| ∃∃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 &
/2 width=1 by lfxs_inv_gref/ qed-.
lemma lfpx_inv_bind: ∀h,p,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ⬈[h, ⓑ{p,I}V.T] L2 →
- â¦\83G, L1â¦\84 â\8a¢ â¬\88[h, V] L2 â\88§ ⦃G, L1.ⓑ{I}V⦄ ⊢ ⬈[h, T] L2.ⓑ{I}V.
+ â\88§â\88§ â¦\83G, L1â¦\84 â\8a¢ â¬\88[h, V] L2 & ⦃G, L1.ⓑ{I}V⦄ ⊢ ⬈[h, T] L2.ⓑ{I}V.
/2 width=2 by lfxs_inv_bind/ qed-.
lemma lfpx_inv_flat: ∀h,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ⬈[h, ⓕ{I}V.T] L2 →
- â¦\83G, L1â¦\84 â\8a¢ â¬\88[h, V] L2 â\88§ ⦃G, L1⦄ ⊢ ⬈[h, T] L2.
+ â\88§â\88§ â¦\83G, L1â¦\84 â\8a¢ â¬\88[h, V] L2 & ⦃G, L1⦄ ⊢ ⬈[h, T] L2.
/2 width=2 by lfxs_inv_flat/ qed-.
(* Advanced inversion lemmas ************************************************)