internlm/Lean-Github huggingface dataset:
Theorem: Regex.VM.captureNext_spec
Proof state before:
case refine_2
nfa : NFA
it : String.Iterator
saveSize : ℕ
matched : Option (Array (Option String.Pos))
v : it.Valid
hsome : matched.isSome = true
saveSlots✝ : Vec (Array (Option String.Pos)) nfa.nodes.size
_hs : (Vec.ofFn fun x => captureNext.initSave saveSize) = saveSlots✝
init : Option (Array (Option String.Pos)) × SparseSet nfa.nodes.size × Vec (Array (Option String.Pos)) nfa.nodes.size
matched' : Option (Array (Option String.Pos))
init' : SparseSet nfa.nodes.size
saveSlots : Vec (Array (Option String.Pos)) nfa.nodes.size
he :
  exploreεClosure nfa it.i SparseSet.empty (captureNext.initSave saveSize) none saveSlots✝ nfa.start #[] =
    (matched', init', saveSlots)
h : captureNext.go nfa saveSize it init' SparseSet.empty saveSlots matched' = matched
hnotMem : ∀ (i : Fin nfa.nodes.size), i ∉ SparseSet.empty
⊢ matched'.isSome = true →
    ∃ s l m r,
      Substring.ValidFor l m r s ∧ it.toString = { data := l ++ m ++ r } ∧ ∃ i, nfa.reaches i m ∧ nfa[i] = Node.done
Tactic:
intro hsome
Proof state after:
case refine_2
nfa : NFA
it : String.Iterator
saveSize : ℕ
matched : Option (Array (Option String.Pos))
v : it.Valid
hsome✝ : matched.isSome = true
saveSlots✝ : Vec (Array (Option String.Pos)) nfa.nodes.size
_hs : (Vec.ofFn fun x => captureNext.initSave saveSize) = saveSlots✝
init : Option (Array (Option String.Pos)) × SparseSet nfa.nodes.size × Vec (Array (Option String.Pos)) nfa.nodes.size
matched' : Option (Array (Option String.Pos))
init' : SparseSet nfa.nodes.size
saveSlots : Vec (Array (Option String.Pos)) nfa.nodes.size
he :
  exploreεClosure nfa it.i SparseSet.empty (captureNext.initSave saveSize) none saveSlots✝ nfa.start #[] =
    (matched', init', saveSlots)
h : captureNext.go nfa saveSize it init' SparseSet.empty saveSlots matched' = matched
hnotMem : ∀ (i : Fin nfa.nodes.size), i ∉ SparseSet.empty
hsome : matched'.isSome = true
⊢ ∃ s l m r,
    Substring.ValidFor l m r s ∧ it.toString = { data := l ++ m ++ r } ∧ ∃ i, nfa.reaches i m ∧ nfa[i] = Node.done
Theorem: Regex.VM.captureNext_spec
Proof state before:
case refine_2
nfa : NFA
it : String.Iterator
saveSize : ℕ
matched : Option (Array (Option String.Pos))
v : it.Valid
hsome✝ : matched.isSome = true
saveSlots✝ : Vec (Array (Option String.Pos)) nfa.nodes.size
_hs : (Vec.ofFn fun x => captureNext.initSave saveSize) = saveSlots✝
init : Option (Array (Option String.Pos)) × SparseSet nfa.nodes.size × Vec (Array (Option String.Pos)) nfa.nodes.size
matched' : Option (Array (Option String.Pos))
init' : SparseSet nfa.nodes.size
saveSlots : Vec (Array (Option String.Pos)) nfa.nodes.size
he :
  exploreεClosure nfa it.i SparseSet.empty (captureNext.initSave saveSize) none saveSlots✝ nfa.start #[] =
    (matched', init', saveSlots)
