cases path with
| base _ =>
  simp [*]
  exact .char c
| step step rest =>
  cases step with
  | charStep _ _ step =>
    simp [NFA.Node.charStep] at step
    have := le_of_pathIn_left rest
    exact absurd next.isLt (Nat.not_lt_of_ge (step.right ▸ this))
  | εStep _ _ step => simp [NFA.Node.εStep] at step
case intro.intro.intro.intro.intro.charStep
c : Char
nfa : NFA
next : Fin nfa.nodes.size
result : { nfa' // nfa.nodes.size < nfa'.nodes.size }
cs : List Char
eq✝ : nfa.pushRegex next (Expr.char c) = result
eq : result = nfa.pushNode (Node.char c ↑next) ⋯
i : ℕ
w✝ : List Char
c✝ : Char
h₂✝ : i < (↑(nfa.pushNode (Node.char c ↑next) ⋯)).nodes.size
left✝ : cs = w✝ ++ [c✝]
path : (↑(nfa.pushNode (Node.char c ↑next) ⋯)).pathIn nfa.nodes.size nfa.nodes.size nfa.nodes.size w✝
this✝ this h₁✝ : True
step✝ : c✝ = c
⊢ Expr.matches cs (Expr.char c)
no goals