proposition: Lemma paddR_eq0 (x y : R) : 0 <= x -> 0 <= y -> (x + y = 0) <-> (x = 0) /\ (y = 0).
proof: Proof. move=> x0 y0; split => [|[-> ->]]; last by rewrite addR0. move=> H; move: (H) => /Rplus_eq_0_l -> //. by move: H; rewrite addRC => /Rplus_eq_0_l ->. Qed.
imports: mathcomp(all_ssreflect ssralg ssrnum) Reals mathcomp(lra) mathcomp(Rstruct)