End ConjBig.
Section InertiaBig.
Variable L : {group gT}.
Hypothesis nAL : forall i, P i -> L \subset 'N(A i).

(* Specifications: *)
Lemma inertia_bigdprodi i (phi : 'CF(A i)) :
P i -> 'I_L[cfBigdprodi defG phi] = 'I_L[phi].
Lemma inertia_bigdprod phi (Phi := cfBigdprod defG phi) :
Phi 1%g != 0 -> 'I_L[Phi] = L :&: \bigcap_(i | P i) 'I_L[phi i].
Lemma inertia_bigdprod_irr Iphi (phi := fun i => 'chi_(Iphi i)) :
'I_L[cfBigdprod defG phi] = L :&: \bigcap_(i | P i) 'I_L[phi i].