h : captureNext.go nfa saveSize it init' SparseSet.empty saveSlots matched' = matched
hnotMem : ∀ (i : Fin nfa.nodes.size), i ∉ SparseSet.empty
hsome : matched'.isSome = true
⊢ ∃ s l m r,
    Substring.ValidFor l m r s ∧ it.toString = { data := l ++ m ++ r } ∧ ∃ i, nfa.reaches i m ∧ nfa[i] = Node.done
Tactic:
have ⟨i, hi, hdone⟩ := (exploreεClosure_mem_done_iff he (by simp only [hnotMem]; simp)).mpr hsome
Proof state after:
case refine_2
nfa : NFA
it : String.Iterator
saveSize : ℕ
matched : Option (Array (Option String.Pos))
v : it.Valid
hsome✝ : matched.isSome = true
saveSlots✝ : Vec (Array (Option String.Pos)) nfa.nodes.size
_hs : (Vec.ofFn fun x => captureNext.initSave saveSize) = saveSlots✝
init : Option (Array (Option String.Pos)) × SparseSet nfa.nodes.size × Vec (Array (Option String.Pos)) nfa.nodes.size
matched' : Option (Array (Option String.Pos))
init' : SparseSet nfa.nodes.size
saveSlots : Vec (Array (Option String.Pos)) nfa.nodes.size
he :
  exploreεClosure nfa it.i SparseSet.empty (captureNext.initSave saveSize) none saveSlots✝ nfa.start #[] =
    (matched', init', saveSlots)
h : captureNext.go nfa saveSize it init' SparseSet.empty saveSlots matched' = matched
hnotMem : ∀ (i : Fin nfa.nodes.size), i ∉ SparseSet.empty
hsome : matched'.isSome = true
i : Fin nfa.nodes.size
hi : i ∈ init'
hdone : nfa[i] = Node.done
⊢ ∃ s l m r,
    Substring.ValidFor l m r s ∧ it.toString = { data := l ++ m ++ r } ∧ ∃ i, nfa.reaches i m ∧ nfa[i] = Node.done
Theorem: Regex.VM.captureNext_spec
Proof state before:
case refine_2
nfa : NFA
it : String.Iterator
saveSize : ℕ
matched : Option (Array (Option String.Pos))
v : it.Valid
hsome✝ : matched.isSome = true
saveSlots✝ : Vec (Array (Option String.Pos)) nfa.nodes.size
_hs : (Vec.ofFn fun x => captureNext.initSave saveSize) = saveSlots✝
init : Option (Array (Option String.Pos)) × SparseSet nfa.nodes.size × Vec (Array (Option String.Pos)) nfa.nodes.size
matched' : Option (Array (Option String.Pos))
init' : SparseSet nfa.nodes.size
saveSlots : Vec (Array (Option String.Pos)) nfa.nodes.size
he :
  exploreεClosure nfa it.i SparseSet.empty (captureNext.initSave saveSize) none saveSlots✝ nfa.start #[] =
    (matched', init', saveSlots)
h : captureNext.go nfa saveSize it init' SparseSet.empty saveSlots matched' = matched
hnotMem : ∀ (i : Fin nfa.nodes.size), i ∉ SparseSet.empty
hsome : matched'.isSome = true
i : Fin nfa.nodes.size
hi : i ∈ init'
hdone : nfa[i] = Node.done
⊢ ∃ s l m r,
    Substring.ValidFor l m r s ∧ it.toString = { data := l ++ m ++ r } ∧ ∃ i, nfa.reaches i m ∧ nfa[i] = Node.done
Tactic:
have cls := (exploreεClosure_spec.mem_next_iff he (by simp only [hnotMem]; simp) i).mp hi
Proof state after:
case refine_2
nfa : NFA
it : String.Iterator
saveSize : ℕ
matched : Option (Array (Option String.Pos))
v : it.Valid
hsome✝ : matched.isSome = true
