proposition: Lemma posxP x : eq0_xor_gt0 x (x == \bot) (\bot < x).
proof: Proof. by rewrite lt0x; have [] := eqVneq; constructor; rewrite ?lt0x. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(path fintype tuple bigop finset div prime finfun) mathcomp(finset)