proposition: Lemma orbit_rcoset A a x y : (to y a \in orbit to (A :* a) x) = (y \in orbit to A x).
proof: Proof. by rewrite orbit_rcoset_in ?subsetT ?inE. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(fintype bigop finset fingroup morphism perm) mathcomp(automorphism quotient)