proposition: Lemma le_word_le_nat : forall (sz:nat) (n:word sz) (m:nat), (n <= (natToWord sz m))%word -> (wordToNat n <= m)%nat.
proof: Proof. intros. apply wle_le in H. destruct (wordToNat_natToWord' sz m). rewrite <- H0. apply Nat.le_trans with (2 := (Nat.le_add_r _ (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