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.

Lemma morphpre_comp (C : {set rT}) : gof @*^-1 C = f @*^-1 (g @*^-1 C).