proposition: Lemma empty_interval r a: order r -> inc a (substrate r) -> [/\ empty (interval_co r a a), empty (interval_oc r a a) & empty (interval_oo r a a)].
proof: Proof. move=> or asr; split => // y /Zo_hi [p1 p2]; order_tac. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)