proposition: Lemma cymap_id (U : finType) (s : {perm U}) (CM : porbits_map s s) : {in porbits s, CM =1 id} -> cymap CM =1 id.
proof: Proof. Proof using. move=> H x; rewrite /cymap /=. rewrite -[RHS](indporbitP s). rewrite /cymapcan /canporbit H ?imset_f //. by case: pickP => // /(_ x); rewrite porbit_id. 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