proposition: Theorem Zle_Zpred_Zpred : forall z1 z2 : Z, (z1 <= z2)%Z -> (Z.pred z1 <= Z.pred z2)%Z.
proof: Proof. intros z1 z2 H; apply Zsucc_le_reg. repeat rewrite <- Zsucc_pred; auto. Qed.
imports: Reals ZArith List PeanoNat Psatz