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