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

(* Specifications: *)
Lemma cfConjgMorph (phi : 'CF(f @* H)) y :
y \in D -> y \in 'N(H) -> (cfMorph phi ^ y)%CF = cfMorph (phi ^ f y).
Lemma inertia_morph_pre (phi : 'CF(f @* H)) :
H <| G -> G \subset D -> 'I_G[cfMorph phi] = G :&: f @*^-1 'I_(f @* G)[phi].
Lemma inertia_morph_im (phi : 'CF(f @* H)) :
H <| G -> G \subset D -> f @* 'I_G[cfMorph phi] = 'I_(f @* G)[phi].