proposition: Lemma combine_natToWord_wzero n: forall x, x < pow2 n -> combine (natToWord n x) (natToWord 1 0) = natToWord (n+1) x.
proof: Proof. intros. apply wordToNat_eq2. rewrite ?wordToNat_combine. simpl. rewrite Nat.mul_0_r. rewrite Nat.add_0_r. pose proof (pow2_lt_pow2_S n) as sth2. rewrite ?wordToNat_natToWord_idempotent' by lia. 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