∀ {α : Type u_1} [inst : Group α] (s : Subgroup α) (t : Set (α ⧸ s)) (x : ↑(QuotientGroup.mk ⁻¹' t)),
  ⟨Quotient.out ↑(⟨(Quotient.out ↑↑x)⁻¹ * ↑x, ⋯⟩, ⟨↑↑x, ⋯⟩).2 * ↑(⟨(Quotient.out ↑↑x)⁻¹ * ↑x, ⋯⟩, ⟨↑↑x, ⋯⟩).1, ⋯⟩ = x