proposition: Lemma classes_of_permP s t : (t \in (s ^: [set: {perm T}])%g) = (cycle_type s == cycle_type t).
proof: Proof. Proof using. apply /idP/conj_permP => [| [c ->]]. - by move=> /imsetP[c Hc ->]; exists c. - by apply: imset_f; 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