proposition: Lemma combine_zero_general sz1 sz2: forall (w: word sz1) (b: word sz2), (combine w b = $ 0 -> w = $ 0 /\ b = $ 0)%word.
proof: Proof. intros. pre_word_omega. rewrite wordToNat_combine in *. assert (sth1: wordToNat w = 0) by lia. pose proof (pow2_zero sz1) as sth2. assert (sth3: wordToNat b = 0) by nia. split; eapply wordToNat_zero; eauto. 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