Definition Typing_weakening  := first  typing_weakening_mutual.
Definition PropWff_weakening := second typing_weakening_mutual.
Definition Iso_weakening     := third  typing_weakening_mutual.
Definition DefEq_weakening   := fourth typing_weakening_mutual.
End ext_weak_sig.
(**************** Ext Substitution ****************)
Module Type ext_subst_sig.
Include ext_weak_sig.

Axiom tm_subst_tm_tm_dom_invariance: forall x a F,
dom F = dom (map (tm_subst_tm_sort a x) F).