-- Lean 4 proof step from Mathlib.Data.WSeq.Defs (goal)
Goal:
α : Type u
s_1 : WSeq α
s1 s2 : Computation ℕ
l : List α
s : WSeq α
h :
  s1 =
      Computation.corec
        (fun (x : ℕ × WSeq α) ↦
          match (motive := ℕ × WSeq α → ℕ ⊕ ℕ × WSeq α) x with
          | (n, s) =>
            match (motive := Option (Seq1 (Option α)) → ℕ ⊕ ℕ × WSeq α) Seq.destruct s with
            | none => Sum.inl n
            | some (none, s') => Sum.inr (n, s')
            | some (some val, s') => Sum.inr (n + 1, s'))
        (l.length, s) ∧
    s2 =
      Computation.map (α := List α) List.length
        (Computation.corec
          (fun (x : List α × WSeq α) ↦
            match (motive := List α × WSeq α → List α ⊕ List α × WSeq α) x with
            | (l, s) =>
              match (motive := Option (Seq1 (Option α)) → List α ⊕ List α × WSeq α) 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))
⊢ Computation.BisimO
    (fun (c1 c2 : Computation ℕ) ↦
      ∃ (l : List α) (s : WSeq α),
        c1 =
            Computation.corec
              (fun (x : ℕ × WSeq α) ↦
                match (motive := ℕ × WSeq α → ℕ ⊕ ℕ × WSeq α) x with
                | (n, s) =>
                  match (motive := Option (Seq1 (Option α)) → ℕ ⊕ ℕ × WSeq α) Seq.destruct s with
                  | none => Sum.inl n
                  | some (none, s') => Sum.inr (n, s')
                  | some (some val, s') => Sum.inr (n + 1, s'))
              (l.length, s) ∧
          c2 =
            Computation.map (α := List α) List.length
              (Computation.corec
                (fun (x : List α × WSeq α) ↦
                  match (motive := List α × WSeq α → List α ⊕ List α × WSeq α) x with
                  | (l, s) =>
                    match (motive := Option (Seq1 (Option α)) → List α ⊕ List α × WSeq α) 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)))
    s1.destruct s2.destruct
have rw : Computation.BisimO
  (fun (c1 c2 : Computation ℕ) ↦
    ∃ (l : List α) (s : WSeq α),
      c1 =
          Computation.corec
            (fun (x : ℕ × WSeq α) ↦
              match (motive := ℕ × WSeq α → ℕ ⊕ ℕ × WSeq α) x with
              | (n, s) =>
                match (motive := Option (Seq1 (Option α)) → ℕ ⊕ ℕ × WSeq α) Seq.destruct s with
                | none => Sum.inl n
                | some (none, s') => Sum.inr (n, s')
                | some (some val, s') => Sum.inr (n + 1, s'))
            (l.length, s) ∧
        c2 =
          Computation.map (α := List α) List.length
            (Computation.corec
              (fun (x : List α × WSeq α) ↦
                match (motive := List α × WSeq α → List α ⊕ List α × WSeq α) x with
                | (l, s) =>
                  match (motive := Option (Seq1 (Option α)) → List α ⊕ List α × WSeq α) 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)))
  (Computation.destruct
    (Computation.corec
      (fun (x : ℕ × WSeq α) ↦
        match (motive := ℕ × WSeq α → ℕ ⊕ ℕ × WSeq α) x with
        | (n, s) =>
          match (motive := Option (Seq1 (Option α)) → ℕ ⊕ ℕ × WSeq α) Seq.destruct s with
          | none => Sum.inl n
          | some (none, s') => Sum.inr (n, s')
          | some (some val, s') => Sum.inr (n + 1, s'))
      (l.length, s)))
  (Computation.map (α := List α) List.length
      (Computation.corec
        (fun (x : List α × WSeq α) ↦
          match (motive := List α × WSeq α → List α ⊕ List α × WSeq α) x with
          | (l, s) =>
            match (motive := Option (Seq1 (Option α)) → List α ⊕ List α × WSeq α) 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))).destruct
Tactic: rw [h.left, h.right]