proposition: Lemma countLeadingZerosWord_le_len_nat no ni: ni < pow2 no -> forall w: word ni, #(countLeadingZerosWord no w) <= ni.
proof: Proof. intros H w. pose proof (countLeadingZerosWord_le_len H w) as sth. pre_word_omega. rewrite wordToNat_natToWord_idempotent' in * by assumption. assumption. 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