Documentation Verification Report

Lemmas

πŸ“ Source: Batteries/Data/String/Lemmas.lean

Statistics

MetricCount
DefinitionsValid, ValidFor, Valid, utf8InductionOn, utf8Len, Valid, ValidFor
7
Theoremsnext, prev, prevn, remainingBytes_le, remainingToString, setCurr, toEnd, validFor, atEnd, curr, extract, hasNext, hasPrev, mk', next, nextn, of_eq, out, out', pos, pos_eq_endPos, pos_eq_rawEndPos, pos_eq_zero, prev, prev_nil, prevn, remainingBytes, remainingToString, setCurr, setCurr', toEnd, toEnd', toString, valid, forward_eq_nextn, hasNext_cons_addChar, length_eq_of_map_eq, length_map, exists, intro, le_endPos, le_rawEndPos, go₁_add_right_cancel, go₁_append_right, go₁_cons_addChar, go₁_zero_utf8Len, goβ‚‚_add_right_cancel, goβ‚‚_append_left, lt_addChar, offsetBy_eq, valid_endPos, valid_rawEndPos, valid_zero, all_eq, all_iff, anyAux_of_valid, any_eq, any_iff, atEnd_iff, atEnd_of_valid, back_eq, back_eq_get_prev_rawEndPos, contains_iff, data_join, dropWhile_eq, drop_empty, drop_eq, endPos_asString, endPos_eq_zero, endPos_mk, extract_cons_addChar, extract_of_valid, extract_zero_endPos, extract_zero_rawEndPos, findAux_of_valid, find_of_valid, firstDiffPos_eq, firstDiffPos_loop_eq, foldlAux_of_valid, foldl_eq, foldrAux_of_valid, foldr_eq, front_eq, get?_of_valid, get_cons_addChar, get_of_valid, instLawfulLTOrd, isEmpty_iff, join_eq, length_eq_of_map_eq, lt_antisymm, mapAux_of_valid, map_eq, map_eq_empty_iff, map_isEmpty_eq_isEmpty, mk_length, modify_of_valid, next_of_valid, next_of_valid', offsetOfPosAux_of_valid, offsetOfPos_of_valid, posOfAux_eq, posOf_eq, prev_of_valid, prev_of_valid', rawEndPos_asString, rawEndPos_mk, rawEndPos_ofList, revFindAux_of_valid, revFind_of_valid, revPosOfAux_eq, revPosOf_eq, set_of_valid, splitAux_of_valid, splitToList_of_valid, split_of_valid, takeWhileAux_of_valid, takeWhile_eq, take_eq, toList_drop, toList_dropWhile, toList_join, toList_take, toList_takeWhile, toString_toSubstring, utf8ByteSize_mk, utf8ByteSize_ofList, utf8GetAux?_of_valid, utf8GetAux_addChar_right_cancel, utf8GetAux_add_right_cancel, utf8GetAux_of_valid, utf8Len_append, utf8Len_cons, utf8Len_data, utf8Len_eq_zero, utf8Len_le_of_infix, utf8Len_le_of_prefix, utf8Len_le_of_sublist, utf8Len_le_of_suffix, utf8Len_nil, utf8Len_reverse, utf8Len_reverseAux, utf8Len_toList, utf8PrevAux_of_valid, utf8SetAux_of_valid, validFor_mkIterator, validFor_toSubstring, valid_mkIterator, valid_next, valid_toSubstring, all, any, atEnd, bsize, contains, data_drop, data_dropWhile, data_take, data_takeWhile, drop, dropWhile, extract, foldl, foldr, front, get, isEmpty, le, next, next_stop, nextn, nextn_stop, prev, prevn, startValid, stopValid, take, takeWhile, toString_extract, valid, validFor, all, any, atEnd, bsize, contains, drop, dropWhile, extract, extract', foldl, foldr, front, get, isEmpty, next, next_stop, nextn, nextn_stop, of_eq, prev, prevn, startPos, stopPos, str, take, takeWhile, toIterator, toString, valid, Valid_default
211
Total218

