proposition: Theorem Zpred_Zle_Zabs_intro : forall z1 z2 : Z, (- Z.pred z2 <= z1)%Z -> (z1 <= Z.pred z2)%Z -> (Z.abs z1 < z2)%Z.
proof: Proof. intros z1 z2 H H0; apply Zle_Zpred_inv. apply Zabs_intro with (P := fun x => (x <= Z.pred z2)%Z); auto with zarith. Qed.
imports: Reals ZArith List PeanoNat Psatz