proposition: Lemma card_classes_perm : #|classes [set: {perm T}]| = #|{: 'P_#|T| }|.
proof: Proof. Proof using. rewrite -imset_classCT card_imset; last exact: classCT_inj. by apply eq_card => s; rewrite !inE. 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