proposition: Lemma zext_wordToNat_equal_Z: forall sz (w: word sz) n, n <> 0 -> wordToZ (zext w n) = Z.of_nat (wordToNat w).
proof: Proof. unfold wordToZ, zext; intros. rewrite wmsb_combine with (b2:= false) by assumption. rewrite wmsb_wzero. replace (combine w (wzero n)) with (zext w n) by reflexivity. rewrite wordToN_zext. rewrite wordToN_nat. rewrite <-nat_N_Z. unfold Z.of_N; reflexivity. 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