Ltac wlt_ind :=
  match goal with
  | [ |- forall (n: word ?len), ?P ] =>
    refine (well_founded_ind (@wlt_wf len) (fun n => P) _)
  end.

Lemma wordToNat_split1: forall sz1 sz2 (w: word (sz1 + sz2)), wordToNat (split1 _ _ w) = Nat.modulo (wordToNat w) (pow2 sz1).