proposition: Fact le_anti : antisymmetric le.
proof: Proof. move=> x y; rewrite !le_def; case: eqVneq => //= _ /andP [] hxy. by move/(lt_trans hxy); rewrite lt_irr. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(path fintype tuple bigop finset div prime finfun) mathcomp(finset)