proposition: Lemma Dade_restrictionE B x : B \in calP -> 'aa_B x = aa (remgr 'H(B) 'N_L(B) x) *+ (x \in 'M(B)).
proof: Proof. move=> calP_B; have /sdprodP[_ /= defM _ _] := Dade_set_sdprod calP_B. have [Mx | /cfun0-> //] := boolP (x \in 'M(B)). rewrite mulrb cfMorphE // morphimEdom /= /Dade_restrm calP_B. rewrite cfResE ?imset_f {x Mx}//= -defM. by apply/subsetP=> _ /imsetP[x /mem_remgr/setIP[Lx _] ->]. Qed.
imports: HB(structures) mathcomp.ssreflect.ssreflect mathcomp(ssrbool ssrfun eqtype ssrnat seq path div choice) mathcomp(fintype tuple finfun bigop prime ssralg poly finset center) mathcomp(fingroup morphism perm automorphism quotient action zmodp) mathcomp(gfunctor gproduct cyclic pgroup frobenius ssrnum) mathcomp(matrix mxalgebra mxrepresentation vector algC classfun character) mathcomp(inertia vcharacter) odd_order(PFsection1)