internlm/Lean-Github huggingface dataset:
Theorem: Regex.VM.mem_stack_mem_εClosure
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
i : Fin nfa.nodes.size
hmem : StackEntry.explore i ∈ stack
hemp : ¬stack.isEmpty = true
h :
  (match stack.back' hemp 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.mem_stack_mem_εClosure
Proof state before:
case inl
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
i : Fin nfa.nodes.size
hmem✝ : StackEntry.explore i ∈ stack
hemp : ¬stack.isEmpty = true
h :
  (match stack.back' hemp 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
hmem : StackEntry.explore i ∈ stack.pop
⊢ i ∈ next'
Tactic:
split at h
Proof state after:
case inl.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
i : Fin nfa.nodes.size
hmem✝ : StackEntry.explore i ∈ stack
hemp : ¬stack.isEmpty = true
this : stack.pop.size < stack.size
hmem : StackEntry.explore i ∈ stack.pop
entry✝ : StackEntry nfa.nodes.size
target✝ : Fin nfa.nodes.size
heq✝ : stack.back' hemp = StackEntry.explore target✝
h : exploreεClosure nfa pos next currentSave matched saveSlots target✝ stack.pop = (matched', next', saveSlots')
⊢ i ∈ next'

case inl.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
i : Fin nfa.nodes.size
hmem✝ : StackEntry.explore i ∈ stack
hemp : ¬stack.isEmpty = true
this : stack.pop.size < stack.size
hmem : StackEntry.explore i ∈ stack.pop
entry✝ : StackEntry nfa.nodes.size
save✝ : Array (Option String.Pos)
heq✝ : stack.back' hemp = StackEntry.restore save✝
h : εClosure nfa pos next save✝ matched saveSlots stack.pop = (matched', next', saveSlots')
⊢ i ∈ next'
Theorem: Regex.VM.mem_stack_mem_εClosure
Proof state before:
case inl.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
i : Fin nfa.nodes.size
hmem✝ : StackEntry.explore i ∈ stack
hemp : ¬stack.isEmpty = true
this : stack.pop.size < stack.size
hmem : StackEntry.explore i ∈ stack.pop
entry✝ : StackEntry nfa.nodes.size
target✝ : Fin nfa.nodes.size
heq✝ : stack.back' hemp = StackEntry.explore target✝
h : exploreεClosure nfa pos next currentSave matched saveSlots target✝ stack.pop = (matched', next', saveSlots')
⊢ i ∈ next'

case inl.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
i : Fin nfa.nodes.size
hmem✝ : StackEntry.explore i ∈ stack
hemp : ¬stack.isEmpty = true
this : stack.pop.size < stack.size
hmem : StackEntry.explore i ∈ stack.pop
entry✝ : StackEntry nfa.nodes.size
save✝ : Array (Option String.Pos)
heq✝ : stack.back' hemp = StackEntry.restore save✝
h : εClosure nfa pos next save✝ matched saveSlots stack.pop = (matched', next', saveSlots')
⊢ i ∈ next'
Tactic:
next => exact mem_stack_mem_exploreεClosure h hmem
Proof state after:
case inl.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
i : Fin nfa.nodes.size
hmem✝ : StackEntry.explore i ∈ stack
hemp : ¬stack.isEmpty = true
this : stack.pop.size < stack.size
hmem : StackEntry.explore i ∈ stack.pop
entry✝ : StackEntry nfa.nodes.size
save✝ : Array (Option String.Pos)
heq✝ : stack.back' hemp = StackEntry.restore save✝
h : εClosure nfa pos next save✝ matched saveSlots stack.pop = (matched', next', saveSlots')
⊢ i ∈ next'
Theorem: Regex.VM.mem_stack_mem_εClosure
Proof state before:
case inl.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
i : Fin nfa.nodes.size
hmem✝ : StackEntry.explore i ∈ stack
hemp : ¬stack.isEmpty = true
this : stack.pop.size < stack.size
hmem : StackEntry.explore i ∈ stack.pop
