 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-8))
 (5 1 (:REWRITE SET-EQUIV-OF-CONS-SELF))
 (4 4 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (3 3 (:TYPE-PRESCRIPTION SET-EQUIV))
 (2 2 (:REWRITE CONSP-OF-APPEND))
 (1 1 (:REWRITE SUBSETP-MEMBER . 1))
 (1 1 (:REWRITE FLATTEN-WHEN-NOT-CONSP))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-61
 (108893 325 (:DEFINITION LOFAT-TO-HIFAT-HELPER))
 (58624 644 (:REWRITE NOT-INTERSECTP-LIST-OF-APPEND-1))
 (40347 1929 (:DEFINITION NOT-INTERSECTP-LIST))
 (36829 1300 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-56))
 (22575 7527 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (10539 3 (:LINEAR LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-6))
 (7523 7523 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (7510 5326 (:REWRITE DEFAULT-+-2))
 (6680 5326 (:REWRITE DEFAULT-+-1))
 (6121 325 (:REWRITE COMMUTATIVITY-2-OF-+))
 (3948 3948 (:TYPE-PRESCRIPTION COUNT-OF-CLUSTERS))
 (3893 7 (:REWRITE LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-2-LEMMA-2))
 (3372 2064 (:REWRITE FOLD-CONSTS-IN-+))
 (3282 1944 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (3082 407 (:REWRITE ASSOCIATIVITY-OF-+))
 (3059 2207 (:REWRITE DEFAULT-<-2))
 (2896 2207 (:REWRITE DEFAULT-<-1))
 (2795 2795 (:TYPE-PRESCRIPTION FIND-D-E-CORRECTNESS-1))
 (2706 689 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (2625 2625 (:REWRITE DEFAULT-CDR))
 (2564 2564 (:TYPE-PRESCRIPTION INTERSECTP-EQUAL))
 (2273 2273 (:REWRITE DEFAULT-CAR))
 (2266 3 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-2 . 1))
 (2251 19 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-93))
 (2010 2010 (:TYPE-PRESCRIPTION D-E-FIRST-CLUSTER))
 (1929 1929 (:REWRITE INTERSECT-WITH-SUBSET . 12))
 (1929 1929 (:REWRITE FLATTEN-SUBSET-NO-DUPLICATESP-LEMMA-1))
 (1910 325 (:REWRITE M1-FILE-HIFAT-FILE-ALIST-FIX-NORMALISATION))
 (1634 1634 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (1326 1308 (:REWRITE APPEND-WHEN-NOT-CONSP))
 (1300 325 (:REWRITE DISTRIBUTIVITY-OF-MINUS-OVER-+))
 (1029 331 (:DEFINITION NFIX))
 (955 955 (:TYPE-PRESCRIPTION HIFAT-FILE-ALIST-FIX))
 (667 660 (:REWRITE DEFAULT-UNARY-MINUS))
 (665 665 (:REWRITE MEMBER-INTERSECTP-WITH-SUBSET))
 (650 650 (:TYPE-PRESCRIPTION NO-DUPLICATESP-EQUAL))
 (650 650 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (650 325 (:REWRITE APPEND-OF-CONS))
 (630 210 (:REWRITE HIFAT-FILE-ALIST-FIX-WHEN-HIFAT-NO-DUPS-P))
 (423 423 (:TYPE-PRESCRIPTION HIFAT-NO-DUPS-P))
 (346 3 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-31))
 (325 325 (:TYPE-PRESCRIPTION SUBDIR-CONTENTS-P))
 (325 325 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (290 290 (:TYPE-PRESCRIPTION LOFAT-FS-P))
 (195 65 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-17))
 (195 65 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-16))
 (144 18 (:REWRITE DELETE-D-E-CORRECTNESS-1))
 (132 18 (:LINEAR LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-1-LEMMA-1))
 (132 6 (:DEFINITION DELETE-D-E))
 (132 4 (:REWRITE REMOVE-ASSOC-WHEN-ABSENT-1))
 (130 130 (:REWRITE COUNT-OF-CLUSTERS-OF-LOFAT-REMOVE-FILE))
 (126 3 (:LINEAR HIFAT-ENTRY-COUNT-OF-REMOVE-ASSOC-EQUAL))
 (122 7 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-23))
 (56 14 (:TYPE-PRESCRIPTION ASSOC-WHEN-ZP-LEN))
 (42 42 (:TYPE-PRESCRIPTION DELETE-D-E))
 (33 11 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-2))
 (32 32 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-83))
 (28 7 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-1))
 (21 7 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-2))
 (21 7 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (20 20 (:TYPE-PRESCRIPTION LOFAT-TO-HIFAT-HELPER-CORRECTNESS-1 . 2))
 (14 14 (:TYPE-PRESCRIPTION LEN))
 (14 6 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (12 12 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (9 3 (:REWRITE M1-FILE-ALIST-P-OF-LOFAT-TO-HIFAT-HELPER))
 (4 4 (:REWRITE FLATTEN-WHEN-NOT-CONSP))
 (3 3 (:REWRITE HIFAT-NO-DUPS-P-OF-LOFAT-TO-HIFAT-HELPER))
 (3 3 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-7 . 4))
 (3 3 (:LINEAR LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-52))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-45
 (906701 2508 (:DEFINITION LOFAT-TO-HIFAT-HELPER))
 (191286 5016 (:REWRITE NOT-INTERSECTP-LIST-OF-APPEND-1))
 (181977 3386 (:REWRITE NFIX-WHEN-ZP))
 (178764 10032 (:DEFINITION FIND-D-E))
 (170545 4861 (:DEFINITION MEMBER-INTERSECTP-EQUAL))
 (124494 7524 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
