proposition: Lemma wordToZ_WS_0: forall sz (w: word sz), wordToZ w~0 = (2 * wordToZ w)%Z.
proof: Proof. dependent destruction w; [reflexivity|]. unfold wordToZ. rewrite wmsb_ws. destruct (wmsb (WS b w) false). - rewrite wneg_WS_0. rewrite wordToN_WS_0. destruct (wordToN (wneg (WS b w))); cbn; lia. - rewrite wordToN_WS_0. destruct (wordToN (WS b w)); cbn; lia. 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