Program Definition Monic_Iso_Monic_Factor_Iso :
(A ≃≃ Monic_Image_of ::> Type_Cat)%isomorphism
:=
Monic_is_split_Epic_Iso
_
_
(is_Monic_Monic Monic_From_Image_back_is_Monic)
(
@Build_is_split_Monic
(Type_Cat ^op)
_
_
Monic_To_Image
_
Monic_To_Image_form_split_epic
)
.

Theorem Monic_Iso_Monic_Factorization :
f = fun x =>  Monic_From_Image_forward (Monic_To_Image x).