internlm/Lean-Github huggingface dataset:
Theorem: Regex.VM.εClosure_mem_done_iff
Proof state before:
nfa : NFA
pos : String.Pos
next : SparseSet nfa.nodes.size
currentSave : Array (Option String.Pos)
matched : Option (Array (Option String.Pos))
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
stack : Array (StackEntry 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 ∈ next, nfa[i] = Node.done) ↔ matched.isSome = true
h✝ : stack.isEmpty = true
h : (matched, next, saveSlots) = (matched', next', saveSlots')
⊢ (∃ i ∈ next', nfa[i] = Node.done) ↔ matched'.isSome = true
Tactic:
simp at h
Proof state after:
nfa : NFA
pos : String.Pos
next : SparseSet nfa.nodes.size
currentSave : Array (Option String.Pos)
matched : Option (Array (Option String.Pos))
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
stack : Array (StackEntry 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 ∈ next, nfa[i] = Node.done) ↔ matched.isSome = true
h✝ : stack.isEmpty = true
h : matched = matched' ∧ next = next' ∧ saveSlots = saveSlots'
⊢ (∃ i ∈ next', nfa[i] = Node.done) ↔ matched'.isSome = true
Theorem: Regex.VM.εClosure_mem_done_iff
Proof state before:
nfa : NFA
pos : String.Pos
next : SparseSet nfa.nodes.size
currentSave : Array (Option String.Pos)
matched : Option (Array (Option String.Pos))
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
stack : Array (StackEntry 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 ∈ next, nfa[i] = Node.done) ↔ matched.isSome = true
h✝ : stack.isEmpty = true
h : matched = matched' ∧ next = next' ∧ saveSlots = saveSlots'
⊢ (∃ i ∈ next', nfa[i] = Node.done) ↔ matched'.isSome = true
Tactic:
simp only [h] at inv
Proof state after:
nfa : NFA
pos : String.Pos
next : SparseSet nfa.nodes.size
currentSave : Array (Option String.Pos)
matched : Option (Array (Option String.Pos))
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
stack : Array (StackEntry nfa.nodes.size)
matched' : Option (Array (Option String.Pos))
next' : SparseSet nfa.nodes.size
saveSlots' : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
h✝ : stack.isEmpty = true
h : matched = matched' ∧ next = next' ∧ saveSlots = saveSlots'
inv : (∃ i ∈ next', nfa[i] = Node.done) ↔ matched'.isSome = true
⊢ (∃ i ∈ next', nfa[i] = Node.done) ↔ matched'.isSome = true
Theorem: Regex.VM.εClosure_mem_done_iff
Proof state before:
nfa : NFA
pos : String.Pos
next : SparseSet nfa.nodes.size
currentSave : Array (Option String.Pos)
matched : Option (Array (Option String.Pos))
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
stack : Array (StackEntry nfa.nodes.size)
matched' : Option (Array (Option String.Pos))
next' : SparseSet nfa.nodes.size
saveSlots' : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
h✝ : stack.isEmpty = true
h : matched = matched' ∧ next = next' ∧ saveSlots = saveSlots'
inv : (∃ i ∈ next', nfa[i] = Node.done) ↔ matched'.isSome = true
⊢ (∃ i ∈ next', nfa[i] = Node.done) ↔ matched'.isSome = true
Tactic:
exact inv
Proof state after:
no goals
Theorem: Regex.VM.εClosure_mem_done_iff
Proof state before:
nfa : NFA
pos : String.Pos
next : SparseSet nfa.nodes.size
currentSave : Array (Option String.Pos)
matched : Option (Array (Option String.Pos))
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
stack : Array (StackEntry 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 ∈ next, nfa[i] = Node.done) ↔ matched.isSome = true