 (122921 27166 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-2 . 2))
 (98508 10032 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (96107 17134 (:REWRITE NOT-INTERSECTP-LIST-OF-LOFAT-TO-HIFAT-HELPER))
 (72279 7524 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (69771 2508 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (62751 20962 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (59231 9853 (:DEFINITION FREE-INDEX-LISTP))
 (52948 5291 (:REWRITE SUBSETP-CONS-2))
 (52392 52392 (:TYPE-PRESCRIPTION SUBSETP-EQUAL))
 (51727 40684 (:REWRITE DEFAULT-+-2))
 (49301 49301 (:TYPE-PRESCRIPTION FREE-INDEX-LISTP))
 (48259 40684 (:REWRITE DEFAULT-+-1))
 (40128 40128 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (37239 2508 (:REWRITE COMMUTATIVITY-2-OF-+))
 (35112 35112 (:TYPE-PRESCRIPTION FIND-D-E-CORRECTNESS-1))
 (30369 153 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-93))
 (29811 29774 (:REWRITE DEFAULT-CDR))
 (27310 27304 (:REWRITE DEFAULT-CAR))
 (27041 21778 (:REWRITE DEFAULT-<-2))
 (26815 21778 (:REWRITE DEFAULT-<-1))
 (25710 17430 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (24237 14927 (:REWRITE FOLD-CONSTS-IN-+))
 (21122 21122 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (20960 20960 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (20064 5016 (:REWRITE COMMUTATIVITY-OF-+))
 (15180 2508 (:REWRITE ASSOCIATIVITY-OF-+))
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 (10359 10183 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 2))
 (10326 2508 (:REWRITE M1-FILE-HIFAT-FILE-ALIST-FIX-NORMALISATION))
 (10044 2508 (:REWRITE DISTRIBUTIVITY-OF-MINUS-OVER-+))
 (10037 10034 (:REWRITE APPEND-WHEN-NOT-CONSP))
 (10032 10032 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (10028 10028 (:REWRITE MEMBER-INTERSECTP-WITH-SUBSET))
 (9276 2504 (:DEFINITION NFIX))
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 (5083 5058 (:REWRITE DEFAULT-UNARY-MINUS))
 (5016 5016 (:TYPE-PRESCRIPTION NO-DUPLICATESP-EQUAL))
 (5016 5016 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (5016 2508 (:REWRITE APPEND-OF-CONS))
 (2655 885 (:REWRITE HIFAT-FILE-ALIST-FIX-WHEN-HIFAT-NO-DUPS-P))
 (2508 2508 (:TYPE-PRESCRIPTION SUBDIR-CONTENTS-P))
 (2499 2499 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2313 3 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-31))
 (1770 1770 (:TYPE-PRESCRIPTION HIFAT-NO-DUPS-P))
 (1065 62 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (646 1 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-38))
 (590 590 (:TYPE-PRESCRIPTION D-E-FILE-SIZE))
 (504 504 (:REWRITE COUNT-OF-CLUSTERS-OF-LOFAT-REMOVE-FILE))
 (335 11 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-2))
 (45 45 (:TYPE-PRESCRIPTION LOFAT-REMOVE-FILE-CORRECTNESS-3))
 (34 6 (:REWRITE CONSP-OF-APPEND))
 (18 3 (:REWRITE CAR-OF-APPEND))
 (6 2 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-5))
 (5 2 (:REWRITE CDR-OF-APPEND-WHEN-CONSP))
 (1 1 (:REWRITE SUBSETP-REFL))
 (1 1 (:REWRITE FLATTEN-WHEN-NOT-CONSP))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-49
 (3651 10 (:DEFINITION LOFAT-TO-HIFAT-HELPER))
 (1026 86 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-56))
 (800 20 (:REWRITE NOT-INTERSECTP-LIST-OF-APPEND-1))
 (720 40 (:DEFINITION FIND-D-E))
 (549 86 (:REWRITE NOT-INTERSECTP-LIST-OF-LOFAT-TO-HIFAT-HELPER))
 (539 21 (:DEFINITION MEMBER-INTERSECTP-EQUAL))
 (506 126 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-2 . 2))
 (500 30 (:REWRITE HIFAT-ENTRY-COUNT-OF-LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-LEMMA-3))
 (396 40 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (371 46 (:DEFINITION FREE-INDEX-LISTP))
 (312 40 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (290 30 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (280 10 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (240 80 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (230 230 (:TYPE-PRESCRIPTION FREE-INDEX-LISTP))
 (216 40 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (200 200 (:TYPE-PRESCRIPTION SUBSETP-EQUAL))
 (200 20 (:REWRITE SUBSETP-CONS-2))
 (169 130 (:REWRITE DEFAULT-CDR))
 (165 125 (:REWRITE DEFAULT-+-2))
 (165 55 (:REWRITE USEFUL-D-E-LIST-P-OF-CDR))
 (160 160 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (155 125 (:REWRITE DEFAULT-+-1))
 (142 134 (:REWRITE DEFAULT-CAR))
 (140 140 (:TYPE-PRESCRIPTION FIND-D-E-CORRECTNESS-1))
 (124 79 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (120 120 (:TYPE-PRESCRIPTION COUNT-OF-CLUSTERS))
