proposition: Lemma lub_set0 r: order r -> forall x, (least_upper_bound r emptyset x = least r x).
proof: Proof. move=> or; rewrite /least_upper_bound set_of_upper_bounds_set0. by rewrite /least_induced iorder_substrate. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)