entry✝ : StackEntry nfa.nodes.size
save✝ : Array (Option String.Pos)
heq✝ : stack.back' hemp = StackEntry.restore save✝
h : εClosure nfa pos next save✝ matched saveSlots stack.pop = (matched', next', saveSlots')
⊢ i ∈ next'
Tactic:
next => exact mem_stack_mem_εClosure h hmem
Proof state after:
no goals
Theorem: Regex.VM.mem_stack_mem_εClosure
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
i : Fin nfa.nodes.size
hmem✝ : StackEntry.explore i ∈ stack
hemp : ¬stack.isEmpty = true
this : stack.pop.size < stack.size
hmem : StackEntry.explore i ∈ stack.pop
entry✝ : StackEntry nfa.nodes.size
target✝ : Fin nfa.nodes.size
heq✝ : stack.back' hemp = StackEntry.explore target✝
h : exploreεClosure nfa pos next currentSave matched saveSlots target✝ stack.pop = (matched', next', saveSlots')
⊢ i ∈ next'
Tactic:
exact mem_stack_mem_exploreεClosure h hmem
Proof state after:
no goals
Theorem: Regex.VM.mem_stack_mem_εClosure
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
i : Fin nfa.nodes.size
hmem✝ : StackEntry.explore i ∈ stack
hemp : ¬stack.isEmpty = true
this : stack.pop.size < stack.size
hmem : StackEntry.explore i ∈ stack.pop
entry✝ : StackEntry nfa.nodes.size
save✝ : Array (Option String.Pos)
heq✝ : stack.back' hemp = StackEntry.restore save✝
h : εClosure nfa pos next save✝ matched saveSlots stack.pop = (matched', next', saveSlots')
⊢ i ∈ next'
Tactic:
exact mem_stack_mem_εClosure h hmem
Proof state after:
no goals
Theorem: Regex.VM.mem_stack_mem_εClosure
Proof state before:
case inr
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
i : Fin nfa.nodes.size
hmem : StackEntry.explore i ∈ stack
hemp : ¬stack.isEmpty = true
h :
  (match stack.back' hemp 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
heq : StackEntry.explore i = stack.back' hemp
⊢ i ∈ next'
Tactic:
split at h
Proof state after:
case inr.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
i : Fin nfa.nodes.size
hmem : StackEntry.explore i ∈ stack
hemp : ¬stack.isEmpty = true
this : stack.pop.size < stack.size
heq : StackEntry.explore i = stack.back' hemp
entry✝ : StackEntry nfa.nodes.size
target✝ : Fin nfa.nodes.size
heq✝ : stack.back' hemp = StackEntry.explore target✝
h : exploreεClosure nfa pos next currentSave matched saveSlots target✝ stack.pop = (matched', next', saveSlots')
⊢ i ∈ next'

case inr.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
i : Fin nfa.nodes.size
hmem : StackEntry.explore i ∈ stack
hemp : ¬stack.isEmpty = true
this : stack.pop.size < stack.size
heq : StackEntry.explore i = stack.back' hemp
entry✝ : StackEntry nfa.nodes.size
save✝ : Array (Option String.Pos)
heq✝ : stack.back' hemp = StackEntry.restore save✝
h : εClosure nfa pos next save✝ matched saveSlots stack.pop = (matched', next', saveSlots')
⊢ i ∈ next'
Theorem: Regex.VM.mem_stack_mem_εClosure
Proof state before:
case inr.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
i : Fin nfa.nodes.size
hmem : StackEntry.explore i ∈ stack
hemp : ¬stack.isEmpty = true
this : stack.pop.size < stack.size
heq : StackEntry.explore i = stack.back' hemp
entry✝ : StackEntry nfa.nodes.size
target✝ : Fin nfa.nodes.size
heq✝ : stack.back' hemp = StackEntry.explore target✝
h : exploreεClosure nfa pos next currentSave matched saveSlots target✝ stack.pop = (matched', next', saveSlots')
⊢ i ∈ next'

case inr.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
i : Fin nfa.nodes.size