saveSlots✝ : Vec (Array (Option String.Pos)) nfa.nodes.size
_hs : (Vec.ofFn fun x => captureNext.initSave saveSize) = saveSlots✝
init : Option (Array (Option String.Pos)) × SparseSet nfa.nodes.size × Vec (Array (Option String.Pos)) nfa.nodes.size
matched' : Option (Array (Option String.Pos))
init' : SparseSet nfa.nodes.size
saveSlots : Vec (Array (Option String.Pos)) nfa.nodes.size
he :
  exploreεClosure nfa it.i SparseSet.empty (captureNext.initSave saveSize) none saveSlots✝ nfa.start #[] =
    (matched', init', saveSlots)
h : captureNext.go nfa saveSize it init' SparseSet.empty saveSlots matched' = matched
hnotMem : ∀ (i : Fin nfa.nodes.size), i ∉ SparseSet.empty
hsome : matched'.isSome = true
i : Fin nfa.nodes.size
hi : i ∈ init'
hdone : nfa[i] = Node.done
cls : i ∈ SparseSet.empty ∨ ↑i ∈ nfa.εClosure ↑nfa.start
⊢ ∃ s l m r,
    Substring.ValidFor l m r s ∧ it.toString = { data := l ++ m ++ r } ∧ ∃ i, nfa.reaches i m ∧ nfa[i] = Node.done
Theorem: Regex.VM.captureNext_spec
Proof state before:
case refine_2
nfa : NFA
it : String.Iterator
saveSize : ℕ
matched : Option (Array (Option String.Pos))
v : it.Valid
hsome✝ : matched.isSome = true
saveSlots✝ : Vec (Array (Option String.Pos)) nfa.nodes.size
_hs : (Vec.ofFn fun x => captureNext.initSave saveSize) = saveSlots✝
init : Option (Array (Option String.Pos)) × SparseSet nfa.nodes.size × Vec (Array (Option String.Pos)) nfa.nodes.size
matched' : Option (Array (Option String.Pos))
init' : SparseSet nfa.nodes.size
saveSlots : Vec (Array (Option String.Pos)) nfa.nodes.size
he :
  exploreεClosure nfa it.i SparseSet.empty (captureNext.initSave saveSize) none saveSlots✝ nfa.start #[] =
    (matched', init', saveSlots)
h : captureNext.go nfa saveSize it init' SparseSet.empty saveSlots matched' = matched
hnotMem : ∀ (i : Fin nfa.nodes.size), i ∉ SparseSet.empty
hsome : matched'.isSome = true
i : Fin nfa.nodes.size
hi : i ∈ init'
hdone : nfa[i] = Node.done
cls : i ∈ SparseSet.empty ∨ ↑i ∈ nfa.εClosure ↑nfa.start
⊢ ∃ s l m r,
    Substring.ValidFor l m r s ∧ it.toString = { data := l ++ m ++ r } ∧ ∃ i, nfa.reaches i m ∧ nfa[i] = Node.done
Tactic:
simp only [hnotMem] at cls
Proof state after:
case refine_2
nfa : NFA
it : String.Iterator
saveSize : ℕ
matched : Option (Array (Option String.Pos))
v : it.Valid
hsome✝ : matched.isSome = true
saveSlots✝ : Vec (Array (Option String.Pos)) nfa.nodes.size
_hs : (Vec.ofFn fun x => captureNext.initSave saveSize) = saveSlots✝
init : Option (Array (Option String.Pos)) × SparseSet nfa.nodes.size × Vec (Array (Option String.Pos)) nfa.nodes.size
matched' : Option (Array (Option String.Pos))
init' : SparseSet nfa.nodes.size
saveSlots : Vec (Array (Option String.Pos)) nfa.nodes.size
he :
  exploreεClosure nfa it.i SparseSet.empty (captureNext.initSave saveSize) none saveSlots✝ nfa.start #[] =
    (matched', init', saveSlots)
