proposition: Lemma inertia_Ind_irr t : H <| G -> 'I_G['chi[H]_t] \subset H -> 'Ind[G] 'chi_t \in irr G.
proof: Proof. rewrite -indexg_eq1 => nsHG /eqP r1. by rewrite irrEchar cfInd_char ?irr_char //= cfnorm_Ind_irr ?r1. 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)