Module ext_invert (subst : ext_subst_sig) <: ext_invert_sig.
Include subst.
Set Bullet Behavior "Strict Subproofs".
Set Implicit Arguments.

Lemma invert_a_CPi: forall G phi A B0,
Typing G (a_CPi phi B0) A ->
DefEq G (dom G) A a_Star a_Star /\ (exists L, forall c, c `notin` L -> Typing ([(c, Co phi)] ++ G) (open_tm_wrt_co B0 (g_Var_f c) ) a_Star) /\ PropWff G phi.