 (107 85 (:REWRITE DEFAULT-<-2))
 (106 85 (:REWRITE DEFAULT-<-1))
 (90 13 (:REWRITE NFIX-WHEN-ZP))
 (80 80 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (80 20 (:REWRITE COMMUTATIVITY-OF-+))
 (80 10 (:REWRITE M1-FILE-HIFAT-FILE-ALIST-FIX-NORMALISATION))
 (69 10 (:REWRITE COMMUTATIVITY-2-OF-+))
 (63 63 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (60 60 (:TYPE-PRESCRIPTION D-E-FIRST-CLUSTER))
 (50 50 (:TYPE-PRESCRIPTION D-E-DIRECTORY-P))
 (45 42 (:REWRITE APPEND-WHEN-NOT-CONSP))
 (44 44 (:TYPE-PRESCRIPTION D-E-P))
 (43 43 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 2))
 (43 43 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 1))
 (42 42 (:REWRITE MEMBER-INTERSECTP-WITH-SUBSET))
 (42 42 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-46))
 (40 40 (:TYPE-PRESCRIPTION HIFAT-FILE-ALIST-FIX))
 (40 40 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (40 10 (:REWRITE DISTRIBUTIVITY-OF-MINUS-OVER-+))
 (37 33 (:REWRITE FOLD-CONSTS-IN-+))
 (34 6 (:REWRITE CONSP-OF-APPEND))
 (30 10 (:REWRITE HIFAT-FILE-ALIST-FIX-WHEN-HIFAT-NO-DUPS-P))
 (30 10 (:DEFINITION NFIX))
 (30 10 (:DEFINITION NATP))
 (20 20 (:TYPE-PRESCRIPTION NO-DUPLICATESP-EQUAL))
 (20 20 (:TYPE-PRESCRIPTION HIFAT-NO-DUPS-P))
 (20 20 (:REWRITE DEFAULT-UNARY-MINUS))
 (20 20 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (20 10 (:REWRITE APPEND-OF-CONS))
 (18 3 (:REWRITE CAR-OF-APPEND))
 (14 14 (:REWRITE COUNT-OF-CLUSTERS-OF-LOFAT-REMOVE-FILE))
 (11 11 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-58))
 (10 10 (:TYPE-PRESCRIPTION SUBDIR-CONTENTS-P))
 (10 10 (:TYPE-PRESCRIPTION NATP))
 (10 10 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (10 10 (:REWRITE LOFAT-TO-HIFAT-HELPER-CORRECTNESS-4))
 (10 4 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-2))
 (8 8 (:TYPE-PRESCRIPTION LOFAT-FS-P))
 (8 8 (:REWRITE D-E-LIST-P-WHEN-SUBSETP-EQUAL))
 (6 1 (:REWRITE ASSOCIATIVITY-OF-+))
 (5 2 (:REWRITE CDR-OF-APPEND-WHEN-CONSP))
 (4 4 (:REWRITE D-E-LIST-P-WHEN-NOT-CONSP))
 (4 4 (:REWRITE D-E-FILENAME-OF-D-E-FIX))
 (3 1 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (1 1 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-31))
 (1 1 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-93))
 (1 1 (:REWRITE FLATTEN-WHEN-NOT-CONSP))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-51
 (23209 112 (:DEFINITION LOFAT-TO-HIFAT-HELPER))
 (16338 112 (:REWRITE LOFAT-TO-HIFAT-HELPER-CORRECTNESS-4))
 (12348 82 (:DEFINITION NATP))
 (8579 169 (:REWRITE NFIX-WHEN-NATP))
 (5596 222 (:REWRITE NOT-INTERSECTP-LIST-OF-APPEND-1))
 (4360 591 (:DEFINITION NOT-INTERSECTP-LIST))
 (4122 24 (:LINEAR LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-54))
 (2551 1878 (:REWRITE DEFAULT-+-2))
 (2493 371 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-56))
 (2357 1878 (:REWRITE DEFAULT-+-1))
 (2111 112 (:REWRITE COMMUTATIVITY-2-OF-+))
 (1292 732 (:REWRITE FOLD-CONSTS-IN-+))
 (1105 846 (:REWRITE DEFAULT-<-2))
 (1094 114 (:REWRITE ZP-OPEN))
 (1074 846 (:REWRITE DEFAULT-<-1))
 (1045 141 (:REWRITE ASSOCIATIVITY-OF-+))
 (1011 594 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (917 10 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-93))
 (896 896 (:TYPE-PRESCRIPTION FIND-D-E-CORRECTNESS-1))
 (896 224 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (896 224 (:REWRITE COMMUTATIVITY-OF-+))
 (896 112 (:REWRITE M1-FILE-HIFAT-FILE-ALIST-FIX-NORMALISATION))
 (819 819 (:REWRITE DEFAULT-CDR))
 (738 738 (:TYPE-PRESCRIPTION INTERSECTP-EQUAL))
 (711 711 (:REWRITE DEFAULT-CAR))
 (691 1 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-2))
 (591 591 (:REWRITE INTERSECT-WITH-SUBSET . 12))
 (591 591 (:REWRITE FLATTEN-SUBSET-NO-DUPLICATESP-LEMMA-1))
 (587 587 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (581 581 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (448 448 (:TYPE-PRESCRIPTION HIFAT-FILE-ALIST-FIX))
 (448 448 (:REWRITE APPEND-WHEN-NOT-CONSP))
 (448 112 (:REWRITE DISTRIBUTIVITY-OF-MINUS-OVER-+))
 (398 1 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-38))
 (336 112 (:REWRITE HIFAT-FILE-ALIST-FIX-WHEN-HIFAT-NO-DUPS-P))
 (280 280 (:TYPE-PRESCRIPTION NATP))
 (268 134 (:DEFINITION FIX))
 (233 233 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-46))
 (230 230 (:REWRITE MEMBER-INTERSECTP-WITH-SUBSET))
 (228 226 (:REWRITE DEFAULT-UNARY-MINUS))
 (224 224 (:TYPE-PRESCRIPTION NO-DUPLICATESP-EQUAL))
 (224 224 (:TYPE-PRESCRIPTION HIFAT-NO-DUPS-P))
 (224 224 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (224 112 (:REWRITE APPEND-OF-CONS))
