∀ {F : Type v'} {R : Type u} {A : Type v} {B : Type w} [inst : CommSemiring R] [inst_1 : NonUnitalNonAssocSemiring A]
  [inst_2 : NonUnitalNonAssocSemiring B] [inst_3 : Module R A] [inst_4 : Module R B] [inst_5 : FunLike F A B]
  [inst_6 : NonUnitalAlgHomClass F R A B] {S : NonUnitalSubalgebra R A} {f : F} {U : NonUnitalSubalgebra R B},
  NonUnitalSubalgebra.map f S ≤ U ↔ S ≤ NonUnitalSubalgebra.comap f U