(* Forward lemmas with length for local environments ************************)
-lemma rpx_fwd_length: ∀h,G,L1,L2,T. ⦃G, L1⦄ ⊢ ⬈[h, T] L2 → |L1| = |L2|.
+lemma rpx_fwd_length: ∀h,G,L1,L2,T. ⦃G,L1⦄ ⊢ ⬈[h,T] L2 → |L1| = |L2|.
/2 width=3 by rex_fwd_length/ qed-.
(* Inversion lemmas with length for local environments **********************)
-lemma rpx_inv_zero_length: ∀h,G,Y1,Y2. ⦃G, Y1⦄ ⊢ ⬈[h, #0] Y2 →
+lemma rpx_inv_zero_length: ∀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 &
+ | ∃∃I,L1,L2,V1,V2. ⦃G,L1⦄ ⊢ ⬈[h,V1] L2 &
+ ⦃G,L1⦄ ⊢ V1 ⬈[h] V2 &
Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2
| ∃∃I,L1,L2. |L1| = |L2| & Y1 = L1.ⓤ{I} & Y2 = L2.ⓤ{I}.
/2 width=1 by rex_inv_zero_length/ qed-.