proposition: Lemma cfInd_irr_eq1 i : H <| G -> ('Ind[G, H] 'chi_i == 'Ind[G, H] 1) = (i == 0).
proof: Proof. case/andP=> sHG nHG; apply/eqP/idP=> [chi1 | /eqP->]; last by rewrite irr0. rewrite -subGcfker -(sub_cfker_Ind_irr _ sHG nHG) chi1 -irr0. by rewrite sub_cfker_Ind_irr ?cfker_irr0. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrbool ssrfun eqtype ssrnat seq path div choice fintype) mathcomp(tuple finfun bigop prime order ssralg finset fingroup morphism) mathcomp(perm automorphism quotient action zmodp finalg center commutator) mathcomp(poly cyclic pgroup nilpotent matrix mxalgebra mxrepresentation) mathcomp(vector falgebra fieldext ssrnum algC rat algnum galois) mathcomp(classfun character inertia integral_char vcharacter)