proposition: Lemma cfBigdprod_Res_lin chi : chi \is a linear_char -> cfBigdprod defG (fun i => 'Res[A i] chi) = chi.
proof: Proof. move=> Lchi; apply/cfun_inP=> _ /(mem_bigdprod defG)[x [Ax -> _]]. rewrite (lin_char_prod Lchi) ?cfBigdprodE // => [|i Pi]; last first. by rewrite (subsetP (sAG Pi)) ?Ax. by apply/eq_bigr=> i Pi; rewrite cfResE ?sAG ?Ax. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype choice ssrnat seq) mathcomp(path div fintype tuple finfun bigop prime order) mathcomp(ssralg poly finset gproduct fingroup morphism) mathcomp(perm automorphism quotient finalg action zmodp) mathcomp(commutator cyclic center pgroup nilpotent sylow) mathcomp(abelian matrix mxalgebra mxpoly mxrepresentation) mathcomp(vector ssrnum algC classfun archimedean)