+
+(* Advanced inversion lemmas ************************************************)
+
+lemma lfpr_inv_bind_void: ∀h,p,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ➡[h, ⓑ{p,I}V.T] L2 →
+ ∧∧ ⦃G, L1⦄ ⊢ ➡[h, V] L2 & ⦃G, L1.ⓧ⦄ ⊢ ➡[h, T] L2.ⓧ.
+/2 width=3 by lfxs_inv_bind_void/ qed-.
+
+(* Advanced forward lemmas **************************************************)
+
+lemma lfpr_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 lfxs_fwd_bind_dx_void/ qed-.