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 injm_proper A B :
A \subset G -> B \subset G -> (f @* A \proper f @* B) = (A \proper B).