proposition: Lemma wmsb_split2': forall sz (w: word (S sz)) b, wmsb w b = negb (weqb (split2 sz 1 (nat_cast _ (eq_sym (Nat.add_1_r sz)) w)) (natToWord _ 0)).
proof: Proof. apply (induct_word_S (fun sz w => forall b, wmsb w b = negb (weqb (split2 sz 1 (nat_cast _ (eq_sym (Nat.add_1_r sz)) w)) (natToWord _ 0)))); intros. - destruct b; reflexivity. - cbn in *. rewrite (H false). repeat f_equal. clear. apply (nat_cast_inj (Nat.add_1_r n)). erewrite wtl_nat_cast_WS. 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