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

Lemma E_AbsCong2
: ∀ (L : atoms) (G : context) (D : available_props) (rho : relflag) (b1 b2 A1 B : tm),
(∀ x : atom,
x `notin` L
→ DefEq ([(x, Tm A1)] ++ G) D (open_tm_wrt_tm b1 (a_Var_f x)) (open_tm_wrt_tm b2 (a_Var_f x))
(open_tm_wrt_tm B (a_Var_f x)))
→ (∀ x : atom, x `notin` L → RhoCheck rho x (open_tm_wrt_tm b1 (a_Var_f x)))
→ (∀ x : atom, x `notin` L → RhoCheck rho x (open_tm_wrt_tm b2 (a_Var_f x)))
→ DefEq G D (a_UAbs rho b1) (a_UAbs rho b2) (a_Pi rho A1 B).