 (112 112 (:TYPE-PRESCRIPTION SUBDIR-CONTENTS-P))
 (41 1 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-2))
 (38 16 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (36 2 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (20 20 (:TYPE-PRESCRIPTION D-E-FILE-SIZE))
 (5 5 (:TYPE-PRESCRIPTION LOFAT-REMOVE-FILE-CORRECTNESS-3))
 (2 2 (:TYPE-PRESCRIPTION ZP))
 (1 1 (:TYPE-PRESCRIPTION D-E-P))
 (1 1 (:REWRITE FIND-D-E-CORRECTNESS-1))
 (1 1 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-7 . 4))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-56
 (312469 1467 (:DEFINITION LOFAT-TO-HIFAT-HELPER))
 (71904 2814 (:REWRITE NOT-INTERSECTP-LIST-OF-APPEND-1))
 (69184 7862 (:DEFINITION NOT-INTERSECTP-LIST))
 (69063 61 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-6))
 (48331 173 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-2))
 (38681 25971 (:REWRITE DEFAULT-+-2))
 (37936 5100 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-56))
 (33861 25971 (:REWRITE DEFAULT-+-1))
 (33382 1467 (:REWRITE COMMUTATIVITY-2-OF-+))
 (17918 2313 (:REWRITE ASSOCIATIVITY-OF-+))
 (17600 10368 (:REWRITE FOLD-CONSTS-IN-+))
 (14919 10486 (:REWRITE DEFAULT-<-2))
 (13485 10486 (:REWRITE DEFAULT-<-1))
 (13015 8164 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (11940 11940 (:TYPE-PRESCRIPTION FIND-D-E-CORRECTNESS-1))
 (11856 2976 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (10870 10869 (:REWRITE DEFAULT-CDR))
 (10090 10090 (:TYPE-PRESCRIPTION INTERSECTP-EQUAL))
 (9370 9369 (:REWRITE DEFAULT-CAR))
 (7862 7862 (:REWRITE INTERSECT-WITH-SUBSET . 12))
 (7862 7862 (:REWRITE FLATTEN-SUBSET-NO-DUPLICATESP-LEMMA-1))
 (7524 1467 (:REWRITE M1-FILE-HIFAT-FILE-ALIST-FIX-NORMALISATION))
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 (5868 1467 (:REWRITE DISTRIBUTIVITY-OF-MINUS-OVER-+))
 (5645 66 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-17))
 (5645 66 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-16))
 (4449 1473 (:DEFINITION NFIX))
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 (3200 3200 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-46))
 (3199 3199 (:REWRITE MEMBER-INTERSECTP-WITH-SUBSET))
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 (2969 2953 (:REWRITE DEFAULT-UNARY-MINUS))
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 (2934 2934 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (2934 1467 (:REWRITE APPEND-OF-CONS))
 (2295 765 (:REWRITE HIFAT-FILE-ALIST-FIX-WHEN-HIFAT-NO-DUPS-P))
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 (1640 1640 (:TYPE-PRESCRIPTION D-E-FILE-SIZE))
 (1467 1467 (:TYPE-PRESCRIPTION SUBDIR-CONTENTS-P))
 (1467 1467 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1040 3 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-2 . 1))
 (770 132 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (538 18 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-2))
 (423 141 (:REWRITE D-E-LIST-P-WHEN-USEFUL-D-E-LIST-P))
 (159 9 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-23))
 (145 145 (:TYPE-PRESCRIPTION D-E-P))
 (132 132 (:REWRITE COUNT-OF-CLUSTERS-OF-LOFAT-REMOVE-FILE))
 (132 6 (:REWRITE PUT-ASSOC-EQUAL-WITHOUT-CHANGE . 2))
 (126 3 (:LINEAR HIFAT-ENTRY-COUNT-OF-REMOVE-ASSOC-EQUAL))
 (120 15 (:REWRITE DELETE-D-E-CORRECTNESS-1))
 (110 5 (:DEFINITION DELETE-D-E))
 (99 27 (:TYPE-PRESCRIPTION ASSOC-WHEN-ZP-LEN))
 (99 3 (:REWRITE REMOVE-ASSOC-WHEN-ABSENT-1))
 (65 65 (:TYPE-PRESCRIPTION LOFAT-REMOVE-FILE-CORRECTNESS-3))
 (57 3 (:DEFINITION PUT-ASSOC-EQUAL))
 (52 52 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-7 . 4))
 (36 9 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-1))
 (27 27 (:TYPE-PRESCRIPTION LEN))
 (27 9 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-2))
 (25 25 (:TYPE-PRESCRIPTION DELETE-D-E))
 (15 5 (:REWRITE USEFUL-D-E-LIST-P-OF-DELETE-D-E))
 (13 13 (:REWRITE FIND-D-E-CORRECTNESS-1))
 (10 10 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (9 3 (:REWRITE M1-FILE-ALIST-P-OF-LOFAT-TO-HIFAT-HELPER))
 (4 4 (:LINEAR LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-52))
 (3 3 (:REWRITE HIFAT-NO-DUPS-P-OF-LOFAT-TO-HIFAT-HELPER))
 (2 2 (:REWRITE FLATTEN-WHEN-NOT-CONSP))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-27
 (56873 15 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-6))
 (55179 38052 (:REWRITE DEFAULT-+-2))
 (49078 38052 (:REWRITE DEFAULT-+-1))
 (26539 15457 (:REWRITE FOLD-CONSTS-IN-+))
 (25827 3396 (:REWRITE ASSOCIATIVITY-OF-+))
 (20862 16244 (:REWRITE DEFAULT-<-1))
