proposition: Lemma pdadde_eq0 x y : 0 <= x -> 0 <= y -> x + y == 0 = (x == 0) && (y == 0).
proof: Proof. move: x y => [x||] [y||] //. - by rewrite !lee_fin -dEFinD !eqe; exact: paddr_eq0. - by rewrite /adde/= (_ : +oo == 0 = false)// andbF. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap) mathcomp(mathcomp_extra) signed