proposition: Lemma triv_restr_perm p : p \notin 'N(S | 'P) -> restr_perm p = 1.
proof: Proof. move=> not_nSp; apply/permP=> x. by rewrite !permE /= /actby (negPf not_nSp) andbF. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(fintype bigop finset fingroup morphism perm) mathcomp(automorphism quotient)