String

Definitions

NameCategoryTheorems
utf8InductionOn πŸ“–CompOpβ€”
utf8Len πŸ“–CompOp
66 mathmath: next_of_valid, utf8Len_le_of_sublist, Pos.Raw.extract.go₁_zero_utf8Len, utf8Len_nil, splitAux_of_valid, utf8ByteSize_ofList, revFindAux_of_valid, Legacy.Iterator.ValidFor.out, Substring.Raw.ValidFor.stopPos, Substring.Raw.ValidFor.next_stop, utf8Len_reverse, anyAux_of_valid, next_of_valid', Substring.Raw.ValidFor.nextn_stop, get_of_valid, Substring.Raw.ValidFor.nextn, Legacy.Iterator.ValidFor.remainingBytes, set_of_valid, utf8Len_le_of_suffix, foldrAux_of_valid, Substring.Raw.ValidFor.atEnd, Legacy.Iterator.ValidFor.pos, Substring.Raw.Valid.next, Legacy.Iterator.ValidFor.mk', utf8Len_cons, offsetOfPos_of_valid, Substring.Raw.ValidFor.bsize, utf8ByteSize_mk, Substring.Raw.Valid.prev, Substring.Raw.Valid.bsize, utf8Len_le_of_infix, get?_of_valid, offsetOfPosAux_of_valid, rawEndPos_ofList, Substring.Raw.ValidFor.get, mapAux_of_valid, utf8Len_le_of_prefix, Substring.Raw.Valid.prevn, foldlAux_of_valid, atEnd_of_valid, Substring.Raw.ValidFor.prev, Substring.Raw.ValidFor.next, endPos_asString, prev_of_valid, utf8Len_toList, utf8Len_append, Substring.Raw.Valid.nextn, rawEndPos_asString, Substring.Raw.ValidFor.startPos, endPos_mk, Substring.Raw.ValidFor.prevn, rawEndPos_mk, Substring.Raw.Valid.get, modify_of_valid, find_of_valid, extract_of_valid, firstDiffPos_eq, revFind_of_valid, utf8Len_eq_zero, prev_of_valid', utf8Len_reverseAux, Legacy.Iterator.ValidFor.out', Pos.Raw.Valid.exists, utf8Len_data, findAux_of_valid, takeWhileAux_of_valid

