proposition: Lemma subcent1C x y G : x \in G -> y \in 'C_G[x] -> x \in 'C_G[y].
proof: Proof. by move=> Gx /subcent1P[_ cxy]; apply/subcent1P. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(fintype bigop finset fingroup morphism perm) mathcomp(automorphism quotient action gproduct gfunctor) mathcomp(cyclic)