h : captureNext.go nfa saveSize it init' SparseSet.empty saveSlots matched' = matched
hnotMem : ∀ (i : Fin nfa.nodes.size), i ∉ SparseSet.empty
hsome : matched'.isSome = true
i : Fin nfa.nodes.size
hi : i ∈ init'
hdone : nfa[i] = Node.done
cls : False ∨ ↑i ∈ nfa.εClosure ↑nfa.start
⊢ ∃ s l m r,
    Substring.ValidFor l m r s ∧ it.toString = { data := l ++ m ++ r } ∧ ∃ i, nfa.reaches i m ∧ nfa[i] = Node.done
Theorem: Regex.VM.captureNext_spec
Proof state before:
case refine_2
nfa : NFA
it : String.Iterator
saveSize : ℕ
matched : Option (Array (Option String.Pos))
v : it.Valid
hsome✝ : matched.isSome = true
saveSlots✝ : Vec (Array (Option String.Pos)) nfa.nodes.size
_hs : (Vec.ofFn fun x => captureNext.initSave saveSize) = saveSlots✝
init : Option (Array (Option String.Pos)) × SparseSet nfa.nodes.size × Vec (Array (Option String.Pos)) nfa.nodes.size
matched' : Option (Array (Option String.Pos))
init' : SparseSet nfa.nodes.size
saveSlots : Vec (Array (Option String.Pos)) nfa.nodes.size
he :
  exploreεClosure nfa it.i SparseSet.empty (captureNext.initSave saveSize) none saveSlots✝ nfa.start #[] =
    (matched', init', saveSlots)
h : captureNext.go nfa saveSize it init' SparseSet.empty saveSlots matched' = matched
hnotMem : ∀ (i : Fin nfa.nodes.size), i ∉ SparseSet.empty
hsome : matched'.isSome = true
i : Fin nfa.nodes.size
hi : i ∈ init'
hdone : nfa[i] = Node.done
cls : False ∨ ↑i ∈ nfa.εClosure ↑nfa.start
⊢ ∃ s l m r,
    Substring.ValidFor l m r s ∧ it.toString = { data := l ++ m ++ r } ∧ ∃ i, nfa.reaches i m ∧ nfa[i] = Node.done
Tactic:
simp at cls
Proof state after:
case refine_2
nfa : NFA
it : String.Iterator
saveSize : ℕ
matched : Option (Array (Option String.Pos))
v : it.Valid
hsome✝ : matched.isSome = true
saveSlots✝ : Vec (Array (Option String.Pos)) nfa.nodes.size
_hs : (Vec.ofFn fun x => captureNext.initSave saveSize) = saveSlots✝
init : Option (Array (Option String.Pos)) × SparseSet nfa.nodes.size × Vec (Array (Option String.Pos)) nfa.nodes.size
matched' : Option (Array (Option String.Pos))
init' : SparseSet nfa.nodes.size
saveSlots : Vec (Array (Option String.Pos)) nfa.nodes.size
he :
  exploreεClosure nfa it.i SparseSet.empty (captureNext.initSave saveSize) none saveSlots✝ nfa.start #[] =
    (matched', init', saveSlots)
h : captureNext.go nfa saveSize it init' SparseSet.empty saveSlots matched' = matched
hnotMem : ∀ (i : Fin nfa.nodes.size), i ∉ SparseSet.empty
hsome : matched'.isSome = true
i : Fin nfa.nodes.size
hi : i ∈ init'
hdone : nfa[i] = Node.done
cls : ↑i ∈ nfa.εClosure ↑nfa.start
⊢ ∃ s l m r,
    Substring.ValidFor l m r s ∧ it.toString = { data := l ++ m ++ r } ∧ ∃ i, nfa.reaches i m ∧ nfa[i] = Node.done
Theorem: Regex.VM.captureNext_spec
Proof state before:
case refine_2
nfa : NFA
it : String.Iterator
saveSize : ℕ
matched : Option (Array (Option String.Pos))
v : it.Valid
