(***************************************************  1. Define two well-founded relation here and one induction principle here  ***************************************************)
Module TypeTree.
Section TypeTree.
Context {cs: compspecs}.
Definition typeR (t1: type) (t2: type): Prop :=
match t2 with
| Tstruct sid => exists i1, In (i1, t1) (co_members (get_co sid))
| _ => False
end.

Lemma wf_typeR: well_founded typeR.
Definition default_val_fix_aux (y: type): (forall x, TypeTree.typeR x y -> reptype x) -> reptype y.