∀ {R : Type u_1} [inst : CommRing R] {S : Submonoid R} {P : Type u_2} [inst_1 : CommRing P] [inst_2 : Algebra R P]
  {P' : Type u_3} [inst_3 : CommRing P'] [inst_4 : Algebra R P'] (g : P ≃ₐ[R] P') (I : FractionalIdeal S P),
  (FractionalIdeal.mapEquiv g) I = FractionalIdeal.map (↑g) I