split at h
nfa : NFA
saveSize : ℕ
it : String.Iterator
current next : SparseSet nfa.nodes.size
saveSlots : Vec (Array (Option String.Pos)) nfa.nodes.size
lastMatch matched : Option (Array (Option String.Pos))
haystack : String
inv : captureNext.go.Inv nfa it haystack current lastMatch
v : it.Valid
eqs : haystack = it.toString
hemp : next.isEmpty = true
atEnd : ¬it.atEnd = true
h :
  (if (current.isEmpty && lastMatch.isSome) = true then lastMatch
    else
      let currentAndSaveSlots :=
        if lastMatch.isNone = true then
          let explored :=
            exploreεClosure nfa it.pos current (captureNext.initSave saveSize) none saveSlots nfa.start #[];
          explored.2
        else (current, saveSlots);
      let stepped := eachStepChar nfa it.curr it.next.pos currentAndSaveSlots.1 next currentAndSaveSlots.2;
      captureNext.go nfa saveSize it.next stepped.2.1 current.clear stepped.2.2
        (HOrElse.hOrElse stepped.1 fun x => lastMatch)) =
    matched
⊢ matched.isSome = true →
    ∃ s l m r,
      Substring.ValidFor l m r s ∧ haystack = { data := l ++ m ++ r } ∧ ∃ i, nfa.reaches i m ∧ nfa[i] = Node.done
case inl
nfa : NFA
saveSize : ℕ
it : String.Iterator
current next : SparseSet nfa.nodes.size
saveSlots : Vec (Array (Option String.Pos)) nfa.nodes.size
lastMatch matched : Option (Array (Option String.Pos))
haystack : String
inv : captureNext.go.Inv nfa it haystack current lastMatch
v : it.Valid
eqs : haystack = it.toString
hemp : next.isEmpty = true
atEnd : ¬it.atEnd = true
h✝ : (current.isEmpty && lastMatch.isSome) = true
h : lastMatch = matched
⊢ matched.isSome = true →
    ∃ s l m r,
      Substring.ValidFor l m r s ∧ haystack = { data := l ++ m ++ r } ∧ ∃ i, nfa.reaches i m ∧ nfa[i] = Node.done

case inr
nfa : NFA
saveSize : ℕ
it : String.Iterator
current next : SparseSet nfa.nodes.size
saveSlots : Vec (Array (Option String.Pos)) nfa.nodes.size
lastMatch matched : Option (Array (Option String.Pos))
haystack : String
inv : captureNext.go.Inv nfa it haystack current lastMatch
v : it.Valid
eqs : haystack = it.toString
hemp : next.isEmpty = true
atEnd : ¬it.atEnd = true
h✝ : ¬(current.isEmpty && lastMatch.isSome) = true
h :
  (let currentAndSaveSlots :=
      if lastMatch.isNone = true then
        let explored := exploreεClosure nfa it.pos current (captureNext.initSave saveSize) none saveSlots nfa.start #[];
        explored.2
      else (current, saveSlots);
    let stepped := eachStepChar nfa it.curr it.next.pos currentAndSaveSlots.1 next currentAndSaveSlots.2;
    captureNext.go nfa saveSize it.next stepped.2.1 current.clear stepped.2.2
      (HOrElse.hOrElse stepped.1 fun x => lastMatch)) =
    matched
⊢ matched.isSome = true →
    ∃ s l m r,
      Substring.ValidFor l m r s ∧ haystack = { data := l ++ m ++ r } ∧ ∃ i, nfa.reaches i m ∧ nfa[i] = Node.done