h✝ : ¬stack.isEmpty = true
h :
  (let entry := stack.back' h✝;
    let stack' := stack.pop;
    let_fun this := ⋯;
    match entry with
    | StackEntry.explore target => exploreεClosure nfa pos next currentSave matched saveSlots target stack'
    | StackEntry.restore save => εClosure nfa pos next save matched saveSlots stack') =
    (matched', next', saveSlots')
⊢ (∃ i ∈ next', nfa[i] = Node.done) ↔ matched'.isSome = true
Tactic:
simp at h
Proof state after:
nfa : NFA
pos : String.Pos
next : SparseSet nfa.nodes.size
currentSave : Array (Option String.Pos)
matched : Option (Array (Option String.Pos))
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
stack : Array (StackEntry 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 ∈ next, nfa[i] = Node.done) ↔ matched.isSome = true
h✝ : ¬stack.isEmpty = true
h :
  (match stack.back' h✝ with
    | StackEntry.explore target => exploreεClosure nfa pos next currentSave matched saveSlots target stack.pop
    | StackEntry.restore save => εClosure nfa pos next save matched saveSlots stack.pop) =
    (matched', next', saveSlots')
⊢ (∃ i ∈ next', nfa[i] = Node.done) ↔ matched'.isSome = true
Theorem: Regex.VM.εClosure_mem_done_iff
Proof state before:
nfa : NFA
pos : String.Pos
next : SparseSet nfa.nodes.size
currentSave : Array (Option String.Pos)
matched : Option (Array (Option String.Pos))
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
stack : Array (StackEntry 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 ∈ next, nfa[i] = Node.done) ↔ matched.isSome = true
h✝ : ¬stack.isEmpty = true
h :
  (match stack.back' h✝ with
    | StackEntry.explore target => exploreεClosure nfa pos next currentSave matched saveSlots target stack.pop
    | StackEntry.restore save => εClosure nfa pos next save matched saveSlots stack.pop) =
    (matched', next', saveSlots')
⊢ (∃ i ∈ next', nfa[i] = Node.done) ↔ matched'.isSome = true
Tactic:
have : stack.pop.size < stack.size := Array.lt_size_of_pop_of_not_empty _ (by assumption)
Proof state after:
nfa : NFA
pos : String.Pos
next : SparseSet nfa.nodes.size
currentSave : Array (Option String.Pos)
matched : Option (Array (Option String.Pos))
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
stack : Array (StackEntry 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 ∈ next, nfa[i] = Node.done) ↔ matched.isSome = true
h✝ : ¬stack.isEmpty = true
h :
  (match stack.back' h✝ with
    | StackEntry.explore target => exploreεClosure nfa pos next currentSave matched saveSlots target stack.pop
    | StackEntry.restore save => εClosure nfa pos next save matched saveSlots stack.pop) =
    (matched', next', saveSlots')
this : stack.pop.size < stack.size
⊢ (∃ i ∈ next', nfa[i] = Node.done) ↔ matched'.isSome = true
Theorem: Regex.VM.εClosure_mem_done_iff
Proof state before:
nfa : NFA
pos : String.Pos
next : SparseSet nfa.nodes.size
currentSave : Array (Option String.Pos)
matched : Option (Array (Option String.Pos))
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
stack : Array (StackEntry 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 ∈ next, nfa[i] = Node.done) ↔ matched.isSome = true
h✝ : ¬stack.isEmpty = true
h :
  (match stack.back' h✝ with
    | StackEntry.explore target => exploreεClosure nfa pos next currentSave matched saveSlots target stack.pop
    | StackEntry.restore save => εClosure nfa pos next save matched saveSlots stack.pop) =
