proposition: Theorem subgroup_transitiveP G H S x : x \in S -> H \subset G -> [transitive G, on S | to] -> reflect ('C_G[x | to] * H = G) [transitive H, on S | to].
proof: Proof. by move=> Sx sHG; apply: subgroup_transitivePin (subsetT G). Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(fintype bigop finset fingroup morphism perm) mathcomp(automorphism quotient)