proposition: Lemma cfResIsom phi : 'Res[S] (cfIsom isoG phi) = cfIsom isoH ('Res[H] phi).
proof: Proof. have [[injg defR] [injh defS]] := (isomP isoG, isomP isoH). rewrite !morphimEdom in defS defR; apply/cfun_inP=> s. rewrite -{1}defS => /imsetP[x Hx ->] {s}; have Gx := subsetP sHG x Hx. rewrite {1}eq_hg ?(cfResE, cfIsomE) // -defS -?eq_hg ?imset_f // -defR. by rewrite (eq_in_imset eq_hg) imsetS. 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)