proposition: Lemma wordToZ_wplus_bound': forall sz (w1 w2: word sz), sz <> 0 -> (- Z.of_nat (pow2 (pred sz)) <= wordToZ w1 + wordToZ w2 < Z.of_nat (pow2 (pred sz)))%Z -> (wordToZ w1 + wordToZ w2 = wordToZ (w1 ^+ w2))%Z.
proof: Proof. intros. destruct sz; [exfalso; auto|clear H]. apply wordToZ_wplus_bound; auto. 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