∀ {α : Type u_1} [inst : AddGroup α] {ι : Type u_2} (f : ι → AddSubgroup α) (a₁ a₂ : α),
  (fun q i => AddSubgroup.quotientMapOfLE ⋯ q) (Quotient.mk'' a₁) =
      (fun q i => AddSubgroup.quotientMapOfLE ⋯ q) (Quotient.mk'' a₂) →
    Quotient.mk'' a₁ = Quotient.mk'' a₂