proposition: Lemma wordToN_inj : forall sz (a b : word sz), wordToN a = wordToN b -> a = b.
proof: Proof. induction a; intro b0; rewrite (shatter_word b0); intuition. simpl in H. destruct b; destruct (whd b0); intros. f_equal. eapply IHa. eapply N.succ_inj in H. destruct (wordToN a); destruct (wordToN (wtl b0)); try congruence. destruct (wordToN (wtl b0)); destruct (wordToN a); inversion H. destruct (wordToN (wtl b0)); destruct (wordToN a); inversion H. f_equal. eapply IHa. destruct (wordToN a); destruct (wordToN (wtl b0)); try congruence. 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