proposition: Lemma cfdot_dirr_eq1 : {in dirr G &, forall phi psi, ('[phi, psi] == 1) = (phi == psi)}.
proof: Proof. move=> _ _ /dirrP[b1 [i1 ->]] /dirrP[b2 [i2 ->]]. rewrite eq_signed_irr cfdotZl cfdotZr rmorph_sign cfdot_irr mulrA -signr_addb. rewrite pmulrn -rmorphMsign (eqr_int _ _ 1) -negb_add. by case: (b1 (+) b2) (i1 == i2) => [] []. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div choice fintype tuple finfun bigop prime order) mathcomp(ssralg poly finset fingroup morphism perm) mathcomp(automorphism quotient finalg action gproduct) mathcomp(zmodp commutator cyclic center pgroup sylow) mathcomp(frobenius vector ssrnum ssrint archimedean intdiv) mathcomp(algC algnum classfun character integral_char)