proposition: Lemma cfuniCTnE (ct : 'P_n) (s : 'S_n) : '1_[ct] s = (cycle_typeSn s == ct)%:R.
proof: Proof. Proof using. rewrite cfuniCTE /cycle_typeSn /=. by rewrite partnCTE CTpartnK. 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