Theorems

NameKindAssumesProvesValidatesDepends On
all_eq πŸ“–mathematicalβ€”Legacy.allβ€”any_eq
all_iff πŸ“–bridging (iff)β€”Legacy.allLegacy.allall_eq
anyAux_of_valid πŸ“–mathematicalβ€”Legacy.anyAux
utf8Len
β€”get_of_valid
next_of_valid
utf8Len_append
any_eq πŸ“–mathematicalβ€”Legacy.anyβ€”utf8Len_toList
anyAux_of_valid
any_iff πŸ“–bridging (iff)β€”Legacy.anyLegacy.anyany_eq
atEnd_iff πŸ“–β€”β€”β€”β€”β€”
atEnd_of_valid πŸ“–mathematicalβ€”utf8Lenβ€”atEnd_iff
utf8ByteSize_ofList
back_eq πŸ“–mathematicalβ€”Legacy.backβ€”utf8ByteSize_ofList
prev_of_valid
get_of_valid
back_eq_get_prev_rawEndPos πŸ“–mathematicalβ€”Legacy.backβ€”β€”
contains_iff πŸ“–bridging (iff)β€”Legacy.containsLegacy.containsβ€”
data_join πŸ“–β€”β€”β€”β€”toList_join
dropWhile_eq πŸ“–mathematicalβ€”Legacy.dropWhileβ€”Substring.Raw.ValidFor.toString
Substring.Raw.ValidFor.dropWhile
validFor_toSubstring
drop_empty πŸ“–mathematicalβ€”Legacy.dropβ€”drop_eq
drop_eq πŸ“–mathematicalβ€”Legacy.dropβ€”Substring.Raw.ValidFor.toString
Substring.Raw.ValidFor.drop
validFor_toSubstring
endPos_asString πŸ“–mathematicalβ€”utf8Lenβ€”rawEndPos_ofList
endPos_eq_zero πŸ“–β€”β€”β€”β€”β€”
endPos_mk πŸ“–mathematicalβ€”utf8Lenβ€”rawEndPos_ofList
extract_cons_addChar πŸ“–β€”β€”β€”β€”Pos.Raw.extract.go₁_cons_addChar
extract_of_valid πŸ“–mathematicalβ€”utf8Lenβ€”Pos.Raw.extract.go₁_append_right
Pos.Raw.extract.goβ‚‚_append_left
utf8Len_eq_zero
extract_zero_endPos πŸ“–β€”β€”β€”β€”extract_zero_rawEndPos
extract_zero_rawEndPos πŸ“–β€”β€”β€”β€”rawEndPos_ofList
Pos.Raw.extract.go₁_zero_utf8Len
findAux_of_valid πŸ“–mathematicalβ€”Legacy.findAux
utf8Len
β€”get_of_valid
next_of_valid
utf8Len_append
find_of_valid πŸ“–mathematicalβ€”Legacy.find
utf8Len
β€”utf8Len_toList
findAux_of_valid
firstDiffPos_eq πŸ“–mathematicalβ€”utf8Len
List.takeWhileβ‚‚
β€”utf8Len_toList
firstDiffPos_loop_eq
firstDiffPos_loop_eq πŸ“–mathematicalutf8LenList.takeWhileβ‚‚β€”β€”
foldlAux_of_valid πŸ“–mathematicalβ€”Legacy.foldlAux
utf8Len
β€”next_of_valid
get_of_valid
utf8Len_append
foldl_eq πŸ“–mathematicalβ€”Legacy.foldlβ€”utf8Len_toList
foldlAux_of_valid
foldrAux_of_valid πŸ“–mathematicalβ€”Legacy.foldrAux
utf8Len
β€”utf8Len_append
utf8Len_reverse
prev_of_valid
get_of_valid
foldr_eq πŸ“–mathematicalβ€”Legacy.foldrβ€”utf8Len_toList
foldrAux_of_valid
front_eq πŸ“–mathematicalβ€”Legacy.frontβ€”get_of_valid
get?_of_valid πŸ“–mathematicalβ€”utf8Lenβ€”Pos.Raw.get?.eq_1
utf8GetAux?_of_valid
get_cons_addChar πŸ“–β€”β€”β€”β€”utf8GetAux_addChar_right_cancel
get_of_valid πŸ“–mathematicalβ€”utf8Lenβ€”Pos.Raw.get.eq_1
utf8GetAux_of_valid
instLawfulLTOrd πŸ“–mathematicalβ€”Std.LawfulLTOrdβ€”Std.LawfulLTCmp.compareOfLessAndEq_of_irrefl_of_trans_of_antisymm
lt_antisymm
isEmpty_iff πŸ“–β€”β€”β€”β€”β€”
join_eq πŸ“–β€”β€”β€”β€”β€”
length_eq_of_map_eq πŸ“–β€”β€”β€”β€”β€”
lt_antisymm πŸ“–β€”β€”β€”β€”β€”
mapAux_of_valid πŸ“–mathematicalβ€”Legacy.mapAux
utf8Len
β€”rawEndPos_ofList
atEnd_of_valid
get_of_valid
set_of_valid
next_of_valid
utf8Len_append
map_eq πŸ“–mathematicalβ€”Legacy.mapβ€”mapAux_of_valid
map_eq_empty_iff πŸ“–mathematicalβ€”Legacy.mapβ€”map_eq
map_isEmpty_eq_isEmpty πŸ“–mathematicalβ€”Legacy.mapβ€”β€”
mk_length πŸ“–β€”β€”β€”β€”β€”
modify_of_valid πŸ“–mathematicalβ€”utf8Lenβ€”Pos.Raw.modify.eq_1
set_of_valid
get_of_valid
next_of_valid πŸ“–mathematicalβ€”utf8Lenβ€”next_of_valid'
next_of_valid' πŸ“–mathematicalβ€”utf8Lenβ€”get_of_valid
offsetOfPosAux_of_valid πŸ“–mathematicalβ€”utf8Lenβ€”atEnd_of_valid
next_of_valid
utf8Len_append