hsome✝ : matched.isSome = true
saveSlots✝ : Vec (Array (Option String.Pos)) nfa.nodes.size
_hs : (Vec.ofFn fun x => captureNext.initSave saveSize) = saveSlots✝
init : Option (Array (Option String.Pos)) × SparseSet nfa.nodes.size × Vec (Array (Option String.Pos)) nfa.nodes.size
matched' : Option (Array (Option String.Pos))
init' : SparseSet nfa.nodes.size
saveSlots : Vec (Array (Option String.Pos)) nfa.nodes.size
he :
  exploreεClosure nfa it.i SparseSet.empty (captureNext.initSave saveSize) none saveSlots✝ nfa.start #[] =
    (matched', init', saveSlots)
h : captureNext.go nfa saveSize it init' SparseSet.empty saveSlots matched' = matched
hnotMem : ∀ (i : Fin nfa.nodes.size), i ∉ SparseSet.empty
hsome : matched'.isSome = true
i : Fin nfa.nodes.size
hi : i ∈ init'
hdone : nfa[i] = Node.done
cls : ↑i ∈ nfa.εClosure ↑nfa.start
⊢ ∃ s l m r,
    Substring.ValidFor l m r s ∧ it.toString = { data := l ++ m ++ r } ∧ ∃ i, nfa.reaches i m ∧ nfa[i] = Node.done
Tactic:
have ⟨l, r, v'⟩ := v.validFor
Proof state after:
case refine_2
nfa : NFA
it : String.Iterator
saveSize : ℕ
matched : Option (Array (Option String.Pos))
v : it.Valid
hsome✝ : matched.isSome = true
saveSlots✝ : Vec (Array (Option String.Pos)) nfa.nodes.size
_hs : (Vec.ofFn fun x => captureNext.initSave saveSize) = saveSlots✝
init : Option (Array (Option String.Pos)) × SparseSet nfa.nodes.size × Vec (Array (Option String.Pos)) nfa.nodes.size
matched' : Option (Array (Option String.Pos))
init' : SparseSet nfa.nodes.size
saveSlots : Vec (Array (Option String.Pos)) nfa.nodes.size
he :
  exploreεClosure nfa it.i SparseSet.empty (captureNext.initSave saveSize) none saveSlots✝ nfa.start #[] =
    (matched', init', saveSlots)
h : captureNext.go nfa saveSize it init' SparseSet.empty saveSlots matched' = matched
hnotMem : ∀ (i : Fin nfa.nodes.size), i ∉ SparseSet.empty
hsome : matched'.isSome = true
i : Fin nfa.nodes.size
hi : i ∈ init'
hdone : nfa[i] = Node.done
cls : ↑i ∈ nfa.εClosure ↑nfa.start
l r : List Char
v' : String.Iterator.ValidFor l r it
⊢ ∃ s l m r,
    Substring.ValidFor l m r s ∧ it.toString = { data := l ++ m ++ r } ∧ ∃ i, nfa.reaches i m ∧ nfa[i] = Node.done
Theorem: Regex.VM.captureNext_spec
Proof state before:
case refine_2
nfa : NFA
it : String.Iterator
saveSize : ℕ
matched : Option (Array (Option String.Pos))
v : it.Valid
hsome✝ : matched.isSome = true
saveSlots✝ : Vec (Array (Option String.Pos)) nfa.nodes.size
_hs : (Vec.ofFn fun x => captureNext.initSave saveSize) = saveSlots✝
init : Option (Array (Option String.Pos)) × SparseSet nfa.nodes.size × Vec (Array (Option String.Pos)) nfa.nodes.size
matched' : Option (Array (Option String.Pos))
init' : SparseSet nfa.nodes.size
saveSlots : Vec (Array (Option String.Pos)) nfa.nodes.size
he :
  exploreεClosure nfa it.i SparseSet.empty (captureNext.initSave saveSize) none saveSlots✝ nfa.start #[] =