hmem : StackEntry.explore i ∈ stack
hemp : ¬stack.isEmpty = true
this : stack.pop.size < stack.size
heq : StackEntry.explore i = stack.back' hemp
entry✝ : StackEntry nfa.nodes.size
save✝ : Array (Option String.Pos)
heq✝ : stack.back' hemp = StackEntry.restore save✝
h : εClosure nfa pos next save✝ matched saveSlots stack.pop = (matched', next', saveSlots')
⊢ i ∈ next'
Tactic:
next target heq' =>
  rw [heq'] at heq
  have : target = i := by
    simp at heq
    rw [heq]
  rw [this] at h
  exact target_mem_exploreεClosure h
Proof state after:
case inr.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
i : Fin nfa.nodes.size
hmem : StackEntry.explore i ∈ stack
hemp : ¬stack.isEmpty = true
this : stack.pop.size < stack.size
heq : StackEntry.explore i = stack.back' hemp
entry✝ : StackEntry nfa.nodes.size
save✝ : Array (Option String.Pos)
heq✝ : stack.back' hemp = StackEntry.restore save✝
h : εClosure nfa pos next save✝ matched saveSlots stack.pop = (matched', next', saveSlots')
⊢ i ∈ next'
Theorem: Regex.VM.mem_stack_mem_εClosure
Proof state before:
case inr.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
i : Fin nfa.nodes.size
hmem : StackEntry.explore i ∈ stack
hemp : ¬stack.isEmpty = true
this : stack.pop.size < stack.size
heq : StackEntry.explore i = stack.back' hemp
entry✝ : StackEntry nfa.nodes.size
save✝ : Array (Option String.Pos)
heq✝ : stack.back' hemp = StackEntry.restore save✝
h : εClosure nfa pos next save✝ matched saveSlots stack.pop = (matched', next', saveSlots')
⊢ i ∈ next'
Tactic:
next _ heq' =>
  rw [heq'] at heq
  contradiction
Proof state after:
no goals
Theorem: Regex.VM.mem_stack_mem_εClosure
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
i : Fin nfa.nodes.size
hmem : StackEntry.explore i ∈ stack
hemp : ¬stack.isEmpty = true
this : stack.pop.size < stack.size
heq : StackEntry.explore i = stack.back' hemp
entry✝ : StackEntry nfa.nodes.size
target : Fin nfa.nodes.size
heq' : stack.back' hemp = StackEntry.explore target
h : exploreεClosure nfa pos next currentSave matched saveSlots target stack.pop = (matched', next', saveSlots')
⊢ i ∈ next'
Tactic:
rw [heq'] at heq
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
i : Fin nfa.nodes.size
hmem : StackEntry.explore i ∈ stack
hemp : ¬stack.isEmpty = true
this : stack.pop.size < stack.size
entry✝ : StackEntry nfa.nodes.size
target : Fin nfa.nodes.size
heq : StackEntry.explore i = StackEntry.explore target
heq' : stack.back' hemp = StackEntry.explore target
h : exploreεClosure nfa pos next currentSave matched saveSlots target stack.pop = (matched', next', saveSlots')
⊢ i ∈ next'
Theorem: Regex.VM.mem_stack_mem_εClosure
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
i : Fin nfa.nodes.size
hmem : StackEntry.explore i ∈ stack
hemp : ¬stack.isEmpty = true
this : stack.pop.size < stack.size
entry✝ : StackEntry nfa.nodes.size
target : Fin nfa.nodes.size
heq : StackEntry.explore i = StackEntry.explore target
heq' : stack.back' hemp = StackEntry.explore target
h : exploreεClosure nfa pos next currentSave matched saveSlots target stack.pop = (matched', next', saveSlots')
⊢ i ∈ next'
Tactic:
have : target = i := by
  simp at heq
  rw [heq]
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
i : Fin nfa.nodes.size
hmem : StackEntry.explore i ∈ stack
hemp : ¬stack.isEmpty = true
this✝ : stack.pop.size < stack.size
entry✝ : StackEntry nfa.nodes.size
