proposition: Lemma ndadde_eq0 x y : x <= 0 -> y <= 0 -> x + y == 0 = (x == 0) && (y == 0).
proof: Proof. move: x y => [x||] [y||] //. - by rewrite !lee_fin -dEFinD !eqe; exact: naddr_eq0. - by rewrite /adde/= (_ : -oo == 0 = false)// andbF. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap) mathcomp(mathcomp_extra) signed