proposition: Lemma wordToZ_wplus_bound: forall sz (w1 w2: word (S sz)), (- Z.of_nat (pow2 sz) <= wordToZ w1 + wordToZ w2 < Z.of_nat (pow2 sz))%Z -> (wordToZ w1 + wordToZ w2 = wordToZ (w1 ^+ w2))%Z.
proof: Proof. intros. rewrite wplus_wplusZ. unfold wplusZ, wordBinZ. remember (wordToZ w1 + wordToZ w2)%Z as z; clear Heqz. apply eq_sym, wordToZ_ZToWord; 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