proposition: Lemma class1g x A : x \in A -> 1 ^: A = 1.
proof: Proof. move=> Ax; apply/setP=> y. by apply/imsetP/set1P=> [[a Aa]|] ->; last exists x; rewrite ?conj1g. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)