+
+(* Advanced inversion lemmas ************************************************)
+
+lemma lfdeq_inv_bind_void: ∀h,o,p,I,L1,L2,V,T. L1 ≡[h, o, ⓑ{p,I}V.T] L2 →
+ L1 ≡[h, o, V] L2 ∧ L1.ⓧ ≡[h, o, T] L2.ⓧ.
+/2 width=3 by lfxs_inv_bind_void/ qed-.
+
+(* Advanced forward lemmas **************************************************)
+
+lemma lfdeq_fwd_bind_dx_void: ∀h,o,p,I,L1,L2,V,T.
+ L1 ≡[h, o, ⓑ{p,I}V.T] L2 → L1.ⓧ ≡[h, o, T] L2.ⓧ.
+/2 width=4 by lfxs_fwd_bind_dx_void/ qed-.