offsetOfPos_of_valid πŸ“–mathematicalβ€”utf8Lenβ€”offsetOfPosAux_of_valid
posOfAux_eq πŸ“–mathematicalβ€”Legacy.posOfAux
Legacy.findAux
β€”β€”
posOf_eq πŸ“–mathematicalβ€”Legacy.posOf
Legacy.find
β€”β€”
prev_of_valid πŸ“–mathematicalβ€”utf8Lenβ€”utf8PrevAux_of_valid
prev_of_valid' πŸ“–mathematicalβ€”utf8Lenβ€”utf8Len_append
prev_of_valid
rawEndPos_asString πŸ“–mathematicalβ€”utf8Lenβ€”rawEndPos_ofList
rawEndPos_mk πŸ“–mathematicalβ€”utf8Lenβ€”rawEndPos_ofList
rawEndPos_ofList πŸ“–mathematicalβ€”utf8Lenβ€”utf8ByteSize_ofList
revFindAux_of_valid πŸ“–mathematicalβ€”Legacy.revFindAux
utf8Len
β€”get_of_valid
prev_of_valid
utf8Len_reverse
revFind_of_valid πŸ“–mathematicalβ€”Legacy.revFind
utf8Len
β€”utf8Len_reverse
utf8Len_toList
revFindAux_of_valid
revPosOfAux_eq πŸ“–mathematicalβ€”Legacy.revPosOfAux
Legacy.revFindAux
β€”β€”
revPosOf_eq πŸ“–mathematicalβ€”Legacy.revPosOf
Legacy.revFind
β€”β€”
set_of_valid πŸ“–mathematicalβ€”utf8Lenβ€”Pos.Raw.set.eq_1
utf8SetAux_of_valid
splitAux_of_valid πŸ“–mathematicalβ€”utf8Len
List.splitOnP.go
β€”β€”
splitToList_of_valid πŸ“–mathematicalβ€”List.splitOnPβ€”splitAux_of_valid
split_of_valid πŸ“–mathematicalβ€”List.splitOnPβ€”splitToList_of_valid
takeWhileAux_of_valid πŸ“–mathematicalβ€”utf8Lenβ€”get_of_valid
next_of_valid
utf8Len_append
takeWhile_eq πŸ“–mathematicalβ€”Legacy.takeWhileβ€”Substring.Raw.ValidFor.toString
Substring.Raw.ValidFor.takeWhile
validFor_toSubstring
take_eq πŸ“–mathematicalβ€”Legacy.takeβ€”Substring.Raw.ValidFor.toString
Substring.Raw.ValidFor.take
validFor_toSubstring
toList_drop πŸ“–mathematicalβ€”Legacy.dropβ€”drop_eq
toList_dropWhile πŸ“–mathematicalβ€”Legacy.dropWhileβ€”dropWhile_eq
toList_join πŸ“–β€”β€”β€”β€”join_eq
toList_take πŸ“–mathematicalβ€”Legacy.takeβ€”take_eq
toList_takeWhile πŸ“–mathematicalβ€”Legacy.takeWhileβ€”takeWhile_eq
toString_toSubstring πŸ“–β€”β€”β€”β€”extract_zero_rawEndPos
utf8ByteSize_mk πŸ“–mathematicalβ€”utf8Lenβ€”utf8ByteSize_ofList
utf8ByteSize_ofList πŸ“–mathematicalβ€”utf8Lenβ€”utf8Len.eq_2
utf8GetAux?_of_valid πŸ“–β€”utf8Lenβ€”β€”β€”
utf8GetAux_addChar_right_cancel πŸ“–β€”β€”β€”β€”utf8GetAux_add_right_cancel
utf8GetAux_add_right_cancel πŸ“–β€”β€”β€”β€”β€”
utf8GetAux_of_valid πŸ“–β€”utf8Lenβ€”β€”β€”
utf8Len_append πŸ“–mathematicalβ€”utf8Lenβ€”β€”
utf8Len_cons πŸ“–mathematicalβ€”utf8Lenβ€”β€”
utf8Len_data πŸ“–mathematicalβ€”utf8Lenβ€”utf8Len_toList
utf8Len_eq_zero πŸ“–mathematicalβ€”utf8Lenβ€”β€”
utf8Len_le_of_infix πŸ“–mathematicalβ€”utf8Lenβ€”utf8Len_le_of_sublist
utf8Len_le_of_prefix πŸ“–mathematicalβ€”utf8Lenβ€”utf8Len_le_of_sublist
utf8Len_le_of_sublist πŸ“–mathematicalβ€”utf8Lenβ€”β€”
utf8Len_le_of_suffix πŸ“–mathematicalβ€”utf8Lenβ€”utf8Len_le_of_sublist
utf8Len_nil πŸ“–mathematicalβ€”utf8Lenβ€”β€”
utf8Len_reverse πŸ“–mathematicalβ€”utf8Lenβ€”utf8Len_reverseAux
utf8Len_reverseAux πŸ“–mathematicalβ€”utf8Lenβ€”utf8Len_append
utf8Len_toList πŸ“–mathematicalβ€”utf8Lenβ€”utf8ByteSize_ofList
utf8PrevAux_of_valid πŸ“–β€”utf8Lenβ€”β€”β€”
utf8SetAux_of_valid πŸ“–β€”utf8Lenβ€”β€”β€”
validFor_mkIterator πŸ“–mathematicalβ€”Legacy.Iterator.ValidForβ€”Legacy.Iterator.ValidFor.of_eq
validFor_toSubstring πŸ“–mathematicalβ€”Substring.Raw.ValidForβ€”Substring.Raw.ValidFor.of_eq
utf8Len_toList
valid_mkIterator πŸ“–mathematicalβ€”Legacy.Iterator.Validβ€”Legacy.Iterator.ValidFor.valid
validFor_mkIterator
valid_next πŸ“–β€”Pos.Raw.Validβ€”β€”rawEndPos_ofList
next_of_valid
utf8Len_append
valid_toSubstring πŸ“–mathematicalβ€”Substring.Raw.Validβ€”Substring.Raw.ValidFor.valid
validFor_toSubstring

