proposition: Lemma countLeadingZerosWord_nat_le_len ni (w: word ni): countLeadingZerosWord_nat w <= ni.
proof: Proof. induction ni; simpl; auto; intros. match goal with | |- ((if ?P then _ else _) <= _) => destruct P; simpl; auto end. apply ->Nat.succ_le_mono. eapply IHni. 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