proposition: Lemma cfnorm_Ind_irr t : H <| G -> '['Ind[G] 'chi[H]_t] = #|'I_G['chi_t] : H|%:R.
proof: Proof. set r := _%:R => HnG; have HsG := normal_sub HnG. rewrite -Frobenius_reciprocity cfResInd_sum_cfclass //= cfdotZr rmorph_nat -/r. rewrite reindex_cfclass // cfdot_sumr (bigD1 t) ?cfclass_refl //= cfnorm_irr. rewrite big1 ?addr0 ?mulr1 // => j /andP[_ /negbTE]. by rewrite eq_sym cfdot_irr => ->. 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)