(* Forward lemmas with length for local environments ************************)
-lemma rpx_fwd_length: â\88\80h,G,L1,L2,T. â¦\83G,L1â¦\84 ⊢ ⬈[h,T] L2 → |L1| = |L2|.
+lemma rpx_fwd_length: â\88\80h,G,L1,L2,T. â\9dªG,L1â\9d« ⊢ ⬈[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: â\88\80h,G,Y1,Y2. â¦\83G,Y1â¦\84 ⊢ ⬈[h,#0] Y2 →
+lemma rpx_inv_zero_length: â\88\80h,G,Y1,Y2. â\9dªG,Y1â\9d« ⊢ ⬈[h,#0] Y2 →
∨∨ ∧∧ Y1 = ⋆ & Y2 = ⋆
- | â\88\83â\88\83I,L1,L2,V1,V2. â¦\83G,L1â¦\84 ⊢ ⬈[h,V1] L2 &
- â¦\83G,L1â¦\84 ⊢ V1 ⬈[h] V2 &
- Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2
- | ∃∃I,L1,L2. |L1| = |L2| & Y1 = L1.ⓤ{I} & Y2 = L2.ⓤ{I}.
+ | â\88\83â\88\83I,L1,L2,V1,V2. â\9dªG,L1â\9d« ⊢ ⬈[h,V1] L2 &
+ â\9dªG,L1â\9d« ⊢ 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-.