    (matched', init', saveSlots)
h : captureNext.go nfa saveSize it init' SparseSet.empty saveSlots matched' = matched
hnotMem : ∀ (i : Fin nfa.nodes.size), i ∉ SparseSet.empty
hsome : matched'.isSome = true
i : Fin nfa.nodes.size
hi : i ∈ init'
hdone : nfa[i] = Node.done
cls : ↑i ∈ nfa.εClosure ↑nfa.start
l r : List Char
v' : String.Iterator.ValidFor l r it
⊢ ∃ s l m r,
    Substring.ValidFor l m r s ∧ it.toString = { data := l ++ m ++ r } ∧ ∃ i, nfa.reaches i m ∧ nfa[i] = Node.done
Tactic:
let pos : String.Pos := ⟨String.utf8Len l⟩
Proof state after:
case refine_2
nfa : NFA
it : String.Iterator
saveSize : ℕ
matched : Option (Array (Option String.Pos))
v : it.Valid
hsome✝ : matched.isSome = true
saveSlots✝ : Vec (Array (Option String.Pos)) nfa.nodes.size
_hs : (Vec.ofFn fun x => captureNext.initSave saveSize) = saveSlots✝
init : Option (Array (Option String.Pos)) × SparseSet nfa.nodes.size × Vec (Array (Option String.Pos)) nfa.nodes.size
matched' : Option (Array (Option String.Pos))
init' : SparseSet nfa.nodes.size
saveSlots : Vec (Array (Option String.Pos)) nfa.nodes.size
he :
  exploreεClosure nfa it.i SparseSet.empty (captureNext.initSave saveSize) none saveSlots✝ nfa.start #[] =
    (matched', init', saveSlots)
h : captureNext.go nfa saveSize it init' SparseSet.empty saveSlots matched' = matched
hnotMem : ∀ (i : Fin nfa.nodes.size), i ∉ SparseSet.empty
hsome : matched'.isSome = true
i : Fin nfa.nodes.size
hi : i ∈ init'
hdone : nfa[i] = Node.done
cls : ↑i ∈ nfa.εClosure ↑nfa.start
l r : List Char
v' : String.Iterator.ValidFor l r it
pos : String.Pos := { byteIdx := String.utf8Len l }
⊢ ∃ s l m r,
    Substring.ValidFor l m r s ∧ it.toString = { data := l ++ m ++ r } ∧ ∃ i, nfa.reaches i m ∧ nfa[i] = Node.done
Theorem: Regex.VM.captureNext_spec
Proof state before:
case refine_2
nfa : NFA
it : String.Iterator
saveSize : ℕ
matched : Option (Array (Option String.Pos))
v : it.Valid
hsome✝ : matched.isSome = true
saveSlots✝ : Vec (Array (Option String.Pos)) nfa.nodes.size
_hs : (Vec.ofFn fun x => captureNext.initSave saveSize) = saveSlots✝
init : Option (Array (Option String.Pos)) × SparseSet nfa.nodes.size × Vec (Array (Option String.Pos)) nfa.nodes.size
matched' : Option (Array (Option String.Pos))
init' : SparseSet nfa.nodes.size
saveSlots : Vec (Array (Option String.Pos)) nfa.nodes.size
he :
  exploreεClosure nfa it.i SparseSet.empty (captureNext.initSave saveSize) none saveSlots✝ nfa.start #[] =
    (matched', init', saveSlots)
h : captureNext.go nfa saveSize it init' SparseSet.empty saveSlots matched' = matched
hnotMem : ∀ (i : Fin nfa.nodes.size), i ∉ SparseSet.empty
hsome : matched'.isSome = true
i : Fin nfa.nodes.size
hi : i ∈ init'
hdone : nfa[i] = Node.done
cls : ↑i ∈ nfa.εClosure ↑nfa.start
l r : List Char
v' : String.Iterator.ValidFor l r it
