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

Lemma inertia_bigdprod phi (Phi := cfBigdprod defG phi) :
Phi 1%g != 0 -> 'I_L[Phi] = L :&: \bigcap_(i | P i) 'I_L[phi i].