proposition: Lemma subcentP A B x : reflect (x \in A /\ centralises x B) (x \in 'C_A(B)).
proof: Proof. rewrite inE. case: (x \in A); last by right; case. by apply: (iffP centP) => [|[]]. 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)