proposition: Lemma combine_lt sz1 sz2: forall (w1 w2: word sz1) (b1 b2: word sz2), (combine w1 b1 < combine w2 b2 -> b1 <= b2)%word.
proof: Proof. intros. pre_word_omega. rewrite ?wordToNat_combine in *. pose proof (pow2_zero sz1). pose proof (wordToNat_bound w1). pose proof (wordToNat_bound w2). nia. 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