String.Legacy

Theorems

NameKindAssumesProvesValidatesDepends On
length_eq_of_map_eq πŸ“–β€”mapβ€”β€”length_map
length_map πŸ“–mathematicalβ€”mapβ€”String.map_eq

String.Legacy.Iterator

Definitions

NameCategoryTheorems
Valid πŸ“–MathDef
3 mathmath: Valid.toEnd, String.valid_mkIterator, ValidFor.valid
ValidFor πŸ“–CompData
6 mathmath: ValidFor.of_eq, Valid.validFor, ValidFor.mk', Substring.Raw.ValidFor.toIterator, ValidFor.toEnd', String.validFor_mkIterator

Theorems

NameKindAssumesProvesValidatesDepends On
forward_eq_nextn πŸ“–β€”β€”β€”β€”β€”
hasNext_cons_addChar πŸ“–β€”β€”β€”β€”String.rawEndPos_ofList

String.Legacy.Iterator.Valid

Theorems

NameKindAssumesProvesValidatesDepends On
next πŸ“–β€”String.Legacy.Iterator.Validβ€”β€”validFor
String.Legacy.Iterator.ValidFor.hasNext
String.Legacy.Iterator.ValidFor.valid
String.Legacy.Iterator.ValidFor.next
prev πŸ“–β€”String.Legacy.Iterator.Validβ€”β€”validFor
String.Legacy.Iterator.ValidFor.valid
String.Legacy.Iterator.ValidFor.prev_nil
String.Legacy.Iterator.ValidFor.prev
prevn πŸ“–β€”String.Legacy.Iterator.Validβ€”β€”prev
remainingBytes_le πŸ“–β€”String.Legacy.Iterator.Validβ€”β€”validFor
String.Legacy.Iterator.ValidFor.remainingBytes
String.Legacy.Iterator.ValidFor.toString
String.utf8ByteSize_ofList
String.utf8Len_reverse
remainingToString πŸ“–β€”String.Legacy.Iterator.ValidForβ€”β€”String.Legacy.Iterator.ValidFor.out
String.rawEndPos_ofList
String.utf8Len_append
String.utf8Len_reverse
String.extract_of_valid
setCurr πŸ“–β€”String.Legacy.Iterator.Validβ€”β€”validFor
String.Legacy.Iterator.ValidFor.valid
String.Legacy.Iterator.ValidFor.setCurr'
toEnd πŸ“–mathematicalβ€”String.Legacy.Iterator.Validβ€”String.Legacy.Iterator.ValidFor.valid
String.Legacy.Iterator.ValidFor.toEnd'
validFor πŸ“–mathematicalString.Legacy.Iterator.ValidString.Legacy.Iterator.ValidForβ€”String.utf8Len_reverse

String.Legacy.Iterator.ValidFor

Theorems

NameKindAssumesProvesValidatesDepends On
atEnd πŸ“–β€”String.Legacy.Iterator.ValidForβ€”β€”pos
toString
String.rawEndPos_ofList
String.utf8Len_reverseAux
String.utf8Len_eq_zero
curr πŸ“–β€”String.Legacy.Iterator.ValidForβ€”β€”out'
String.get_of_valid
extract πŸ“–β€”String.Legacy.Iterator.ValidForβ€”β€”out
String.utf8Len_append
String.utf8Len_reverse
String.extract_of_valid
hasNext πŸ“–β€”String.Legacy.Iterator.ValidForβ€”β€”atEnd
hasPrev πŸ“–β€”String.Legacy.Iterator.ValidForβ€”β€”pos
mk' πŸ“–mathematicalβ€”String.Legacy.Iterator.ValidFor
String.utf8Len
β€”String.utf8Len_reverse
next πŸ“–β€”String.Legacy.Iterator.ValidForβ€”β€”out'
String.next_of_valid
String.utf8Len_reverse
nextn πŸ“–β€”String.Legacy.Iterator.ValidForβ€”β€”next
of_eq πŸ“–mathematicalString.utf8LenString.Legacy.Iterator.ValidForβ€”β€”
out πŸ“–mathematicalString.Legacy.Iterator.ValidForString.utf8Lenβ€”β€”
out' πŸ“–mathematicalString.Legacy.Iterator.ValidForString.utf8Lenβ€”String.utf8Len_reverse
pos πŸ“–mathematicalString.Legacy.Iterator.ValidForString.utf8Lenβ€”β€”
pos_eq_endPos πŸ“–β€”String.Legacy.Iterator.ValidForβ€”β€”pos_eq_rawEndPos
pos_eq_rawEndPos πŸ“–β€”String.Legacy.Iterator.ValidForβ€”β€”pos
toString
String.rawEndPos_ofList
String.utf8Len_reverseAux
String.utf8Len_eq_zero
pos_eq_zero πŸ“–β€”String.Legacy.Iterator.ValidForβ€”β€”pos
prev πŸ“–β€”String.Legacy.Iterator.ValidForβ€”β€”out'
String.prev_of_valid
String.utf8Len_append
String.utf8Len_reverse
of_eq
prev_nil πŸ“–β€”String.Legacy.Iterator.ValidForβ€”β€”toString
pos
prevn πŸ“–β€”String.Legacy.Iterator.ValidForβ€”β€”prev
remainingBytes πŸ“–mathematicalString.Legacy.Iterator.ValidForString.utf8Lenβ€”String.rawEndPos_ofList
String.utf8Len_append
String.utf8Len_reverse
remainingToString πŸ“–β€”String.Legacy.Iterator.ValidForβ€”β€”out
String.rawEndPos_ofList
String.utf8Len_append
String.utf8Len_reverse
String.extract_of_valid
setCurr πŸ“–β€”String.Legacy.Iterator.ValidForβ€”β€”setCurr'
setCurr' πŸ“–β€”String.Legacy.Iterator.ValidForβ€”β€”out'
String.utf8Len_reverse
of_eq
String.set_of_valid
toEnd πŸ“–β€”String.Legacy.Iterator.ValidForβ€”β€”toString
String.rawEndPos_ofList
String.utf8Len_reverseAux
of_eq
String.utf8Len_append
String.utf8Len_reverse
toEnd' πŸ“–mathematicalβ€”String.Legacy.Iterator.ValidForβ€”of_eq
String.utf8Len_reverse
String.utf8Len_toList
toString πŸ“–β€”String.Legacy.Iterator.ValidForβ€”β€”β€”
valid πŸ“–mathematicalString.Legacy.Iterator.ValidForString.Legacy.Iterator.Validβ€”String.utf8Len_reverse

