Theorem: Regex.VM.eachStepChar_spec.preserve_cls.go
Proof state before:
nfa : NFA
c : Char
pos : String.Pos
current : SparseSet nfa.nodes.size
i : ℕ
hle : i ≤ current.count
next : SparseSet nfa.nodes.size
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
matched' : Option (Array (Option String.Pos))
next' : SparseSet nfa.nodes.size
saveSlots' : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
inv : ∀ (i j : Fin nfa.nodes.size), i ∈ next → ↑j ∈ nfa.εStep ↑i → j ∈ next
hi : ¬i = current.count
hlt : i < current.count
result :
  Option (Array (Option String.Pos)) × SparseSet nfa.nodes.size × Data.Vec (Array (Option String.Pos)) nfa.nodes.size
matched'' : Option (Array (Option String.Pos))
next'' : SparseSet nfa.nodes.size
saveSlots'' : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
hres : stepChar nfa c pos next saveSlots current[i] = (matched'', next'', saveSlots'')
h :
  (match (matched'', next'', saveSlots'').1 with
    | none =>
      eachStepChar.go nfa c pos current (i + 1) ⋯ (matched'', next'', saveSlots'').2.1
        (matched'', next'', saveSlots'').2.2
    | some val => (matched'', next'', saveSlots'')) =
    (matched', next', saveSlots')
⊢ ∀ (i j : Fin nfa.nodes.size), i ∈ next' → ↑j ∈ nfa.εStep ↑i → j ∈ next'
Tactic:
split at h
Proof state after:
case h_1
nfa : NFA
c : Char
pos : String.Pos
current : SparseSet nfa.nodes.size
i : ℕ
hle : i ≤ current.count
next : SparseSet nfa.nodes.size
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
matched' : Option (Array (Option String.Pos))
next' : SparseSet nfa.nodes.size
saveSlots' : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
inv : ∀ (i j : Fin nfa.nodes.size), i ∈ next → ↑j ∈ nfa.εStep ↑i → j ∈ next
hi : ¬i = current.count
hlt : i < current.count
result :
  Option (Array (Option String.Pos)) × SparseSet nfa.nodes.size × Data.Vec (Array (Option String.Pos)) nfa.nodes.size
matched'' : Option (Array (Option String.Pos))
next'' : SparseSet nfa.nodes.size
saveSlots'' : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
hres : stepChar nfa c pos next saveSlots current[i] = (matched'', next'', saveSlots'')
x✝ : Option (Array (Option String.Pos))
heq✝ : (matched'', next'', saveSlots'').1 = none
h :
  eachStepChar.go nfa c pos current (i + 1) ⋯ (matched'', next'', saveSlots'').2.1
      (matched'', next'', saveSlots'').2.2 =
    (matched', next', saveSlots')
⊢ ∀ (i j : Fin nfa.nodes.size), i ∈ next' → ↑j ∈ nfa.εStep ↑i → j ∈ next'

case h_2
nfa : NFA
c : Char
pos : String.Pos
current : SparseSet nfa.nodes.size
i : ℕ
hle : i ≤ current.count
next : SparseSet nfa.nodes.size
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
matched' : Option (Array (Option String.Pos))
next' : SparseSet nfa.nodes.size
saveSlots' : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
inv : ∀ (i j : Fin nfa.nodes.size), i ∈ next → ↑j ∈ nfa.εStep ↑i → j ∈ next
hi : ¬i = current.count
hlt : i < current.count
result :
  Option (Array (Option String.Pos)) × SparseSet nfa.nodes.size × Data.Vec (Array (Option String.Pos)) nfa.nodes.size
matched'' : Option (Array (Option String.Pos))
next'' : SparseSet nfa.nodes.size
saveSlots'' : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
hres : stepChar nfa c pos next saveSlots current[i] = (matched'', next'', saveSlots'')
x✝ : Option (Array (Option String.Pos))
val✝ : Array (Option String.Pos)
heq✝ : (matched'', next'', saveSlots'').1 = some val✝
h : (matched'', next'', saveSlots'') = (matched', next', saveSlots')
⊢ ∀ (i j : Fin nfa.nodes.size), i ∈ next' → ↑j ∈ nfa.εStep ↑i → j ∈ next'