proposition: Lemma eq_iff_le x y : x = y <-> x ≤ y /\ y ≤ x.
proof: Proof. split; intros E. - rewrite E. split;apply reflexivity. - apply (antisymmetry (≤) x y);apply E. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.theory.apartness