∀ {α : Type u_1} {β : Type u_2} [inst : Group β] (f : α → β) (a b : FreeGroup α),
  Quot.lift (FreeGroup.Lift.aux f) ⋯ (a * b) =
    Quot.lift (FreeGroup.Lift.aux f) ⋯ a * Quot.lift (FreeGroup.Lift.aux f) ⋯ b