proposition: Lemma wordToZ_combine_WO: forall sz (w: word sz), wordToZ (combine w WO) = wordToZ w.
proof: Proof. dependent induction w; [reflexivity|]. simpl; destruct b. - destruct n; [rewrite (shatter_word w); reflexivity|]. change (S n + 0) with (S (n + 0)) in *. do 2 rewrite wordToZ_WS_1. rewrite IHw; reflexivity. - do 2 rewrite wordToZ_WS_0. rewrite IHw; 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