proposition: Theorem irr_induced_Frobenius_ker i : i != 0 -> 'Ind[G, K] 'chi_i \in irr G.
proof: Proof. move/inertia_Frobenius_ker/group_inj=> defK. have [_ _ nsKG _] := Frobenius_kerP frobGK. have [] := constt_Inertia_bijection i nsKG; rewrite defK cfInd_id => -> //. by rewrite constt_irr !inE. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq path) mathcomp(choice fintype div tuple finfun bigop prime order) mathcomp(ssralg ssrnum finset fingroup morphism perm) mathcomp(automorphism quotient action zmodp cyclic center) mathcomp(gproduct commutator gseries nilpotent pgroup) mathcomp(sylow maximal frobenius matrix mxalgebra) mathcomp(mxrepresentation vector algC classfun character) mathcomp(archimedean)