proposition: Lemma unique_inverse : forall sz (a b1 b2 : word sz), a ^+ b1 = wzero _ -> a ^+ b2 = wzero _ -> b1 = b2.
proof: Proof. intros sz a b1 b2 H *. transitivity (b1 ^+ wzero _). rewrite wplus_comm. rewrite wplus_unit. auto. transitivity (b1 ^+ (a ^+ b2)). congruence. rewrite wplus_assoc. rewrite (wplus_comm b1). rewrite H. rewrite wplus_unit. 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