proposition: Lemma cfdot_prTIred j1 j2 : '[mu_ j1, mu_ j2] = ((j1 == j2) * w1)%:R.
proof: Proof. rewrite cfdot_suml (eq_bigr _ (fun i _ => cfdot_prTIirr_red i _ _)) sumr_const. by rewrite mulrnA card_Iirr_cyclic. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrbool ssrfun eqtype ssrnat seq path div choice fintype) mathcomp(tuple finfun bigop order prime ssralg poly finset fingroup) mathcomp(morphism perm automorphism quotient action gfunctor gproduct) mathcomp(center commutator zmodp cyclic pgroup nilpotent hall frobenius) mathcomp(matrix mxalgebra mxrepresentation vector ssrnum algC classfun) mathcomp(character inertia vcharacter) odd_order(PFsection1 PFsection2 PFsection3)