(* -------------------- *)

Lemma E_Abs_exists :  forall x (G : context) (rho : relflag) (a A B : tm),
x `notin` fv_tm_tm_tm a \u fv_tm_tm_tm B
-> Typing ([(x, Tm A)] ++ G) (open_tm_wrt_tm a (a_Var_f x)) (open_tm_wrt_tm B (a_Var_f x))
-> Typing G A a_Star
-> RhoCheck rho x (open_tm_wrt_tm a (a_Var_f x))
-> Typing G (a_UAbs rho a) (a_Pi rho A B).