apply Quot.sound
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✝¹ : I
x✝¹ y✝¹ : IContainer.M (C F) i✝¹
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✝
nx : IContainer.A (C F) i✝
kx : (y : IContainer.B (C F) i✝ nx) → IContainer.M (C F) (IContainer.N (C F) i✝ nx y)
ny : IContainer.A (C F) i✝
ky : (y : IContainer.B (C F) i✝ ny) → IContainer.M (C F) (IContainer.N (C F) i✝ ny y)
h₂ :
  IFunctor.imap (fun i => Quot.mk (r i))
      (IFunctor.imap (fun x x_1 => Quot.mk (congr F x) x_1) (abs { fst := nx, snd := kx })) =
    IFunctor.imap (fun i => Quot.mk (r i))
      (IFunctor.imap (fun x x_1 => Quot.mk (congr F x) x_1) (abs { fst := ny, snd := ky }))
i : I
x y : IContainer.M (C F) i
h : r i (Quot.mk (congr F i) x) (Quot.mk (congr F i) y)
⊢ Quot.lift (Quot.mk (r' i)) (_ : ∀ (a b : IContainer.M (C F) i), congr F i a b → Quot.mk (r' i) a = Quot.mk (r' i) b)
      (Quot.mk (congr F i) x) =
    Quot.lift (Quot.mk (r' i)) (_ : ∀ (a b : IContainer.M (C F) i), congr F i a b → Quot.mk (r' i) a = Quot.mk (r' i) b)
      (Quot.mk (congr F i) y)
case 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✝¹ : I
x✝¹ y✝¹ : IContainer.M (C F) i✝¹
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✝
nx : IContainer.A (C F) i✝
kx : (y : IContainer.B (C F) i✝ nx) → IContainer.M (C F) (IContainer.N (C F) i✝ nx y)
ny : IContainer.A (C F) i✝
ky : (y : IContainer.B (C F) i✝ ny) → IContainer.M (C F) (IContainer.N (C F) i✝ ny y)
h₂ :
  IFunctor.imap (fun i => Quot.mk (r i))
      (IFunctor.imap (fun x x_1 => Quot.mk (congr F x) x_1) (abs { fst := nx, snd := kx })) =
    IFunctor.imap (fun i => Quot.mk (r i))
      (IFunctor.imap (fun x x_1 => Quot.mk (congr F x) x_1) (abs { fst := ny, snd := ky }))
i : I
x y : IContainer.M (C F) i
h : r i (Quot.mk (congr F i) x) (Quot.mk (congr F i) y)
⊢ r' i x y