proposition: Lemma invDade_cfun1 : 1^\rho = '1_A.
proof: Proof. apply/cfunP=> x; rewrite cfuniE // cfunElock mulrb; case: ifP => //= Ax. apply: canLR (mulKf (neq0CG _)) _; rewrite mulr1 -sumr_const. apply: eq_bigr => u Hu; rewrite cfun1E (subsetP (subsetIl G 'C[x])) //. have /sdprodP[_ <- _ _] := Dade_sdprod ddA Ax. by rewrite mem_mulg // inE cent1id (subsetP sAL). Qed.
imports: HB(structures) mathcomp.ssreflect.ssreflect mathcomp(ssrbool ssrfun eqtype ssrnat seq path div choice fintype) mathcomp(tuple finfun bigop order prime ssralg poly finset center) mathcomp(fingroup morphism perm automorphism quotient action zmodp) mathcomp(gfunctor gproduct cyclic pgroup commutator nilpotent frobenius) mathcomp(matrix mxalgebra mxrepresentation) odd_order(BGsection3) mathcomp(vector ssrnum algC classfun character inertia vcharacter) odd_order(PFsection1 PFsection2 PFsection4 PFsection5 PFsection6)