∀ {α : Type u_1} [inst : AddGroup α] (s : AddSubgroup α) (t : Set (α ⧸ s)) (x : ↥s × ↑t),
  (⟨-Quotient.out ↑↑⟨Quotient.out ↑x.2 + ↑x.1, ⋯⟩ + ↑⟨Quotient.out ↑x.2 + ↑x.1, ⋯⟩, ⋯⟩,
      ⟨↑↑⟨Quotient.out ↑x.2 + ↑x.1, ⋯⟩, ⋯⟩) =
    x