    (matched', next', saveSlots')
this : stack.pop.size < stack.size
⊢ (∃ i ∈ next', nfa[i] = Node.done) ↔ matched'.isSome = true
Tactic:
split at h
Proof state after:
case h_1
nfa : NFA
pos : String.Pos
next : SparseSet nfa.nodes.size
currentSave : Array (Option String.Pos)
matched : Option (Array (Option String.Pos))
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
stack : Array (StackEntry 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 ∈ next, nfa[i] = Node.done) ↔ matched.isSome = true
h✝ : ¬stack.isEmpty = true
this : stack.pop.size < stack.size
entry✝ : StackEntry nfa.nodes.size
target✝ : Fin nfa.nodes.size
heq✝ : stack.back' h✝ = StackEntry.explore target✝
h : exploreεClosure nfa pos next currentSave matched saveSlots target✝ stack.pop = (matched', next', saveSlots')
⊢ (∃ i ∈ next', nfa[i] = Node.done) ↔ matched'.isSome = true

case h_2
nfa : NFA
pos : String.Pos
next : SparseSet nfa.nodes.size
currentSave : Array (Option String.Pos)
matched : Option (Array (Option String.Pos))
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
stack : Array (StackEntry 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 ∈ next, nfa[i] = Node.done) ↔ matched.isSome = true
h✝ : ¬stack.isEmpty = true
this : stack.pop.size < stack.size
entry✝ : StackEntry nfa.nodes.size
save✝ : Array (Option String.Pos)
heq✝ : stack.back' h✝ = StackEntry.restore save✝
h : εClosure nfa pos next save✝ matched saveSlots stack.pop = (matched', next', saveSlots')
⊢ (∃ i ∈ next', nfa[i] = Node.done) ↔ matched'.isSome = true
Theorem: Regex.VM.εClosure_mem_done_iff
Proof state before:
case h_1
nfa : NFA
pos : String.Pos
next : SparseSet nfa.nodes.size
currentSave : Array (Option String.Pos)
matched : Option (Array (Option String.Pos))
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
stack : Array (StackEntry 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 ∈ next, nfa[i] = Node.done) ↔ matched.isSome = true
h✝ : ¬stack.isEmpty = true
this : stack.pop.size < stack.size
entry✝ : StackEntry nfa.nodes.size
target✝ : Fin nfa.nodes.size
heq✝ : stack.back' h✝ = StackEntry.explore target✝
h : exploreεClosure nfa pos next currentSave matched saveSlots target✝ stack.pop = (matched', next', saveSlots')
⊢ (∃ i ∈ next', nfa[i] = Node.done) ↔ matched'.isSome = true

case h_2
nfa : NFA
pos : String.Pos
next : SparseSet nfa.nodes.size
currentSave : Array (Option String.Pos)
matched : Option (Array (Option String.Pos))
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
stack : Array (StackEntry 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 ∈ next, nfa[i] = Node.done) ↔ matched.isSome = true
h✝ : ¬stack.isEmpty = true
this : stack.pop.size < stack.size
entry✝ : StackEntry nfa.nodes.size
save✝ : Array (Option String.Pos)
heq✝ : stack.back' h✝ = StackEntry.restore save✝
h : εClosure nfa pos next save✝ matched saveSlots stack.pop = (matched', next', saveSlots')
⊢ (∃ i ∈ next', nfa[i] = Node.done) ↔ matched'.isSome = true
Tactic:
next => exact exploreεClosure_mem_done_iff h inv
Proof state after:
case h_2
nfa : NFA
pos : String.Pos
next : SparseSet nfa.nodes.size
currentSave : Array (Option String.Pos)
matched : Option (Array (Option String.Pos))
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
stack : Array (StackEntry 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 ∈ next, nfa[i] = Node.done) ↔ matched.isSome = true
h✝ : ¬stack.isEmpty = true
