proposition: Lemma padde_eq0 x y : 0 <= x -> 0 <= y -> (x + y == 0) = (x == 0) && (y == 0).
proof: Proof. move: x y => [x| |] [y| |]//; rewrite !lee_fin; first exact: paddr_eq0. by move=> x0 _ /=; rewrite andbF. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap) mathcomp(mathcomp_extra) signed