String.Pos.Raw

Definitions

NameCategoryTheorems
Valid πŸ“–CompData
6 mathmath: valid_rawEndPos, Substring.Raw.Valid.startValid, valid_zero, Substring.Raw.Valid.stopValid, valid_endPos, Valid.intro

Theorems

NameKindAssumesProvesValidatesDepends On
lt_addChar πŸ“–β€”β€”β€”β€”β€”
offsetBy_eq πŸ“–β€”β€”β€”β€”β€”
valid_endPos πŸ“–mathematicalβ€”Validβ€”valid_rawEndPos
valid_rawEndPos πŸ“–mathematicalβ€”Validβ€”Valid.intro
String.utf8Len_toList
valid_zero πŸ“–mathematicalβ€”Validβ€”Valid.intro

String.Pos.Raw.Valid

Theorems

NameKindAssumesProvesValidatesDepends On
exists πŸ“–mathematicalString.Pos.Raw.ValidString.utf8Lenβ€”β€”
intro πŸ“–mathematicalString.utf8LenString.Pos.Raw.Validβ€”β€”
le_endPos πŸ“–β€”String.Pos.Raw.Validβ€”β€”le_rawEndPos
le_rawEndPos πŸ“–β€”String.Pos.Raw.Validβ€”β€”String.utf8ByteSize_ofList

String.Pos.Raw.extract

Theorems

NameKindAssumesProvesValidatesDepends On
go₁_add_right_cancel πŸ“–β€”β€”β€”β€”goβ‚‚_add_right_cancel
go₁_append_right πŸ“–β€”String.utf8Lenβ€”β€”β€”
go₁_cons_addChar πŸ“–β€”β€”β€”β€”go₁_add_right_cancel
go₁_zero_utf8Len πŸ“–mathematicalβ€”String.utf8Lenβ€”go₁_append_right
goβ‚‚_append_left
goβ‚‚_add_right_cancel πŸ“–β€”β€”β€”β€”β€”
goβ‚‚_append_left πŸ“–β€”String.utf8Lenβ€”β€”β€”

Substring.Raw

Definitions

NameCategoryTheorems
Valid πŸ“–CompData
4 mathmath: String.valid_toSubstring, ValidFor.valid, Valid_default, Valid.valid
ValidFor πŸ“–CompData
3 mathmath: Valid.validFor, ValidFor.of_eq, String.validFor_toSubstring

Theorems

NameKindAssumesProvesValidatesDepends On
Valid_default πŸ“–mathematicalβ€”Validβ€”String.Pos.Raw.valid_zero

