proposition: Lemma lte_spdaddre z x y : z \is a fin_num -> 0 < y -> z <= x -> z < x + y.
proof: Proof. move: z y x => [z| |] [y| |] [x| |] _ //=; rewrite ?(lte_fin,ltry,ltNyr)//. exact: ltr_pwDr. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap) mathcomp(mathcomp_extra) signed