proposition: Lemma cfAutInd (psi : 'CF(H)) : ('Ind[G] psi)^u = 'Ind psi^u.
proof: Proof. have [sHG | not_sHG] := boolP (H \subset G). apply/cfunP=> x; rewrite !(cfunE, cfIndE) // rmorphM /= fmorphV rmorph_nat. by congr (_ * _); rewrite rmorph_sum; apply: eq_bigr => y; rewrite !cfunE. rewrite !cfIndEout // linearZ /= cfAut_cfuni rmorphM rmorph_nat /=. rewrite -cfdot_cfAut ?rmorph1 // => _ /imageP[x Hx ->]. by rewrite cfun1E Hx !rmorph1. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div choice fintype tuple finfun bigop prime order) mathcomp(ssralg poly finset fingroup morphism perm) mathcomp(automorphism quotient finalg action gproduct) mathcomp(zmodp commutator cyclic center pgroup sylow) mathcomp(matrix vector falgebra ssrnum algC algnum) mathcomp(archimedean)