Substring.Raw.Valid

Theorems

NameKindAssumesProvesValidatesDepends On
all πŸ“–mathematicalSubstring.Raw.ValidSubstring.Raw.Legacy.allβ€”validFor
Substring.Raw.ValidFor.all
Substring.Raw.ValidFor.toString
any πŸ“–mathematicalSubstring.Raw.ValidSubstring.Raw.Legacy.anyβ€”validFor
Substring.Raw.ValidFor.any
Substring.Raw.ValidFor.toString
atEnd πŸ“–β€”Substring.Raw.Validβ€”β€”validFor
Substring.Raw.ValidFor.atEnd
Substring.Raw.ValidFor.toString
String.utf8ByteSize_ofList
bsize πŸ“–mathematicalSubstring.Raw.ValidString.utf8Lenβ€”validFor
Substring.Raw.ValidFor.bsize
Substring.Raw.ValidFor.toString
contains πŸ“–bridging (iff)Substring.Raw.ValidSubstring.Raw.Legacy.containsSubstring.Raw.Legacy.containsvalidFor
Substring.Raw.ValidFor.contains
Substring.Raw.ValidFor.toString
data_drop πŸ“–β€”Substring.Raw.Validβ€”β€”validFor
Substring.Raw.ValidFor.toString
Substring.Raw.ValidFor.drop
data_dropWhile πŸ“–β€”Substring.Raw.Validβ€”β€”validFor
Substring.Raw.ValidFor.toString
Substring.Raw.ValidFor.dropWhile
data_take πŸ“–β€”Substring.Raw.Validβ€”β€”validFor
Substring.Raw.ValidFor.toString
Substring.Raw.ValidFor.take
data_takeWhile πŸ“–β€”Substring.Raw.Validβ€”β€”validFor
Substring.Raw.ValidFor.toString
Substring.Raw.ValidFor.takeWhile
drop πŸ“–β€”Substring.Raw.Validβ€”β€”validFor
Substring.Raw.ValidFor.valid
Substring.Raw.ValidFor.drop
dropWhile πŸ“–β€”Substring.Raw.Validβ€”β€”validFor
Substring.Raw.ValidFor.valid
Substring.Raw.ValidFor.dropWhile
extract πŸ“–β€”Substring.Raw.Validβ€”β€”validFor
Substring.Raw.ValidFor.toString
Substring.Raw.ValidFor.extract
Substring.Raw.ValidFor.valid
foldl πŸ“–mathematicalSubstring.Raw.ValidSubstring.Raw.Legacy.foldlβ€”validFor
Substring.Raw.ValidFor.foldl
Substring.Raw.ValidFor.toString
foldr πŸ“–mathematicalSubstring.Raw.ValidSubstring.Raw.Legacy.foldrβ€”validFor
Substring.Raw.ValidFor.foldr
Substring.Raw.ValidFor.toString
front πŸ“–β€”Substring.Raw.Validβ€”β€”get
get πŸ“–mathematicalSubstring.Raw.ValidString.utf8Lenβ€”validFor
Substring.Raw.ValidFor.get
Substring.Raw.ValidFor.toString
isEmpty πŸ“–β€”Substring.Raw.Validβ€”β€”validFor
Substring.Raw.ValidFor.isEmpty
Substring.Raw.ValidFor.toString
le πŸ“–β€”Substring.Raw.Validβ€”β€”β€”
next πŸ“–mathematicalSubstring.Raw.ValidString.utf8Lenβ€”validFor
Substring.Raw.ValidFor.next
Substring.Raw.ValidFor.toString
next_stop πŸ“–β€”Substring.Raw.Validβ€”β€”validFor
Substring.Raw.ValidFor.bsize
Substring.Raw.ValidFor.next_stop
nextn πŸ“–mathematicalSubstring.Raw.ValidString.utf8Lenβ€”validFor
Substring.Raw.ValidFor.nextn
Substring.Raw.ValidFor.toString
nextn_stop πŸ“–β€”Substring.Raw.Validβ€”β€”validFor
Substring.Raw.ValidFor.bsize
Substring.Raw.ValidFor.nextn_stop
prev πŸ“–mathematicalSubstring.Raw.ValidString.utf8Lenβ€”validFor
Substring.Raw.ValidFor.prev
Substring.Raw.ValidFor.toString
prevn πŸ“–mathematicalSubstring.Raw.ValidString.utf8Lenβ€”validFor
Substring.Raw.ValidFor.prevn
Substring.Raw.ValidFor.toString
startValid πŸ“–mathematicalSubstring.Raw.ValidString.Pos.Raw.Validβ€”β€”
stopValid πŸ“–mathematicalSubstring.Raw.ValidString.Pos.Raw.Validβ€”β€”
take πŸ“–β€”Substring.Raw.Validβ€”β€”validFor
Substring.Raw.ValidFor.valid
Substring.Raw.ValidFor.take
takeWhile πŸ“–β€”Substring.Raw.Validβ€”β€”validFor
Substring.Raw.ValidFor.valid
Substring.Raw.ValidFor.takeWhile
toString_extract πŸ“–β€”Substring.Raw.Validβ€”β€”validFor
Substring.Raw.ValidFor.toString
Substring.Raw.ValidFor.extract
valid πŸ“–mathematicalSubstring.Raw.ValidForSubstring.Raw.Validβ€”String.Pos.Raw.Valid.intro
String.utf8Len_append
validFor πŸ“–mathematicalSubstring.Raw.ValidSubstring.Raw.ValidForβ€”String.Pos.Raw.Valid.exists
String.utf8Len_eq_zero
String.utf8Len_append

