proposition: Lemma wordToNat_nonZero sz (w: word sz): w <> wzero sz -> wordToNat w > 0.
proof: Proof. induction w; simpl; unfold wzero; simpl; intros. - tauto. - destruct b. + lia. + assert (sth: w <> (natToWord n 0)). { intro. subst. tauto. } assert (sth2: wordToNat w <> 0). { intro sth3. specialize (IHw sth). lia. } lia. 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