 (19297 16244 (:REWRITE DEFAULT-<-2))
 (15488 15485 (:REWRITE DEFAULT-CDR))
 (13361 13358 (:REWRITE DEFAULT-CAR))
 (11071 11071 (:REWRITE FLATTEN-SUBSET-NO-DUPLICATESP-LEMMA-1))
 (6724 383 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (4751 4751 (:REWRITE MEMBER-INTERSECTP-WITH-SUBSET))
 (4393 4362 (:REWRITE DEFAULT-UNARY-MINUS))
 (4328 4328 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (3439 1463 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (3431 3431 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (582 27 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-2))
 (168 4 (:LINEAR HIFAT-ENTRY-COUNT-OF-REMOVE-ASSOC-EQUAL))
 (140 8 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-23))
 (132 4 (:REWRITE REMOVE-ASSOC-WHEN-ABSENT-1))
 (125 125 (:TYPE-PRESCRIPTION LOFAT-REMOVE-FILE-CORRECTNESS-3))
 (104 13 (:REWRITE DELETE-D-E-CORRECTNESS-1))
 (94 55 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (64 16 (:TYPE-PRESCRIPTION ASSOC-WHEN-ZP-LEN))
 (39 13 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-5))
 (32 8 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-1))
 (26 26 (:REWRITE FIND-D-E-CORRECTNESS-1))
 (24 8 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-2))
 (20 20 (:TYPE-PRESCRIPTION DELETE-D-E))
 (16 16 (:TYPE-PRESCRIPTION LEN))
 (12 4 (:REWRITE USEFUL-D-E-LIST-P-OF-DELETE-D-E))
 (7 7 (:LINEAR LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-52))
 (1 1 (:REWRITE FLATTEN-WHEN-NOT-CONSP))
 (1 1 (:LINEAR POSITION-WHEN-MEMBER-OF-TAKE))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-32
 (705782 1246 (:REWRITE REMOVE-ASSOC-WHEN-ABSENT-1))
 (630648 1013 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-59))
 (539152 1474 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-1))
 (290070 1474 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-2))
 (261185 308 (:REWRITE PUT-ASSOC-EQUAL-WITHOUT-CHANGE . 2))
 (181528 130148 (:REWRITE DEFAULT-+-2))
 (157052 130148 (:REWRITE DEFAULT-+-1))
 (133885 133300 (:REWRITE DEFAULT-CDR))
 (128802 128 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-25))
 (125047 124602 (:REWRITE DEFAULT-CAR))
 (115587 101 (:REWRITE LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-2-LEMMA-2))
 (111944 147 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-38))
 (104537 27201 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 2))
 (87512 70990 (:REWRITE DEFAULT-<-1))
 (84169 70990 (:REWRITE DEFAULT-<-2))
 (72164 308 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-15))
 (67497 591 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-83))
 (62366 39414 (:REWRITE FOLD-CONSTS-IN-+))
 (60129 26903 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-46))
 (55189 27201 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 1))
 (54047 53748 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (46436 46436 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (42492 6302 (:REWRITE ASSOCIATIVITY-OF-+))
 (41385 327 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-2))
 (38513 124 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-7))
 (38480 116 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-1 . 1))
 (26397 694 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-2))
 (16945 15253 (:REWRITE DEFAULT-UNARY-MINUS))
 (13642 13622 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (8664 3 (:REWRITE MEMBER-INTERSECTP-IS-COMMUTATIVE))
 (6712 6712 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (5326 5326 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-D-E-CC))
 (1867 1867 (:TYPE-PRESCRIPTION M1-FILE-HIFAT-FILE-ALIST-FIX))
 (1793 53 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-31))
 (531 207 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-5))
 (485 193 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (346 346 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-FLATTEN))
 (273 273 (:REWRITE FIND-D-E-CORRECTNESS-1))
 (263 82 (:REWRITE CONSP-OF-APPEND))
 (217 193 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (210 42 (:REWRITE SET-EQUIV-OF-CONS-SELF))
 (155 155 (:REWRITE FLATTEN-WHEN-NOT-CONSP))
 (151 151 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (146 146 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (106 52 (:REWRITE INTERSECTP-EQUAL-OF-ATOM-LEFT))
 (100 25 (:REWRITE SET-EQUIV-WITH-APPEND-OTHER-RIGHT))
 (92 92 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-NOT-CONSP))
 (84 13 (:REWRITE CAR-OF-APPEND))
 (68 17 (:REWRITE SET-EQUIV-WITH-APPEND-OTHER-LEFT))
