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 Typing_tm_subst : forall G x A b B (H : Typing ((x ~ Tm A) ++ G) b B),
forall a, Typing G a A ->
Typing G (tm_subst_tm_tm a x b) (tm_subst_tm_tm a x B).