theorem terminates_parallel {S : WSeq (Computation α)} {c} (h : c ∈ S) [T : Terminates c] :
    Terminates (parallel S) := by
  suffices
    ∀ (n) (l : List (Computation α)) (S c),
      c ∈ l ∨ some (some c) = Seq.get? S n → Terminates c → Terminates (corec parallel.aux1 (l, S))
    from
    let ⟨n, h⟩ := h
    this n [] S c (Or.inr h) T
  intro n; induction' n with n IH <;> intro l S c o T
  · cases' o with a a
    · exact terminates_parallel.aux a T
    have H : Seq.destruct S = some (some c, _) := by
      dsimp [Seq.destruct, (· <$> ·)]
      rw [← a]
      simp
      rfl
    induction' h : parallel.aux2 l with a l' <;> have C : corec parallel.aux1 (l, S) = _
    · -- Porting note: To adjust RHS of `C`, these lines are changed.
      apply destruct_eq_pure
      rw [corec_eq, parallel.aux1]
      dsimp only []
      rw [h]
      simp only [rmap]
      rfl
    · rw [C]
      skip
      infer_instance
    · apply destruct_eq_think
      simp only [corec_eq, rmap, parallel.aux1._eq_1]
      rw [h, H]
    · rw [C]
      refine @Computation.think_terminates _ _ ?_
      apply terminates_parallel.aux _ T
      simp
  · cases' o with a a
    · exact terminates_parallel.aux a T
    induction' h : parallel.aux2 l with a l' <;> have C : corec parallel.aux1 (l, S) = _
    · -- Porting note: To adjust RHS of `C`, these lines are changed.
      apply destruct_eq_pure
      rw [corec_eq, parallel.aux1]
      dsimp only []
      rw [h]
      simp only [rmap]
      

Proof state:
case C.a
α : Type u
β : Type v
S✝ : WSeq (Computation α)
c✝ : Computation α
h✝ : c✝ ∈ S✝
T✝ : Terminates c✝
n : ℕ
IH :
  ∀ (l : List (Computation α)) (S : Stream'.Seq (Option (Computation α))) (c : Computation α),
    c ∈ l ∨ some (some c) = Seq.get? S n → Terminates c → Terminates (corec parallel.aux1 (l, S))
l : List (Computation α)
S : Stream'.Seq (Option (Computation α))
c : Computation α
T : Terminates c
a✝ : some (some c) = Seq.get? S (Nat.succ n)
a : α
h : parallel.aux2 l = Sum.inl a
⊢ Sum.inl a = Sum.inl ?C.a
case C.a
α : Type u
β : Type v
S✝ : WSeq (Computation α)
c✝ : Computation α
h✝ : c✝ ∈ S✝
T✝ : Terminates c✝
n : ℕ
IH :
  ∀ (l : List (Computation α)) (S : Stream'.Seq (Option (Computation α))) (c : Computation α),
    c ∈ l ∨ some (some c) = Seq.get? S n → Terminates c → Terminates (corec parallel.aux1 (l, S))
l : List (Computation α)
S : Stream'.Seq (Option (Computation α))
c : Computation α
T : Terminates c
a✝ : some (some c) = Seq.get? S (Nat.succ n)
a : α
h : parallel.aux2 l = Sum.inl a
⊢ α
case C.a
α : Type u
β : Type v
S✝ : WSeq (Computation α)
c✝ : Computation α
h✝ : c✝ ∈ S✝
T✝ : Terminates c✝
n : ℕ
IH :
  ∀ (l : List (Computation α)) (S : Stream'.Seq (Option (Computation α))) (c : Computation α),
    c ∈ l ∨ some (some c) = Seq.get? S n → Terminates c → Terminates (corec parallel.aux1 (l, S))
l : List (Computation α)
S : Stream'.Seq (Option (Computation α))
c : Computation α
T : Terminates c
a✝ : some (some c) = Seq.get? S (Nat.succ n)
a : α
h : parallel.aux2 l = Sum.inl a
⊢ α
case C.a
α : Type u
β : Type v
S✝ : WSeq (Computation α)
c✝ : Computation α
h✝ : c✝ ∈ S✝
T✝ : Terminates c✝
n : ℕ
IH :
  ∀ (l : List (Computation α)) (S : Stream'.Seq (Option (Computation α))) (c : Computation α),
    c ∈ l ∨ some (some c) = Seq.get? S n → Terminates c → Terminates (corec parallel.aux1 (l, S))
l : List (Computation α)
S : Stream'.Seq (Option (Computation α))
c : Computation α
T : Terminates c
a✝ : some (some c) = Seq.get? S (Nat.succ n)
a : α
h : parallel.aux2 l = Sum.inl a
⊢ α
case C.a
α : Type u
β : Type v
S✝ : WSeq (Computation α)
c✝ : Computation α
h✝ : c✝ ∈ S✝
T✝ : Terminates c✝
n : ℕ
IH :
  ∀ (l : List (Computation α)) (S : Stream'.Seq (Option (Computation α))) (c : Computation α),
    c ∈ l ∨ some (some c) = Seq.get? S n → Terminates c → Terminates (corec parallel.aux1 (l, S))
l : List (Computation α)
S : Stream'.Seq (Option (Computation α))
c : Computation α
T : Terminates c
a✝ : some (some c) = Seq.get? S (Nat.succ n)
a : α
h : parallel.aux2 l = Sum.inl a
⊢ α

Next tactic:
rfl