End ConjQuotient.
Section InertiaSdprod.
Variables (gT : finGroupType) (K H G : {group gT}).
Hypothesis defG : K ><| H = G.

(* Specifications: *)
Lemma cfConjgSdprod phi y :
y \in 'N(K) -> y \in 'N(H) ->
(cfSdprod defG phi ^ y = cfSdprod defG (phi ^ y))%CF.
Lemma inertia_sdprod (L : {group gT}) phi :
L \subset 'N(K) -> L \subset 'N(H) -> 'I_L[cfSdprod defG phi] = 'I_L[phi].