proposition: Lemma wordToNat_sext_modulo: forall sz (w: word sz) n, Nat.modulo (wordToNat (sext w n)) (pow2 sz) = wordToNat w.
proof: Proof. unfold sext; intros. pose proof (zero_lt_pow2 sz). destruct (wmsb w false). - rewrite wordToNat_combine. rewrite Nat.mul_comm, Nat.mod_add by lia. apply Nat.mod_small. apply wordToNat_bound. - rewrite wordToNat_combine. rewrite Nat.mul_comm, Nat.mod_add by lia. apply Nat.mod_small. apply wordToNat_bound. 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