proposition: Lemma uwordToZ_ZToWord_0: forall (sz : nat) (z : Z), (0 <= z < Z.of_N (Npow2 sz))%Z -> uwordToZ (ZToWord sz z) = z.
proof: Proof. intros. unfold uwordToZ. pose proof (Z2N.id _ (proj1 H)). remember (Z.to_N z) as n; clear Heqn. subst z. apply proj2 in H. f_equal. rewrite ZToWord_Z_of_N. apply wordToN_NToWord_2. apply N2Z.inj_lt. assumption. Qed.
imports: Coq.Classes.Morphisms Coq.Classes.Morphisms_Prop Coq.Classes.Equivalence Coq.Arith.PeanoNat Coq.ZArith.BinInt  Coq.Arith.Arith Coq.NArith.NArith Coq.Bool.Bool Coq.ZArith.ZArith Coq.Logic.Eqdep_dec Coq.Logic.EqdepFacts Coq.Program.Tactics Coq.Program.Equality Coq.setoid_ring.Ring Coq.setoid_ring.Ring_polynom bbv.Nomega bbv.ZLib bbv.NatLib bbv.NLib bbv.N_Z_nat_conversions bbv.DepEq bbv.DepEqNat bbv.ReservedNotations Coq.micromega.Lia