proposition: Lemma TI_cfker_irr : \bigcap_i cfker 'chi[G]_i = [1].
proof: Proof. apply/trivgP; apply: subset_trans cfaithful_reg; rewrite cfkerE ?cfReg_char //. rewrite subsetI (bigcap_min 0) //=; last by rewrite cfker_irr0. by apply/bigcapsP=> i _; rewrite bigcap_inf. 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)