| ∃∃I1,I2,L1,L2. ⦃G, L1⦄ ⊢ ⬈[h, ⋆s] L2 &
Y1 = L1.ⓘ{I1} & Y2 = L2.ⓘ{I2}.
/2 width=1 by lfxs_inv_sort/ qed-.
-(*
-lemma lfpx_inv_zero: ∀h,G,Y1,Y2. ⦃G, Y1⦄ ⊢ ⬈[h, #0] Y2 →
- (Y1 = ⋆ ∧ Y2 = ⋆) ∨
- ∃∃I,L1,L2,V1,V2. ⦃G, L1⦄ ⊢ ⬈[h, V1] L2 &
- ⦃G, L1⦄ ⊢ V1 ⬈[h] V2 &
- Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2.
-/2 width=1 by lfxs_inv_zero/ qed-.
-*)
+
lemma lfpx_inv_lref: ∀h,G,Y1,Y2,i. ⦃G, Y1⦄ ⊢ ⬈[h, #⫯i] Y2 →
∨∨ Y1 = ⋆ ∧ Y2 = ⋆
| ∃∃I1,I2,L1,L2. ⦃G, L1⦄ ⊢ ⬈[h, #i] L2 &