proposition: Lemma lt_word_lt_nat : forall (sz:nat) (n:word sz) (m:nat), (n < (natToWord sz m))%word -> (wordToNat n < m)%nat.
proof: Proof. intros. apply wlt_lt in H. destruct (wordToNat_natToWord' sz m). rewrite <- H0. apply Nat.lt_lt_add_r with (p := x * pow2 sz). assumption. 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