∀ {F : Type u_2} {R : Type u_4} {A : Type u_3} {B : Type u_1} [inst : CommSemiring R] [inst_1 : NonUnitalSemiring A]
  [inst_2 : Module R A] [inst_3 : Star A] [inst_4 : NonUnitalSemiring B] [inst_5 : Module R B] [inst_6 : Star B]
  [inst_7 : FunLike F A B] [inst_8 : NonUnitalAlgHomClass F R A B] [inst_9 : StarHomClass F A B] {g : B → A} {f : F},
  Function.LeftInverse g ⇑f → ∀ (x : ↥(NonUnitalStarAlgHom.range f)) (x' : A), f x' = ↑x → f (g ↑x) = ↑x