proposition: Lemma irr1_bound (i : Iirr G) : ('chi_i 1%g) ^+ 2 <= #|G : 'Z('chi_i)%CF|%:R ?= iff ('chi_i \in 'CF(G, 'Z('chi_i)%CF)).
proof: Proof. congr (_ <= _ ?= iff _): (cfnorm_Res_leif 'chi_i (cfcenter_sub 'chi_i)). have [xi Lxi ->] := cfcenter_Res 'chi_i. have /irrP[j ->] := lin_char_irr Lxi; rewrite cfdotZl cfdotZr cfdot_irr eqxx. by rewrite mulr1 irr1_degree conjC_nat. by rewrite cfdot_irr eqxx mulr1. 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)