proposition: Lemma Zabs_8 : forall z p : Z, (- p <= z <= p)%Z -> (Z.abs z <= p)%Z.
proof: Proof. intros. apply Zlt_succ_le. apply Zabs_3. elim H. intros. split. apply Zle_lt_succ. assumption. apply Z.lt_le_trans with (m := (- p)%Z). apply Z.gt_lt. apply Zlt_opp. apply Zlt_succ. assumption. Qed.
imports: Coq(Lia)