+theorem lfpx_bind: ∀h,G,L1,L2,V1. ⦃G, L1⦄ ⊢ ⬈[h, V1] L2 →
+ ∀I,V2,T. ⦃G, L1.ⓑ{I}V1⦄ ⊢ ⬈[h, T] L2.ⓑ{I}V2 →
+ ∀p. ⦃G, L1⦄ ⊢ ⬈[h, ⓑ{p,I}V1.T] L2.
+/2 width=2 by lfxs_bind/ qed.
+
+theorem lfpx_flat: ∀h,G,L1,L2,V. ⦃G, L1⦄ ⊢ ⬈[h, V] L2 →
+ ∀I,T. ⦃G, L1⦄ ⊢ ⬈[h, T] L2 → ⦃G, L1⦄ ⊢ ⬈[h, ⓕ{I}V.T] L2.
+/2 width=1 by lfxs_flat/ qed.
+
+theorem lfpx_bind_void: ∀h,G,L1,L2,V. ⦃G, L1⦄ ⊢ ⬈[h, V] L2 →
+ ∀T. ⦃G, L1.ⓧ⦄ ⊢ ⬈[h, T] L2.ⓧ →
+ ∀p,I. ⦃G, L1⦄ ⊢ ⬈[h, ⓑ{p,I}V.T] L2.
+/2 width=1 by lfxs_bind_void/ qed.