proposition: Lemma word_cancel_m sz (a b c a' b': word sz): a ^+ a' = b ^+ b'-> a ^+ c ^+ a' = b ^+ c ^+ b'.
proof: Proof. intros. assert (sth: a ^+ c ^+ a' = a ^+ a'^+ c ). rewrite <- wplus_assoc. rewrite wplus_comm with (y := a'). rewrite wplus_assoc. reflexivity. rewrite sth. rewrite H. rewrite <- wplus_assoc. rewrite wplus_comm with (x := b'). rewrite wplus_assoc. reflexivity. 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