Section ConjMorph.
Variables (aT rT : finGroupType) (D G H : {group aT}) (f : {morphism D >-> rT}).

Lemma inertia_morph_im (phi : 'CF(f @* H)) :
H <| G -> G \subset D -> f @* 'I_G[cfMorph phi] = 'I_(f @* G)[phi].