∀ {α : Type u_1} {β : Type u_2} [inst : AddGroup α] [inst_1 : AddAction α β] (x : β)
  [inst_2 : AddAction.IsPretransitive α β] [inst_3 : IsCancelVAdd α β] (H : AddSubgroup α) (g : α ⧸ H),
  (fun q => Quotient.liftOn' q (fun y => ↑⋯.choose) ⋯) ((fun q => Quotient.liftOn' q (fun g => ⟦-g +ᵥ x⟧) ⋯) g) = g