proposition: Lemma subG1_contra H : G \subset H -> G :!=: 1 -> H :!=: 1.
proof: Proof. by move=> sGH; rewrite -subG1; apply: contraNneq => <-. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)