proposition: Lemma lte_le_sub z u x y : u \is a fin_num -> x < z -> u <= y -> x - y < z - u.
proof: Proof. move: z u x y => [z| |] [u| |] [x| |] [y| |] _ //=; rewrite ?(ltry, ltNyr)//. by rewrite !lte_fin => xltr tley; apply: ltr_leD; rewrite // lerNl opprK. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap) mathcomp(mathcomp_extra) signed