simp [h₁, h₂] at step rest
nfa : NFA
i✝ l : ℕ
c : Char
start : ℕ
cs' : List Char
i j k : ℕ
cs₁ cs₂ : List Char
step : nfa.stepIn start i j cs₁
rest : nfa.pathIn start j k cs₂
ih :
  ∀ {cs : List Char},
    cs ++ [c] = cs₂ → ∃ j_1 k_1, nfa.pathIn start j j_1 cs ∧ k_1 ∈ nfa.charStep j_1 c ∧ k ∈ nfa.εClosure k_1
cs : List Char
h : cs ++ [c] = cs₁ ++ cs₂
h₁ : cs₁ = cs ++ [c]
h₂ : cs₂ = []
⊢ ∃ j k_1, nfa.pathIn start i j cs ∧ k_1 ∈ nfa.charStep j c ∧ k ∈ nfa.εClosure k_1
nfa : NFA
i✝ l : ℕ
c : Char
start : ℕ
cs' : List Char
i j k : ℕ
cs₁ cs₂ : List Char
ih :
  ∀ {cs : List Char},
    cs ++ [c] = cs₂ → ∃ j_1 k_1, nfa.pathIn start j j_1 cs ∧ k_1 ∈ nfa.charStep j_1 c ∧ k ∈ nfa.εClosure k_1
cs : List Char
h : cs ++ [c] = cs₁ ++ cs₂
h₁ : cs₁ = cs ++ [c]
h₂ : cs₂ = []
step : nfa.stepIn start i j (cs ++ [c])
rest : nfa.pathIn start j k []
⊢ ∃ j k_1, nfa.pathIn start i j cs ∧ k_1 ∈ nfa.charStep j c ∧ k ∈ nfa.εClosure k_1