proposition: Lemma ZToWord_opp_wneg{sz: nat}: forall (x: Z), ZToWord sz (- x) = ^~ (ZToWord sz x).
proof: Proof. intros. rewrite wneg_0_wminus. rewrite wminus_wminusZ. unfold wminusZ, wordBinZ. rewrite wordToZ_wzero. rewrite (Z.sub_0_l (wordToZ (ZToWord sz x))). destruct (wordToZ_ZToWord' sz x) as [k E]. rewrite E. rewrite Z.opp_sub_distr. rewrite ZToWord_Npow2_add_k'. 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