this : stack.pop.size < stack.size
entry✝ : StackEntry nfa.nodes.size
save✝ : Array (Option String.Pos)
heq✝ : stack.back' h✝ = StackEntry.restore save✝
h : εClosure nfa pos next save✝ matched saveSlots stack.pop = (matched', next', saveSlots')
⊢ (∃ i ∈ next', nfa[i] = Node.done) ↔ matched'.isSome = true
Theorem: Regex.VM.εClosure_mem_done_iff
Proof state before:
case h_2
nfa : NFA
pos : String.Pos
next : SparseSet nfa.nodes.size
currentSave : Array (Option String.Pos)
matched : Option (Array (Option String.Pos))
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
stack : Array (StackEntry 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 ∈ next, nfa[i] = Node.done) ↔ matched.isSome = true
h✝ : ¬stack.isEmpty = true
this : stack.pop.size < stack.size
entry✝ : StackEntry nfa.nodes.size
save✝ : Array (Option String.Pos)
heq✝ : stack.back' h✝ = StackEntry.restore save✝
h : εClosure nfa pos next save✝ matched saveSlots stack.pop = (matched', next', saveSlots')
⊢ (∃ i ∈ next', nfa[i] = Node.done) ↔ matched'.isSome = true
Tactic:
next => exact εClosure_mem_done_iff h inv
Proof state after:
no goals
Theorem: Regex.VM.εClosure_mem_done_iff
Proof state before:
nfa : NFA
pos : String.Pos
next : SparseSet nfa.nodes.size
currentSave : Array (Option String.Pos)
matched : Option (Array (Option String.Pos))
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
stack : Array (StackEntry 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 ∈ next, nfa[i] = Node.done) ↔ matched.isSome = true
h✝ : ¬stack.isEmpty = true
h :
  (match stack.back' h✝ with
    | StackEntry.explore target => exploreεClosure nfa pos next currentSave matched saveSlots target stack.pop
    | StackEntry.restore save => εClosure nfa pos next save matched saveSlots stack.pop) =
    (matched', next', saveSlots')
⊢ ¬stack.isEmpty = true
Tactic:
assumption
Proof state after:
no goals
Theorem: Regex.VM.εClosure_mem_done_iff
Proof state before:
nfa : NFA
pos : String.Pos
next : SparseSet nfa.nodes.size
currentSave : Array (Option String.Pos)
matched : Option (Array (Option String.Pos))
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
stack : Array (StackEntry 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 ∈ next, nfa[i] = Node.done) ↔ matched.isSome = true
h✝ : ¬stack.isEmpty = true
this : stack.pop.size < stack.size
entry✝ : StackEntry nfa.nodes.size
target✝ : Fin nfa.nodes.size
heq✝ : stack.back' h✝ = StackEntry.explore target✝
h : exploreεClosure nfa pos next currentSave matched saveSlots target✝ stack.pop = (matched', next', saveSlots')
⊢ (∃ i ∈ next', nfa[i] = Node.done) ↔ matched'.isSome = true
Tactic:
exact exploreεClosure_mem_done_iff h inv
Proof state after:
no goals
Theorem: Regex.VM.εClosure_mem_done_iff
Proof state before:
nfa : NFA
pos : String.Pos
next : SparseSet nfa.nodes.size
currentSave : Array (Option String.Pos)
matched : Option (Array (Option String.Pos))
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
stack : Array (StackEntry 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 ∈ next, nfa[i] = Node.done) ↔ matched.isSome = true
h✝ : ¬stack.isEmpty = true
this : stack.pop.size < stack.size
entry✝ : StackEntry nfa.nodes.size
save✝ : Array (Option String.Pos)
heq✝ : stack.back' h✝ = StackEntry.restore save✝
h : εClosure nfa pos next save✝ matched saveSlots stack.pop = (matched', next', saveSlots')
⊢ (∃ i ∈ next', nfa[i] = Node.done) ↔ matched'.isSome = true