 (64 64 (:REWRITE-QUOTED-CONSTANT M1-FILE-CONTENTS-FIX-UNDER-M1-FILE-CONTENTS-EQUIV))
 (42 42 (:REWRITE SUBSETP-MEMBER . 1))
 (40 40 (:TYPE-PRESCRIPTION STRINGP-OF-D-E-CC-CONTENTS))
 (34 34 (:REWRITE INTERSECT-WITH-SUBSET . 12))
 (34 34 (:REWRITE INTERSECT-WITH-SUBSET . 11))
 (34 34 (:REWRITE FLATTEN-SUBSET-NO-DUPLICATESP-LEMMA-1))
 (28 10 (:REWRITE CDR-OF-APPEND-WHEN-CONSP))
 (18 18 (:LINEAR POSITION-WHEN-MEMBER-OF-TAKE))
 (15 15 (:TYPE-PRESCRIPTION M1-FILE))
 (8 8 (:REWRITE SUBSETP-OF-CDR))
 (8 2 (:REWRITE FLATTEN-EQUIV-OF-CONS-WHEN-ATOM))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-24
 (28861 148 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-25))
 (25596 483 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-56))
 (22592 132 (:DEFINITION MEMBER-INTERSECTP-EQUAL))
 (14992 19 (:REWRITE MEMBER-INTERSECTP-IS-COMMUTATIVE))
 (13255 177 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-2))
 (13085 9 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-2 . 2))
 (11992 920 (:DEFINITION FIND-D-E))
 (11541 151 (:REWRITE LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-2-LEMMA-2))
 (8250 351 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-93))
 (6920 326 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-8))
 (6500 924 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (5542 326 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-4))
 (4654 178 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-1 . 1))
 (3621 887 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 2))
 (3247 1388 (:REWRITE DEFAULT-CDR))
 (3229 1524 (:REWRITE DEFAULT-CAR))
 (2804 924 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (2769 515 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (2751 887 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 1))
 (2460 28 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-38))
 (2225 54 (:REWRITE REMOVE-ASSOC-WHEN-ABSENT-1))
 (1848 1848 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (1848 1848 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (1819 77 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (1796 393 (:REWRITE NOT-INTERSECTP-LIST-WHEN-SUBSETP-1))
 (1450 958 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (1326 1326 (:TYPE-PRESCRIPTION FAT32-ENTRY-MASK))
 (1178 848 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (1155 23 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-1))
 (1066 1066 (:TYPE-PRESCRIPTION D-E-P))
 (1041 393 (:REWRITE NOT-INTERSECTP-LIST-WHEN-ATOM))
 (1010 458 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (1000 536 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-46))
 (964 458 (:REWRITE SUBSETP-WHEN-ATOM-RIGHT))
 (920 920 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (871 871 (:TYPE-PRESCRIPTION D-E-FILE-SIZE))
 (726 326 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-5))
 (720 18 (:DEFINITION REMOVE-ASSOC-EQUAL))
 (603 134 (:LINEAR D-E-FILE-SIZE-CORRECTNESS-1))
 (583 583 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-D-E-CC))
 (531 325 (:REWRITE DEFAULT-<-2))
 (509 509 (:REWRITE MEMBER-INTERSECTP-WITH-SUBSET))
 (480 480 (:TYPE-PRESCRIPTION MAKE-D-E-LIST))
 (458 458 (:REWRITE SUBSETP-TRANS2))
 (458 458 (:REWRITE SUBSETP-TRANS))
 (410 61 (:DEFINITION ASSOC-EQUAL))
 (408 12 (:REWRITE DELETE-D-E-CORRECTNESS-1))
 (396 4 (:DEFINITION DELETE-D-E))
 (367 325 (:REWRITE DEFAULT-<-1))
 (310 4 (:REWRITE PUT-ASSOC-EQUAL-WITHOUT-CHANGE . 2))
 (208 4 (:REWRITE CDR-OF-APPEND-WHEN-CONSP))
 (180 4 (:REWRITE CAR-OF-APPEND))
 (142 142 (:REWRITE FIND-D-E-CORRECTNESS-1))
 (108 75 (:REWRITE NFIX-WHEN-ZP))
 (105 105 (:TYPE-PRESCRIPTION FIND-D-E-CORRECTNESS-1))
 (103 75 (:REWRITE NFIX-WHEN-NATP))
 (94 3 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-31))
 (88 4 (:REWRITE CONSP-OF-APPEND))
 (84 12 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-2))
 (84 2 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-1-LEMMA-7))
 (71 71 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-1))
 (67 4 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-15))
 (59 59 (:REWRITE-QUOTED-CONSTANT FAT32-FILENAME-LIST-FIX-UNDER-FAT32-FILENAME-LIST-EQUIV))
 (57 30 (:REWRITE DEFAULT-+-2))
 (52 1 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-59))
 (40 40 (:TYPE-PRESCRIPTION LOFAT-REMOVE-FILE-CORRECTNESS-3))
 (33 30 (:REWRITE DEFAULT-+-1))
 (30 30 (:TYPE-PRESCRIPTION M1-FILE-HIFAT-FILE-ALIST-FIX))
 (28 28 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-FLATTEN))
 (23 23 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-2))
