End InjmChar.
Section CharInjm.
Variables (aT rT : finGroupType) (D : {group aT}) (f : {morphism D >-> rT}).
Hypothesis injf : 'injm f.

Lemma char_injm (G H : {group aT}) :
G \subset D -> H \subset D -> (f @* H \char f @* G) = (H \char G).