theorem toList'_map (l : List α) (s : WSeq α) :
    Computation.corec (fun ⟨l, s⟩ =>
      match Seq.destruct s with
      | none => Sum.inl l.reverse
      | some (none, s') => Sum.inr (l, s')
      | some (some a, s') => Sum.inr (a :: l, s')) (l, s) = (l.reverse ++ ·) <$> toList s := by
  refine'
    Computation.eq_of_bisim
      (fun c1 c2 =>
        ∃ (l' : List α) (s : WSeq α),
          c1 = Computation.corec (fun ⟨l, s⟩ =>
            match Seq.destruct s with
            | none => Sum.inl l.reverse
            | some (none, s') => Sum.inr (l, s')
            | some (some a, s') => Sum.inr (a::l, s')) (l' ++ l, s) ∧
            c2 = Computation.map (l.reverse ++ ·) (Computation.corec (fun ⟨l, s⟩ =>
              match Seq.destruct s with
              | none => Sum.inl l.reverse
              | some (none, s') => Sum.inr (l, s')
              | some (some a, s') => Sum.inr (a::l, s')) (l', s)))
      _ ⟨[], s, rfl, rfl⟩
  intro s1 s2 h; rcases h with ⟨l', s, h⟩; rw [h.left, h.right]
  

Proof state:
case intro.intro
α : Type u
β : Type v
γ : Type w
l : List α
s✝ : WSeq α
s1 s2 : Computation (List α)
l' : List α
s : WSeq α
h :
  s1 =
      Computation.corec
        (fun x =>
          match x with
          | (l, s) =>
            match Seq.destruct s with
            | none => Sum.inl (List.reverse l)
            | some (none, s') => Sum.inr (l, s')
            | some (some a, s') => Sum.inr (a :: l, s'))
        (l' ++ l, s) ∧
    s2 =
      Computation.map (fun x => List.reverse l ++ x)
        (Computation.corec
          (fun x =>
            match x with
            | (l, s) =>
              match Seq.destruct s with
              | none => Sum.inl (List.reverse l)
              | some (none, s') => Sum.inr (l, s')
              | some (some a, s') => Sum.inr (a :: l, s'))
          (l', s))
⊢ Computation.BisimO
    (fun c1 c2 =>
      ∃ l' s,
        c1 =
            Computation.corec
              (fun x =>
                match x with
                | (l, s) =>
                  match Seq.destruct s with
                  | none => Sum.inl (List.reverse l)
                  | some (none, s') => Sum.inr (l, s')
                  | some (some a, s') => Sum.inr (a :: l, s'))
              (l' ++ l, s) ∧
          c2 =
            Computation.map (fun x => List.reverse l ++ x)
              (Computation.corec
                (fun x =>
                  match x with
                  | (l, s) =>
                    match Seq.destruct s with
                    | none => Sum.inl (List.reverse l)
                    | some (none, s') => Sum.inr (l, s')
                    | some (some a, s') => Sum.inr (a :: l, s'))
                (l', s)))
    (Computation.destruct
      (Computation.corec
        (fun x =>
          match x with
          | (l, s) =>
            match Seq.destruct s with
            | none => Sum.inl (List.reverse l)
            | some (none, s') => Sum.inr (l, s')
            | some (some a, s') => Sum.inr (a :: l, s'))
        (l' ++ l, s)))
    (Computation.destruct
      (Computation.map (fun x => List.reverse l ++ x)
        (Computation.corec
          (fun x =>
            match x with
            | (l, s) =>
              match Seq.destruct s with
              | none => Sum.inl (List.reverse l)
              | some (none, s') => Sum.inr (l, s')
              | some (some a, s') => Sum.inr (a :: l, s'))
          (l', s))))

Next tactic:
induction' s using WSeq.recOn with a s s