 (18 9 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (17 11 (:DEFINITION NATP))
 (16 16 (:REWRITE USEFUL-D-E-LIST-P-OF-DELETE-D-E))
 (16 16 (:REWRITE USEFUL-D-E-LIST-P-OF-CDR))
 (12 12 (:TYPE-PRESCRIPTION DELETE-D-E))
 (12 4 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (11 11 (:TYPE-PRESCRIPTION NATP))
 (4 4 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (3 3 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (2 2 (:REWRITE FLATTEN-WHEN-NOT-CONSP))
 (1 1 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-NOT-CONSP))
 (1 1 (:REWRITE DEFAULT-UNARY-MINUS))
 (1 1 (:LINEAR LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-52))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-41
 (79513 67 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-25))
 (58729 3451 (:DEFINITION FIND-D-E))
 (54732 385 (:DEFINITION MEMBER-INTERSECTP-EQUAL))
 (39292 258 (:REWRITE LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-2-LEMMA-2))
 (39128 68 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-59))
 (32332 3521 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (23192 31 (:REWRITE MEMBER-INTERSECTP-IS-COMMUTATIVE))
 (18248 3521 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (18110 2220 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (17367 379 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-1 . 1))
 (17144 6 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-2 . 2))
 (14068 336 (:REWRITE REMOVE-ASSOC-WHEN-ABSENT-1))
 (13524 554 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-93))
 (13178 937 (:REWRITE NOT-INTERSECTP-LIST-OF-LOFAT-TO-HIFAT-HELPER))
 (11464 1980 (:REWRITE SUBSETP-WHEN-SUBSETP))
 (11028 21 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-16))
 (10822 168 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-1))
 (10414 937 (:REWRITE NOT-INTERSECTP-LIST-WHEN-SUBSETP-1))
 (9004 532 (:DEFINITION FREE-INDEX-LISTP))
 (7985 210 (:REWRITE DELETE-D-E-CORRECTNESS-1))
 (7775 70 (:DEFINITION DELETE-D-E))
 (7437 6515 (:REWRITE DEFAULT-CAR))
 (7042 7042 (:REWRITE D-E-P-WHEN-MEMBER-EQUAL-OF-D-E-LIST-P))
 (7022 7022 (:TYPE-PRESCRIPTION D-E-FILENAME))
 (6684 5710 (:REWRITE DEFAULT-CDR))
 (6238 937 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-2 . 2))
 (5904 2187 (:REWRITE HIFAT-TO-LOFAT-INVERSION-LEMMA-17))
 (5516 776 (:REWRITE FIND-D-E-CORRECTNESS-2))
 (4480 112 (:DEFINITION REMOVE-ASSOC-EQUAL))
 (4010 802 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-8))
 (3643 119 (:REWRITE SUBSETP-CONS-2))
 (3456 3456 (:REWRITE-QUOTED-CONSTANT D-E-FIX-UNDER-D-E-EQUIV))
 (3192 3192 (:TYPE-PRESCRIPTION FAT32-ENTRY-MASK))
 (2990 3 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-31))
 (2825 173 (:REWRITE D-E-CC-UNDER-IFF . 3))
 (2688 392 (:DEFINITION ASSOC-EQUAL))
 (2683 1731 (:REWRITE SUBSETP-WHEN-ATOM-RIGHT))
 (2683 1731 (:REWRITE SUBSETP-WHEN-ATOM-LEFT))
 (2660 2660 (:TYPE-PRESCRIPTION FREE-INDEX-LISTP))
 (2496 26 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-5))
 (2186 26 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-9))
 (1777 1340 (:REWRITE DEFAULT-<-1))
 (1772 1340 (:REWRITE DEFAULT-<-2))
 (1756 937 (:REWRITE NOT-INTERSECTP-LIST-WHEN-ATOM))
 (1737 889 (:REWRITE DEFAULT-+-2))
 (1731 1731 (:REWRITE SUBSETP-TRANS2))
 (1731 1731 (:REWRITE SUBSETP-TRANS))
 (1688 1657 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 1))
 (1657 1657 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-121 . 2))
 (1453 1453 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-D-E-CC))
 (1326 1326 (:TYPE-PRESCRIPTION D-E-FILE-SIZE))
 (1111 1103 (:REWRITE NOT-INTERSECTP-LIST-OF-SET-DIFFERENCE$-LEMMA-3))
 (1103 1103 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-46))
 (952 889 (:REWRITE DEFAULT-+-1))
 (918 204 (:LINEAR D-E-FILE-SIZE-CORRECTNESS-1))
 (909 1 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-71))
 (909 1 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-61))
 (840 280 (:REWRITE USEFUL-D-E-LIST-P-OF-CDR))
 (782 200 (:REWRITE NFIX-WHEN-ZP))
 (746 200 (:REWRITE NFIX-WHEN-NATP))
 (660 1 (:REWRITE APPEND-ATOM-UNDER-LIST-EQUIV))
 (649 1 (:REWRITE CONSP-OF-MAKE-LIST-AC))
 (508 18 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-39))
 (504 168 (:REWRITE LOFAT-FIND-FILE-CORRECTNESS-LEMMA-2))
 (433 18 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-36))
 (392 392 (:REWRITE-QUOTED-CONSTANT FAT32-FILENAME-LIST-FIX-UNDER-FAT32-FILENAME-LIST-EQUIV))
 (375 26 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-7))
 (352 194 (:DEFINITION NATP))
 (278 4 (:LINEAR MAKE-CLUSTERS-CORRECTNESS-2))
