∀ {R : Type u_3} [inst : CommSemiring R] {M : Submonoid R} {S : Type u_2} [inst_1 : CommSemiring S]
  [inst_2 : Algebra R S] {P : Type u_1} [inst_3 : CommSemiring P] [inst_4 : IsLocalization M S] {g : R →+* P}
  (hg : ∀ (y : ↥M), IsUnit (g ↑y)),
  (↑((IsLocalization.toLocalizationMap M S).lift₀ g.toMonoidWithZeroHom hg)).toFun 1 = 1