(* *)
(**************************************************************************)
+include "basic_2/static/lfxs_lfxs.ma".
include "basic_2/i_static/tc_lfxs.ma".
(* ITERATED EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ***)
+(* Advanced properties ******************************************************)
+
+lemma tc_lfxs_sym: ∀R. lfxs_fsle_compatible R →
+ (∀L1,L2,T1,T2. R L1 T1 T2 → R L2 T2 T1) →
+ ∀T. symmetric … (tc_lfxs R T).
+#R #H1R #H2R #T #L1 #L2 #H elim H -L2
+/4 width=3 by lfxs_sym, tc_lfxs_step_sn, inj/
+qed-.
+
(* Main properties **********************************************************)
theorem tc_lfxs_trans: ∀R,T. Transitive … (tc_lfxs R T).
-#R #T #L1 #L #HL1 #L2 #HL2 @(trans_TC … HL1 HL2) (**) (* auto fails *)
+#R #T #L1 #L #HL1 #L2 #HL2 @(trans_TC … HL1 HL2) (**) (* auto fails *)
qed-.