proposition: Lemma constt_ortho_char (phi psi : 'CF(G)) i j : phi \is a character -> psi \is a character -> i \in irr_constt phi -> j \in irr_constt psi -> '[phi, psi] = 0 -> '['chi_i, 'chi_j] = 0.
proof: Proof. move=> _ _ /constt_charP[//|phi1 Nphi1 ->] /constt_charP[//|psi1 Npsi1 ->]. rewrite cfdot_irr; case: eqP => // -> /eqP/idPn[]. rewrite cfdotDl !cfdotDr cfnorm_irr -addrA gt_eqF ?ltr_wpDr ?ltr01 //. by rewrite natr_ge0 ?rpredD ?Cnat_cfdot_char ?irr_char. 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)