Substring.Raw.ValidFor

Theorems

NameKindAssumesProvesValidatesDepends On
all πŸ“–mathematicalSubstring.Raw.ValidForSubstring.Raw.Legacy.allβ€”any
any πŸ“–mathematicalSubstring.Raw.ValidForSubstring.Raw.Legacy.anyβ€”String.anyAux_of_valid
atEnd πŸ“–mathematicalSubstring.Raw.ValidForString.utf8Lenβ€”β€”
bsize πŸ“–mathematicalSubstring.Raw.ValidForString.utf8Lenβ€”β€”
contains πŸ“–bridging (iff)Substring.Raw.ValidForSubstring.Raw.Legacy.containsSubstring.Raw.Legacy.containsany
drop πŸ“–β€”Substring.Raw.ValidForβ€”β€”nextn
str
startPos
stopPos
of_eq
String.utf8Len_append
dropWhile πŸ“–β€”Substring.Raw.ValidForβ€”β€”String.takeWhileAux_of_valid
of_eq
String.utf8Len_append
extract πŸ“–β€”Substring.Raw.ValidForβ€”β€”extract'
str
extract' πŸ“–β€”Substring.Raw.ValidForβ€”β€”String.utf8Len_append
of_eq
String.utf8Len_eq_zero
foldl πŸ“–mathematicalSubstring.Raw.ValidForSubstring.Raw.Legacy.foldlβ€”String.foldlAux_of_valid
foldr πŸ“–mathematicalSubstring.Raw.ValidForSubstring.Raw.Legacy.foldrβ€”String.foldrAux_of_valid
front πŸ“–β€”Substring.Raw.ValidForβ€”β€”get
get πŸ“–mathematicalSubstring.Raw.ValidForString.utf8Lenβ€”String.utf8Len_append
String.get_of_valid
isEmpty πŸ“–β€”Substring.Raw.ValidForβ€”β€”bsize
next πŸ“–mathematicalSubstring.Raw.ValidForString.utf8Lenβ€”String.utf8Len_append
String.next_of_valid
String.Pos.Raw.offsetBy_eq
next_stop πŸ“–mathematicalSubstring.Raw.ValidForString.utf8Lenβ€”String.Pos.Raw.offsetBy_eq
nextn πŸ“–mathematicalSubstring.Raw.ValidForString.utf8Lenβ€”next_stop
nextn_stop
next
String.utf8Len_append
nextn_stop πŸ“–mathematicalSubstring.Raw.ValidForString.utf8Lenβ€”next_stop
of_eq πŸ“–mathematicalString.utf8LenSubstring.Raw.ValidForβ€”β€”
prev πŸ“–mathematicalSubstring.Raw.ValidForString.utf8Lenβ€”String.prev_of_valid
String.Pos.Raw.offsetBy_eq
String.utf8Len_append
prevn πŸ“–mathematicalSubstring.Raw.ValidForString.utf8Lenβ€”prev
String.utf8Len_reverse
startPos πŸ“–mathematicalSubstring.Raw.ValidForString.utf8Lenβ€”β€”
stopPos πŸ“–mathematicalSubstring.Raw.ValidForString.utf8Lenβ€”β€”
str πŸ“–β€”Substring.Raw.ValidForβ€”β€”β€”
take πŸ“–β€”Substring.Raw.ValidForβ€”β€”nextn
str
startPos
of_eq
takeWhile πŸ“–β€”Substring.Raw.ValidForβ€”β€”String.takeWhileAux_of_valid
of_eq
toIterator πŸ“–mathematicalSubstring.Raw.ValidForString.Legacy.Iterator.ValidForβ€”String.Legacy.Iterator.ValidFor.of_eq
str
startPos
String.utf8Len_reverse
toString πŸ“–β€”Substring.Raw.ValidForβ€”β€”String.extract_of_valid
valid πŸ“–mathematicalSubstring.Raw.ValidForSubstring.Raw.Validβ€”String.Pos.Raw.Valid.intro
String.utf8Len_append

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