proposition: Lemma cfdot_dchi (i j : dIirr G) : '[dchi i, dchi j] = (i == j)%:R - (i == ndirr j)%:R.
proof: Proof. case: i => bi i; case: j => bj j; rewrite cfdot_dirr ?dirr_dchi // !xpair_eqE. rewrite -dchi_ndirrE !eq_scaled_irr signr_eq0 !(inj_eq signr_inj) /=. by rewrite -!negb_add addbN negbK; case: andP => [[->]|]; rewrite ?subr0 ?add0r. 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)