+(* Advanced properties ******************************************************)
+
+lemma lfpxs_refl: ∀h,G,T. reflexive … (lfpxs h G T).
+/2 width=1 by tc_lfxs_refl/ qed.
+
+(* Advanced forward lemmas **************************************************)
+
+lemma lfpxs_fwd_bind_dx: ∀h,p,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ⬈*[h, ⓑ{p,I}V.T] L2 →
+ ⦃G, L1.ⓑ{I}V⦄ ⊢ ⬈*[h, T] L2.ⓑ{I}V.
+/2 width=2 by tc_lfxs_fwd_bind_dx/ qed-.
+
+lemma lfpxs_fwd_bind_dx_void: ∀h,p,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ⬈*[h, ⓑ{p,I}V.T] L2 →
+ ⦃G, L1.ⓧ⦄ ⊢ ⬈*[h, T] L2.ⓧ.
+/2 width=4 by tc_lfxs_fwd_bind_dx_void/ qed-.
+