∀ {α : Type u} (β : Type v) [inst : AddGroup α] [inst_1 : AddMonoid β] [inst_2 : AddAction β α] (H : AddSubgroup α)
  [inst_3 : AddAction.QuotientAction β H],
  AddAction.quotient β H = { vadd := fun b => Quotient.map' (fun x => b +ᵥ x) ⋯, add_vadd := ⋯, zero_vadd := ⋯ }