proposition: Lemma properD1 A x : x \in A -> A :\ x \proper A.
proof: Proof. move=> Ax; rewrite properE subsetDl; apply/subsetPn; exists x=> //. by rewrite in_setD1 Ax eqxx. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop)