proposition: Lemma wmod_0_l: forall sz (m: word sz), $0 ^% m = $0.
proof: Proof. intros. unfold wmod, wordBin. rewrite wordToN_0. destruct (N.eq_dec (wordToN m) 0%N). - rewrite e. change (0 mod 0)%N with 0%N. apply NToWord_0. - rewrite N.mod_0_l by assumption. apply NToWord_0. 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