pos : String.Pos := { byteIdx := String.utf8Len l }
⊢ ∃ s l m r,
    Substring.ValidFor l m r s ∧ it.toString = { data := l ++ m ++ r } ∧ ∃ i, nfa.reaches i m ∧ nfa[i] = Node.done
Tactic:
refine ⟨⟨it.toString, pos, pos⟩, l.reverse, [], r, ?_, by simp [v'.toString, List.reverseAux_eq], ⟨i, .nil cls, hdone⟩⟩
Proof state after:
case refine_2
nfa : NFA
it : String.Iterator
saveSize : ℕ
matched : Option (Array (Option String.Pos))
v : it.Valid
hsome✝ : matched.isSome = true
saveSlots✝ : Vec (Array (Option String.Pos)) nfa.nodes.size
_hs : (Vec.ofFn fun x => captureNext.initSave saveSize) = saveSlots✝
init : Option (Array (Option String.Pos)) × SparseSet nfa.nodes.size × Vec (Array (Option String.Pos)) nfa.nodes.size
matched' : Option (Array (Option String.Pos))
init' : SparseSet nfa.nodes.size
saveSlots : Vec (Array (Option String.Pos)) nfa.nodes.size
he :
  exploreεClosure nfa it.i SparseSet.empty (captureNext.initSave saveSize) none saveSlots✝ nfa.start #[] =
    (matched', init', saveSlots)
h : captureNext.go nfa saveSize it init' SparseSet.empty saveSlots matched' = matched
hnotMem : ∀ (i : Fin nfa.nodes.size), i ∉ SparseSet.empty
hsome : matched'.isSome = true
i : Fin nfa.nodes.size
hi : i ∈ init'
hdone : nfa[i] = Node.done
cls : ↑i ∈ nfa.εClosure ↑nfa.start
l r : List Char
v' : String.Iterator.ValidFor l r it
pos : String.Pos := { byteIdx := String.utf8Len l }
⊢ Substring.ValidFor l.reverse [] r { str := it.toString, startPos := pos, stopPos := pos }
Theorem: Regex.VM.captureNext_spec
Proof state before:
case refine_2
nfa : NFA
it : String.Iterator
saveSize : ℕ
matched : Option (Array (Option String.Pos))
v : it.Valid
hsome✝ : matched.isSome = true
saveSlots✝ : Vec (Array (Option String.Pos)) nfa.nodes.size
_hs : (Vec.ofFn fun x => captureNext.initSave saveSize) = saveSlots✝
init : Option (Array (Option String.Pos)) × SparseSet nfa.nodes.size × Vec (Array (Option String.Pos)) nfa.nodes.size
matched' : Option (Array (Option String.Pos))
init' : SparseSet nfa.nodes.size
saveSlots : Vec (Array (Option String.Pos)) nfa.nodes.size
he :
  exploreεClosure nfa it.i SparseSet.empty (captureNext.initSave saveSize) none saveSlots✝ nfa.start #[] =
    (matched', init', saveSlots)
h : captureNext.go nfa saveSize it init' SparseSet.empty saveSlots matched' = matched
hnotMem : ∀ (i : Fin nfa.nodes.size), i ∉ SparseSet.empty
hsome : matched'.isSome = true
i : Fin nfa.nodes.size
hi : i ∈ init'
hdone : nfa[i] = Node.done
cls : ↑i ∈ nfa.εClosure ↑nfa.start
l r : List Char
v' : String.Iterator.ValidFor l r it
pos : String.Pos := { byteIdx := String.utf8Len l }
⊢ Substring.ValidFor l.reverse [] r { str := it.toString, startPos := pos, stopPos := pos }
Tactic:
apply Substring.ValidFor.of_eq <;> simp [v'.toString, List.reverseAux_eq]
Proof state after:
no goals
Theorem: Regex.VM.captureNext_spec
Proof state before:
