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