proposition: Lemma le_neq_lt : forall sz (a b : word sz), b <= a -> a <> b -> b < a.
proof: Proof. intros sz a b H H0; destruct (wlt_dec b a) as [?|n]; auto. exfalso. apply H0. unfold wlt, N.lt in *. eapply wordToN_inj. eapply Ncompare_eq_correct. case_eq ((wordToN a ?= wordToN b)%N); auto; try congruence. intros H1. rewrite N.compare_antisym in n. rewrite H1 in n. simpl in *. congruence. 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