proposition: Lemma index_cent1 x : #|G : 'C_G[x]| = #|x ^: G|.
proof: Proof. by rewrite -astab1J -card_orbit. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(fintype bigop finset fingroup morphism perm) mathcomp(automorphism quotient)