Section S.
Variables x y: Z.
Variables XGe : x >= 0.
Variables YGt : y > 0.
Variables YLt : y < 0.
Goal False.
Proof using - XGe.
lia.
Qed.
Goal False.
Proof using YGt YLt x y.
lia.
Qed.
End S.

Lemma ex_pos : forall x, exists z t, x = z - t /\ z >= 0 /\ t >= 0.