(* Forward lemmas with length for local environments ************************)
lemma rpx_fwd_length (G):
- â\88\80L1,L2,T. â\9dªG,L1â\9d« ⊢ ⬈[T] L2 → |L1| = |L2|.
+ â\88\80L1,L2,T. â\9d¨G,L1â\9d© ⊢ ⬈[T] L2 → |L1| = |L2|.
/2 width=3 by rex_fwd_length/ qed-.
(* Inversion lemmas with length for local environments **********************)
lemma rpx_inv_zero_length (G):
- â\88\80Y1,Y2. â\9dªG,Y1â\9d« ⊢ ⬈[#0] Y2 →
+ â\88\80Y1,Y2. â\9d¨G,Y1â\9d© ⊢ ⬈[#0] Y2 →
∨∨ ∧∧ Y1 = ⋆ & Y2 = ⋆
- | â\88\83â\88\83I,L1,L2,V1,V2. â\9dªG,L1â\9d« â\8a¢ â¬\88[V1] L2 & â\9dªG,L1â\9d« ⊢ V1 ⬈ V2 & Y1 = L1.ⓑ[I]V1 & Y2 = L2.ⓑ[I]V2
+ | â\88\83â\88\83I,L1,L2,V1,V2. â\9d¨G,L1â\9d© â\8a¢ â¬\88[V1] L2 & â\9d¨G,L1â\9d© ⊢ V1 ⬈ 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-.