proposition: Lemma wordToZ_ZToWord'': forall (sz: nat), (0 < sz)%nat -> forall n: Z, (- 2 ^ (Z.of_nat sz - 1) <= n < 2 ^ (Z.of_nat sz - 1))%Z -> wordToZ (ZToWord sz n) = n.
proof: Proof. intros. destruct sz; [lia|]. apply wordToZ_ZToWord. replace (Z.of_nat (S sz) - 1)%Z with (Z.of_nat sz) in * by lia. rewrite Nat2Z.inj_pow. 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