proposition: Theorem Zlt_Zabs_Zpred : forall z1 z2 : Z, (Z.abs z1 < z2)%Z -> z1 <> Z.pred z2 -> (Z.abs (Z.succ z1) < z2)%Z.
proof: Proof. intros z1 z2 H H0; case (Zle_or_lt 0 z1); intros H1. rewrite Z.abs_eq; lia. repeat rewrite Zabs_eq_opp; lia. Qed.
imports: Reals ZArith List PeanoNat Psatz