Local Axiom ConstructiveIndefiniteDescription_Type :
  forall T : Type, ConstructiveIndefiniteDescription_on T.Program Definition Epic_Monic_Factor_Monic : @Monic Type_Cat Image_of B :=
    {|
      mono_morphism := From_Image_forward;
      mono_morphism_monomorphic := fun T g h => _
    |}
  .ivial.
  Qed.

  Program Definition Epic_Monic_Factor_split_Epic :
    @is_split_Epic Type_Cat _ _ To_Image :=
    {|
      i

Theorem split_Epic_Monic_Factorization :