∀ {α : Type u_1} {β : Type u_2} [inst : Monoid α] [inst_1 : Monoid β] {F : Type u_3} [inst_2 : EquivLike F α β]
  [MulEquivClass F α β] (f : F) {a b : α}, emultiplicity (f a) (f b) = emultiplicity a b