proposition: Lemma itv_bottom x : unify_itv empty_itv i -> False.
proof: Proof. move: x => [x /subitvP /(_ x)]; rewrite in_itv/= lexx => /(_ erefl) xi. move=> /(@Itv.subitv_map_itv R) /subitvP /(_ _ xi). by rewrite in_itv/= => /andP[] /le_trans /[apply]; rewrite ler10. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool) mathcomp(ssrnat eqtype choice order ssralg ssrnum ssrint) mathcomp(interval) mathcomp(mathcomp_extra boolp) signed