Tactic:
exact εClosure_mem_done_iff h inv
Proof state after:
no goals
Theorem: Regex.VM.stepChar_mem_done_iff
Proof state before:
nfa : NFA
c : Char
pos : String.Pos
next : SparseSet nfa.nodes.size
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
target : Fin nfa.nodes.size
matched' : Option (Array (Option String.Pos))
next' : SparseSet nfa.nodes.size
saveSlots' : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
h : stepChar nfa c pos next saveSlots target = (matched', next', saveSlots')
hnotDone : ∀ i ∈ next, nfa[i] ≠ Node.done
⊢ (∃ i ∈ next', nfa[i] = Node.done) ↔ matched'.isSome = true
Tactic:
unfold stepChar at h
Proof state after:
nfa : NFA
c : Char
pos : String.Pos
next : SparseSet nfa.nodes.size
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
target : Fin nfa.nodes.size
matched' : Option (Array (Option String.Pos))
next' : SparseSet nfa.nodes.size
saveSlots' : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
h :
  (match hn : nfa[target] with
    | Node.char c' target' =>
      if c = c' then
        let_fun isLt := ⋯;
        let currentSave := saveSlots.get ↑target ⋯;
        exploreεClosure nfa pos next currentSave none saveSlots ⟨target', isLt⟩ #[]
      else (none, next, saveSlots)
    | Node.sparse cs target' =>
      if c ∈ cs then
        let_fun isLt := ⋯;
        let currentSave := saveSlots.get ↑target ⋯;
        exploreεClosure nfa pos next currentSave none saveSlots ⟨target', isLt⟩ #[]
      else (none, next, saveSlots)
    | x => (none, next, saveSlots)) =
    (matched', next', saveSlots')
hnotDone : ∀ i ∈ next, nfa[i] ≠ Node.done
⊢ (∃ i ∈ next', nfa[i] = Node.done) ↔ matched'.isSome = true
Theorem: Regex.VM.stepChar_mem_done_iff
Proof state before:
case h_2
nfa : NFA
c : Char
pos : String.Pos
next : SparseSet nfa.nodes.size
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
target : Fin nfa.nodes.size
matched' : Option (Array (Option String.Pos))
next' : SparseSet nfa.nodes.size
saveSlots' : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
hnotDone : ∀ i ∈ next, nfa[i] ≠ Node.done
cs✝ : Data.Classes
target'✝ : ℕ
heq✝ : nfa[target] = Node.sparse cs✝ target'✝
h :
  (if c ∈ cs✝ then
      let_fun isLt := ⋯;
      let currentSave := saveSlots.get ↑target ⋯;
      exploreεClosure nfa pos next currentSave none saveSlots ⟨target'✝, isLt⟩ #[]
    else (none, next, saveSlots)) =
    (matched', next', saveSlots')
⊢ (∃ i ∈ next', nfa[i] = Node.done) ↔ matched'.isSome = true

case h_3
nfa : NFA
c : Char
pos : String.Pos
next : SparseSet nfa.nodes.size
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
target : Fin nfa.nodes.size
matched' : Option (Array (Option String.Pos))
next' : SparseSet nfa.nodes.size
saveSlots' : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
hnotDone : ∀ i ∈ next, nfa[i] ≠ Node.done
x✝¹ : ∀ (c' : Char) (target' : ℕ), nfa[target] = Node.char c' target' → False
x✝ : ∀ (cs : Data.Classes) (target' : ℕ), nfa[target] = Node.sparse cs target' → False
h : (none, next, saveSlots) = (matched', next', saveSlots')
⊢ (∃ i ∈ next', nfa[i] = Node.done) ↔ matched'.isSome = true
Tactic:
next =>
  split at h
  next =>
    simp at h
    exact exploreεClosure_mem_done_iff h (by simp; exact hnotDone)
  next =>
    simp at h
    simp [←h]
    exact hnotDone
Proof state after:
case h_3
nfa : NFA
c : Char
pos : String.Pos
next : SparseSet nfa.nodes.size
