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

Lemma split1_existT: (* Note: not axiom free *) forall n sz1 (w1: word (n + sz1)) sz2 (w2: word (n + sz2)), existT word _ w1 = existT word _ w2 -> split1 n _ w1 = split1 n _ w2.