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_co_fresh_1 :
forall G a A a0 c s,
Typing G a A -> Ctx ((c ~ s) ++ G) -> co_subst_co_tm a0 c A = A.