intro ⟨r, q', HQ', h⟩
case some.mpr
α qs : Type
M : DFA α qs
w : Word { x // x ∈ M.Z }
q : { x // x ∈ M.Q }
x : { x // x ∈ M.Z }
xs : List { x // x ∈ M.Z }
q' : { x // x ∈ M.Q }
hq' : M.δ (q, x) = some q'
⊢ (∃ x_1 z,
      ∃ (H : z ∈ M.δ (q, x)),
        (do
            let r' ← constrRun xs z
            some (NFA.Run.step q ⋯ r' ⋯)) =
          some x_1) →
    Option.isSome (del_star_curried M (x :: xs) q) = true
case some.mpr
α qs : Type
M : DFA α qs
w : Word { x // x ∈ M.Z }
q : { x // x ∈ M.Q }
x : { x // x ∈ M.Z }
xs : List { x // x ∈ M.Z }
q'✝ : { x // x ∈ M.Q }
hq' : M.δ (q, x) = some q'✝
r : NFA.Run (toNFA M) q (x :: xs)
q' : { x // x ∈ M.Q }
HQ' : q' ∈ M.δ (q, x)
h :
  (do
      let r' ← constrRun xs q'
      some (NFA.Run.step q ⋯ r' ⋯)) =
    some r
⊢ Option.isSome (del_star_curried M (x :: xs) q) = true