target : Fin nfa.nodes.size
heq : StackEntry.explore i = StackEntry.explore target
heq' : stack.back' hemp = StackEntry.explore target
h : exploreεClosure nfa pos next currentSave matched saveSlots target stack.pop = (matched', next', saveSlots')
this : target = i
⊢ i ∈ next'
Theorem: Regex.VM.mem_stack_mem_εClosure
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
i : Fin nfa.nodes.size
hmem : StackEntry.explore i ∈ stack
hemp : ¬stack.isEmpty = true
this✝ : stack.pop.size < stack.size
entry✝ : StackEntry nfa.nodes.size
target : Fin nfa.nodes.size
heq : StackEntry.explore i = StackEntry.explore target
heq' : stack.back' hemp = StackEntry.explore target
h : exploreεClosure nfa pos next currentSave matched saveSlots target stack.pop = (matched', next', saveSlots')
this : target = i
⊢ i ∈ next'
Tactic:
rw [this] 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
i : Fin nfa.nodes.size
hmem : StackEntry.explore i ∈ stack
hemp : ¬stack.isEmpty = true
this✝ : stack.pop.size < stack.size
entry✝ : StackEntry nfa.nodes.size
target : Fin nfa.nodes.size
heq : StackEntry.explore i = StackEntry.explore target
heq' : stack.back' hemp = StackEntry.explore target
h : exploreεClosure nfa pos next currentSave matched saveSlots i stack.pop = (matched', next', saveSlots')
this : target = i
⊢ i ∈ next'
Theorem: Regex.VM.mem_stack_mem_εClosure
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
i : Fin nfa.nodes.size
hmem : StackEntry.explore i ∈ stack
hemp : ¬stack.isEmpty = true
this✝ : stack.pop.size < stack.size
entry✝ : StackEntry nfa.nodes.size
target : Fin nfa.nodes.size
heq : StackEntry.explore i = StackEntry.explore target
heq' : stack.back' hemp = StackEntry.explore target
h : exploreεClosure nfa pos next currentSave matched saveSlots i stack.pop = (matched', next', saveSlots')
this : target = i
⊢ i ∈ next'
Tactic:
exact target_mem_exploreεClosure h
Proof state after:
no goals
Theorem: Regex.VM.mem_stack_mem_εClosure
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
i : Fin nfa.nodes.size
hmem : StackEntry.explore i ∈ stack
hemp : ¬stack.isEmpty = true
this : stack.pop.size < stack.size
entry✝ : StackEntry nfa.nodes.size
target : Fin nfa.nodes.size
heq : StackEntry.explore i = StackEntry.explore target
heq' : stack.back' hemp = StackEntry.explore target
h : exploreεClosure nfa pos next currentSave matched saveSlots target stack.pop = (matched', next', saveSlots')
⊢ target = i
Tactic:
simp at heq
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
i : Fin nfa.nodes.size
hmem : StackEntry.explore i ∈ stack
hemp : ¬stack.isEmpty = true
this : stack.pop.size < stack.size
entry✝ : StackEntry nfa.nodes.size
target : Fin nfa.nodes.size
heq' : stack.back' hemp = StackEntry.explore target
h : exploreεClosure nfa pos next currentSave matched saveSlots target stack.pop = (matched', next', saveSlots')
heq : i = target
⊢ target = i
Theorem: Regex.VM.mem_stack_mem_εClosure
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
i : Fin nfa.nodes.size
hmem : StackEntry.explore i ∈ stack
hemp : ¬stack.isEmpty = true
this : stack.pop.size < stack.size
entry✝ : StackEntry nfa.nodes.size
target : Fin nfa.nodes.size
heq' : stack.back' hemp = StackEntry.explore target
h : exploreεClosure nfa pos next currentSave matched saveSlots target stack.pop = (matched', next', saveSlots')
heq : i = target
⊢ target = i
Tactic:
rw [heq]
Proof state after:
no goals