elim x.
intros px; red in px.
simpl in px.
inversion px.
simpl in |- *.
auto with *.
intros p px; red in px.
simpl in px.
inversion px.
Qed.

Lemma Zlt_reg_l : forall a b c : Z, (a < b)%Z -> (c + a < c + b)%Z.
intros a b c; try assumption.