nfa : NFA
it : String.Iterator
saveSize : ℕ
matched : Option (Array (Option String.Pos))
v : it.Valid
hsome✝ : matched.isSome = true
saveSlots✝ : Vec (Array (Option String.Pos)) nfa.nodes.size
_hs : (Vec.ofFn fun x => captureNext.initSave saveSize) = saveSlots✝
init : Option (Array (Option String.Pos)) × SparseSet nfa.nodes.size × Vec (Array (Option String.Pos)) nfa.nodes.size
matched' : Option (Array (Option String.Pos))
init' : SparseSet nfa.nodes.size
saveSlots : Vec (Array (Option String.Pos)) nfa.nodes.size
he :
  exploreεClosure nfa it.i SparseSet.empty (captureNext.initSave saveSize) none saveSlots✝ nfa.start #[] =
    (matched', init', saveSlots)
h : captureNext.go nfa saveSize it init' SparseSet.empty saveSlots matched' = matched
hnotMem : ∀ (i : Fin nfa.nodes.size), i ∉ SparseSet.empty
hsome : matched'.isSome = true
⊢ (∃ i ∈ SparseSet.empty, nfa[i] = Node.done) ↔ none.isSome = true
Tactic:
simp only [hnotMem]
Proof state after:
nfa : NFA
it : String.Iterator
saveSize : ℕ
matched : Option (Array (Option String.Pos))
v : it.Valid
hsome✝ : matched.isSome = true
saveSlots✝ : Vec (Array (Option String.Pos)) nfa.nodes.size
_hs : (Vec.ofFn fun x => captureNext.initSave saveSize) = saveSlots✝
init : Option (Array (Option String.Pos)) × SparseSet nfa.nodes.size × Vec (Array (Option String.Pos)) nfa.nodes.size
matched' : Option (Array (Option String.Pos))
init' : SparseSet nfa.nodes.size
saveSlots : Vec (Array (Option String.Pos)) nfa.nodes.size
he :
  exploreεClosure nfa it.i SparseSet.empty (captureNext.initSave saveSize) none saveSlots✝ nfa.start #[] =
    (matched', init', saveSlots)
h : captureNext.go nfa saveSize it init' SparseSet.empty saveSlots matched' = matched
hnotMem : ∀ (i : Fin nfa.nodes.size), i ∉ SparseSet.empty
hsome : matched'.isSome = true
⊢ (∃ i, False ∧ nfa[i] = Node.done) ↔ none.isSome = true
Theorem: Regex.VM.captureNext_spec
Proof state before:
nfa : NFA
it : String.Iterator
saveSize : ℕ
matched : Option (Array (Option String.Pos))
v : it.Valid
hsome✝ : matched.isSome = true
saveSlots✝ : Vec (Array (Option String.Pos)) nfa.nodes.size
_hs : (Vec.ofFn fun x => captureNext.initSave saveSize) = saveSlots✝
init : Option (Array (Option String.Pos)) × SparseSet nfa.nodes.size × Vec (Array (Option String.Pos)) nfa.nodes.size
matched' : Option (Array (Option String.Pos))
init' : SparseSet nfa.nodes.size
saveSlots : Vec (Array (Option String.Pos)) nfa.nodes.size
he :
  exploreεClosure nfa it.i SparseSet.empty (captureNext.initSave saveSize) none saveSlots✝ nfa.start #[] =
    (matched', init', saveSlots)
h : captureNext.go nfa saveSize it init' SparseSet.empty saveSlots matched' = matched
hnotMem : ∀ (i : Fin nfa.nodes.size), i ∉ SparseSet.empty
hsome : matched'.isSome = true
⊢ (∃ i, False ∧ nfa[i] = Node.done) ↔ none.isSome = true
Tactic:
simp
Proof state after:
no goals