cases x with | mk nx kx =>
cases y with | mk ny ky =>
let f i : Quot (r i) → Quot (r' i) :=
  by
    apply Quot.lift (Quot.lift (Quot.mk (r' _)) _) _
    . intro a b h₃
      apply Quot.sound
      simp only
      rw [Quot.sound h₃]
      apply h₀
    . intro x; apply Quot.inductionOn (motive := _) x; clear x
      intro x y; apply Quot.inductionOn (motive := _) y; clear y
      intro y h
      apply Quot.sound
      apply h
have : ∀ i, f i ∘ Quot.mk (r _) ∘ Quot.mk (congr F _) = Quot.mk (r' _) := by intro i; rfl
conv =>
  congr
  . rhs
    lhs
    intro i
    rw [←this]
    rfl
  . rhs
    lhs
    intro i
    rw [←this]
rw [IContainer.Map_spec, IContainer.Map_spec, IContainer.Map_spec, IContainer.Map_spec]
rw [inst.abs_imap, inst.abs_imap, inst.abs_imap, inst.abs_imap, inst.abs_imap, inst.abs_imap, h₂]
case a.a
I : Type u₁
F : (I → Type u₁) → I → Type u₁
inst : IQPF F
r : (i : I) → M F i → M F i → Prop
h₀ : ∀ (i : I) (x : M F i), r i x x
h₁ :
  ∀ (i : I) (x y : M F i),
    r i x y → IFunctor.imap (fun i => Quot.mk (r i)) (destruct x) = IFunctor.imap (fun i => Quot.mk (r i)) (destruct y)
i✝ : I
x✝¹ y✝¹ : IContainer.M (C F) i✝
r' : (i : I) → IContainer.M (C F) i → IContainer.M (C F) i → Prop :=
  fun i x y => r i (Quot.mk (congr F i) x) (Quot.mk (congr F i) y)
i : I
x✝ y✝ : IContainer.M (C F) i
h₂✝ : r' i x✝ y✝
x y : IContainer.Obj (C F) (IContainer.M (C F)) i
h₂ :
  IFunctor.imap (fun i => Quot.mk (r i)) (IFunctor.imap (fun x x_1 => Quot.mk (congr F x) x_1) (abs x)) =
    IFunctor.imap (fun i => Quot.mk (r i)) (IFunctor.imap (fun x x_1 => Quot.mk (congr F x) x_1) (abs y))
⊢ abs (IContainer.Map (fun i => Quot.mk fun x y => r i (Quot.mk (congr F i) x) (Quot.mk (congr F i) y)) x) =
    abs (IContainer.Map (fun i => Quot.mk fun x y => r i (Quot.mk (congr F i) x) (Quot.mk (congr F i) y)) y)
no goals