Section IdentityMorphism.
Variable gT : finGroupType.
Implicit Types A B : {set gT}.
Implicit Type G : {group gT}.
Definition idm of {set gT} := fun x : gT => x : FinGroup.sort gT.
Canonical comp_morphism := Morphism comp_morphM.
Canonical factm_morphism := Morphism factm_morphM.

Lemma morphim_ifactm (A : {set gT}) :
A \subset D -> ifactm @* (f @* A) = g @* A.