proposition: Lemma combine_1 sz: sz > 1 -> natToWord (sz + 1) 1 = combine ($ 1) WO~0.
proof: Proof. intros. rewrite <- natToWord_wordToNat. f_equal. rewrite wordToNat_combine; simpl. rewrite Nat.mul_0_r, Nat.add_0_r. rewrite wordToNat_natToWord_idempotent'; auto. destruct sz; simpl; try lia; pose proof (pow2_zero sz); 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