proposition: Lemma sext_wordToZ: forall sz n (w: word sz), wordToZ (sext w n) = wordToZ w.
proof: Proof. dependent induction w; cbn; intros; [apply wordToZ_wzero|]. dependent destruction w. - unfold sext; simpl. destruct b; cbn. + rewrite wordToZ_wones by discriminate. reflexivity. + rewrite wordToZ_wzero; reflexivity. - remember (WS b0 w) as ww; clear Heqww. rewrite sext_WS. destruct b. + change (S n0 + n) with (S (n0 + n)) in *. repeat rewrite wordToZ_WS_1. rewrite IHw. reflexivity. + change (S n0 + n) with (S (n0 + n)) in *. repeat 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