proposition: Lemma porbit_set_of_set C : #|C| > 1 -> porbit_set (perm_of_porbit C) = [set C].
proof: Proof. Proof using. move=> Hsize; apply /setP => X. rewrite !inE. apply/andP/eqP => [[/imsetP[x _ ->]] | ->]. - rewrite psupport_card_porbit psupport_perm_of_porbit // => Hx. rewrite [RHS](perm_of_porbitE Hx). by apply/eqP; rewrite eq_porbit_mem -perm_of_porbitE. - split; first exact: porbits_of_set. by rewrite -(psupport_perm_of_porbit Hsize) card_psupport_noteq1. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrfun ssrbool eqtype ssrnat seq choice fintype) mathcomp(tuple finfun finset path bigop) mathcomp(fingroup perm action) mathcomp(ssralg matrix mxalgebra algC classfun) partition tools sorted permcomp fibered_set cycles