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

Lemma DefEq_swap : forall x1 x G A1 D b1 b2 B,
x1 `notin` fv_tm_tm_tm b1 \u fv_tm_tm_tm b2 \u fv_tm_tm_tm B
-> x `notin` dom G \u {{ x1 }}
-> DefEq ([(x1, Tm A1)] ++ G) D
(open_tm_wrt_tm b1 (a_Var_f x1)) (open_tm_wrt_tm b2 (a_Var_f x1))
(open_tm_wrt_tm B (a_Var_f x1))
-> 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)).