proposition: Lemma wplus_cancel : forall sz (a b c : word sz), a ^+ c = b ^+ c -> a = b.
proof: Proof. intros sz a b c H. apply (f_equal (fun x => x ^+ ^~ c)) in H. repeat rewrite <- wplus_assoc in H. rewrite wminus_inv in H. repeat rewrite (wplus_comm _ (wzero sz)) in H. repeat rewrite wplus_unit in H. 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