∀ {M : Type u_1} [inst : Monoid M] (S : Submonoid M) (x x_1 : ↥S.units),
  (match x * x_1 with
    | ⟨val, h⟩ =>
      { val := ⟨(Units.coeHom M) val, ⋯⟩, inv := ⟨(Units.coeHom M) val⁻¹, ⋯⟩, val_inv := ⋯, inv_val := ⋯ }) =
    match x * x_1 with
    | ⟨val, h⟩ => { val := ⟨(Units.coeHom M) val, ⋯⟩, inv := ⟨(Units.coeHom M) val⁻¹, ⋯⟩, val_inv := ⋯, inv_val := ⋯ }