 (261 18 (:DEFINITION LEN))
 (252 21 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT))
 (233 18 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-40))
 (210 210 (:TYPE-PRESCRIPTION DELETE-D-E))
 (194 194 (:TYPE-PRESCRIPTION NATP))
 (186 10 (:REWRITE LENGTH-WHEN-STRINGP))
 (144 18 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-38))
 (140 20 (:REWRITE INTERSECTP-OF-SELF))
 (129 1 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-38))
 (114 4 (:REWRITE LEN-OF-NATS=>CHARS))
 (112 2 (:LINEAR LEN-OF-EXPLODE-WHEN-M1-FILE-CONTENTS-P-1))
 (110 4 (:REWRITE LEN-OF-CLEAR-D-E))
 (106 4 (:REWRITE LEN-OF-STRING=>NATS))
 (96 4 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-11))
 (84 84 (:TYPE-PRESCRIPTION STRINGP-OF-D-E-CC-CONTENTS))
 (80 4 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-12))
 (79 26 (:REWRITE STR::CONSP-OF-EXPLODE))
 (77 57 (:REWRITE DEFAULT-UNARY-MINUS))
 (76 13 (:REWRITE FAT32-FILENAME-P-CORRECTNESS-1))
 (70 70 (:LINEAR D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-12))
 (70 2 (:REWRITE M1-FILE-CONTENTS-P-WHEN-STRINGP))
 (64 2 (:LINEAR LENGTH-OF-D-E-CC-CONTENTS . 3))
 (56 4 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-5))
 (56 4 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-14))
 (56 4 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-COINCIDENT-LEMMA-13))
 (56 2 (:LINEAR LENGTH-OF-D-E-CC-CONTENTS . 2))
 (48 4 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-8))
 (39 39 (:TYPE-PRESCRIPTION STR::TRUE-LISTP-OF-EXPLODE))
 (32 2 (:LINEAR MAKE-CLUSTERS-CORRECTNESS-3))
 (30 10 (:TYPE-PRESCRIPTION MAKE-CLUSTERS-OF-NIL))
 (29 1 (:DEFINITION MAKE-LIST-AC))
 (26 13 (:REWRITE STR::EXPLODE-WHEN-NOT-STRINGP))
 (26 10 (:REWRITE STR::COERCE-TO-LIST-REMOVAL))
 (20 20 (:TYPE-PRESCRIPTION INTERSECTP-EQUAL))
 (16 16 (:TYPE-PRESCRIPTION NATS=>STRING))
 (14 6 (:LINEAR HIFAT-TO-LOFAT-INVERSION-LEMMA-19))
 (10 10 (:TYPE-PRESCRIPTION MAKE-CLUSTERS))
 (10 10 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-43))
 (10 10 (:REWRITE FAT32-FILENAME-LIST-P-WHEN-NOT-CONSP))
 (10 5 (:REWRITE DEFAULT-*-2))
 (10 5 (:REWRITE DEFAULT-*-1))
 (10 2 (:DEFINITION UNSIGNED-BYTE-P))
 (9 9 (:REWRITE SUBSETP-MEMBER . 1))
 (9 9 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-30))
 (8 8 (:TYPE-PRESCRIPTION HIFAT-BOUNDED-FILE-ALIST-P))
 (8 2 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-MAKE-LIST-AC))
 (8 2 (:LINEAR NATP-OF-CLUSTER-SIZE))
 (8 2 (:DEFINITION INTEGER-RANGE-P))
 (6 2 (:LINEAR LEN-WHEN-HIFAT-BOUNDED-FILE-ALIST-P . 2))
 (6 2 (:LINEAR LEN-WHEN-HIFAT-BOUNDED-FILE-ALIST-P . 1))
 (4 4 (:REWRITE EXPLODE-OF-NATS=>STRING))
 (4 4 (:LINEAR LEN-WHEN-FAT32-FILENAME-LIST-PREFIXP))
 (4 1 (:REWRITE APPEND-WHEN-NOT-CONSP))
 (3 3 (:TYPE-PRESCRIPTION NATS=>CHARS))
 (2 2 (:TYPE-PRESCRIPTION MAKE-LIST-AC))
 (2 2 (:TYPE-PRESCRIPTION M1-FILE-CONTENTS-P))
 (2 2 (:TYPE-PRESCRIPTION FAT32$C-P))
 (2 2 (:REWRITE LOFAT-FS-P-CORRECTNESS-1))
 (2 2 (:LINEAR POSITION-WHEN-MEMBER))
 (2 2 (:LINEAR POSITION-EQUAL-AC-WHEN-MEMBER))
 (2 2 (:LINEAR LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-52))
 (2 2 (:LINEAR LENGTH-OF-D-E-CC-CONTENTS . 1))
 (1 1 (:REWRITE FOLD-CONSTS-IN-+))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-44
 (72810 76 (:REWRITE LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-25))
 (66400 3872 (:DEFINITION FIND-D-E))
 (53666 400 (:DEFINITION MEMBER-INTERSECTP-EQUAL))
 (37466 73 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-59))
 (36652 3943 (:REWRITE D-E-FIX-WHEN-D-E-P))
 (36197 275 (:REWRITE LOFAT-TO-HIFAT-HELPER-AFTER-DELETE-AND-CLEAR-2-LEMMA-2))
 (31104 1082 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-56))
 (26944 309 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-2))
 (25073 33 (:REWRITE MEMBER-INTERSECTP-IS-COMMUTATIVE))
 (21570 2497 (:REWRITE D-E-CC-CONTENTS-OF-LOFAT-PLACE-FILE-COINCIDENT-LEMMA-15))
 (20880 3943 (:REWRITE D-E-P-OF-CAR-WHEN-D-E-LIST-P))
 (20174 8 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-DELETE-D-E-2 . 2))
 (18057 394 (:REWRITE LOFAT-TO-HIFAT-HELPER-OF-LOFAT-REMOVE-FILE-DISJOINT-LEMMA-1 . 1))
 (14528 580 (:REWRITE LOFAT-PLACE-FILE-CORRECTNESS-LEMMA-93))
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 )
(INDUCTION-SCHEME
 (22 13 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (10 10 (:TYPE-PRESCRIPTION FAT32-FILENAME-FIX))
 )
(LOFAT-REMOVE-FILE-CORRECTNESS-LEMMA-1
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 )
(LOFAT-REMOVE-FILE-CORRECTNESS-1
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 )