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
target : Fin nfa.nodes.size
matched' : Option (Array (Option String.Pos))
next' : SparseSet nfa.nodes.size
saveSlots' : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
hnotDone : ∀ i ∈ next, nfa[i] ≠ Node.done
x✝¹ : ∀ (c' : Char) (target' : ℕ), nfa[target] = Node.char c' target' → False
x✝ : ∀ (cs : Data.Classes) (target' : ℕ), nfa[target] = Node.sparse cs target' → False
h : (none, next, saveSlots) = (matched', next', saveSlots')
⊢ (∃ i ∈ next', nfa[i] = Node.done) ↔ matched'.isSome = true
Theorem: Regex.VM.stepChar_mem_done_iff
Proof state before:
case h_3
nfa : NFA
c : Char
pos : String.Pos
next : SparseSet nfa.nodes.size
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
target : Fin nfa.nodes.size
matched' : Option (Array (Option String.Pos))
next' : SparseSet nfa.nodes.size
saveSlots' : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
hnotDone : ∀ i ∈ next, nfa[i] ≠ Node.done
x✝¹ : ∀ (c' : Char) (target' : ℕ), nfa[target] = Node.char c' target' → False
x✝ : ∀ (cs : Data.Classes) (target' : ℕ), nfa[target] = Node.sparse cs target' → False
h : (none, next, saveSlots) = (matched', next', saveSlots')
⊢ (∃ i ∈ next', nfa[i] = Node.done) ↔ matched'.isSome = true
Tactic:
next =>
  simp at h
  simp [←h]
  exact hnotDone
Proof state after:
no goals
Theorem: Regex.VM.stepChar_mem_done_iff
Proof state before:
nfa : NFA
c : Char
pos : String.Pos
next : SparseSet nfa.nodes.size
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
target : Fin nfa.nodes.size
matched' : Option (Array (Option String.Pos))
next' : SparseSet nfa.nodes.size
saveSlots' : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
hnotDone : ∀ i ∈ next, nfa[i] ≠ Node.done
c'✝ : Char
target'✝ : ℕ
heq✝ : nfa[target] = Node.char c'✝ target'✝
h :
  (if c = c'✝ then
      let_fun isLt := ⋯;
      let currentSave := saveSlots.get ↑target ⋯;
      exploreεClosure nfa pos next currentSave none saveSlots ⟨target'✝, isLt⟩ #[]
    else (none, next, saveSlots)) =
    (matched', next', saveSlots')
⊢ (∃ i ∈ next', nfa[i] = Node.done) ↔ matched'.isSome = true
Tactic:
split at h
Proof state after:
case inl
nfa : NFA
c : Char
pos : String.Pos
next : SparseSet nfa.nodes.size
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
target : Fin nfa.nodes.size
matched' : Option (Array (Option String.Pos))
next' : SparseSet nfa.nodes.size
saveSlots' : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
hnotDone : ∀ i ∈ next, nfa[i] ≠ Node.done
c'✝ : Char
target'✝ : ℕ
heq✝ : nfa[target] = Node.char c'✝ target'✝
h✝ : c = c'✝
h :
  (let_fun isLt := ⋯;
    let currentSave := saveSlots.get ↑target ⋯;
    exploreεClosure nfa pos next currentSave none saveSlots ⟨target'✝, isLt⟩ #[]) =
    (matched', next', saveSlots')
⊢ (∃ i ∈ next', nfa[i] = Node.done) ↔ matched'.isSome = true

case inr
nfa : NFA
c : Char
pos : String.Pos
next : SparseSet nfa.nodes.size
saveSlots : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
target : Fin nfa.nodes.size
matched' : Option (Array (Option String.Pos))
next' : SparseSet nfa.nodes.size
saveSlots' : Data.Vec (Array (Option String.Pos)) nfa.nodes.size
hnotDone : ∀ i ∈ next, nfa[i] ≠ Node.done
c'✝ : Char
target'✝ : ℕ
heq✝ : nfa[target] = Node.char c'✝ target'✝
h✝ : ¬c = c'✝
h : (none, next, saveSlots) = (matched', next', saveSlots')
⊢ (∃ i ∈ next', nfa[i] = Node.done) ↔ matched'.isSome = true