proposition: Lemma cfnorm_eq0 phi : ('[phi] == 0) = (phi == 0).
proof: Proof. apply/idP/eqP=> [|->]; last by rewrite cfdot0r. rewrite mulf_eq0 invr_eq0 (negbTE (neq0CG G)) /= => /eqP/psumr_eq0P phi0. apply/cfun_inP=> x Gx; apply/eqP; rewrite cfunE -mul_conjC_eq0. by rewrite phi0 // => y _; apply: mul_conjC_ge0. 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(matrix vector falgebra ssrnum algC algnum) mathcomp(archimedean)