∀ {M : Type u_1} [inst : AddCommMonoid M] {S : AddSubmonoid M} (x : M)
  (motive : x ∈ AddSubmonoid.map (AddEquiv.refl M).toAddMonoidHom S → Prop)
  (x_1 : x ∈ AddSubmonoid.map (AddEquiv.refl M).toAddMonoidHom S),
  (∀ (w : M) (hy : w ∈ ↑S) (h : (AddEquiv.refl M).toAddMonoidHom w = x), motive ⋯) → motive x_1