1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "static_2/static/rex_length.ma".
16 include "basic_2/rt_transition/rpx.ma".
18 (* EXTENDED PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS **********)
20 (* Forward lemmas with length for local environments ************************)
22 lemma rpx_fwd_length (G):
23 ∀L1,L2,T. ❪G,L1❫ ⊢ ⬈[T] L2 → |L1| = |L2|.
24 /2 width=3 by rex_fwd_length/ qed-.
26 (* Inversion lemmas with length for local environments **********************)
28 lemma rpx_inv_zero_length (G):
29 ∀Y1,Y2. ❪G,Y1❫ ⊢ ⬈[#0] Y2 →
31 | ∃∃I,L1,L2,V1,V2. ❪G,L1❫ ⊢ ⬈[V1] L2 & ❪G,L1❫ ⊢ V1 ⬈ V2 & Y1 = L1.ⓑ[I]V1 & Y2 = L2.ⓑ[I]V2
32 | ∃∃I,L1,L2. |L1| = |L2| & Y1 = L1.ⓤ[I] & Y2 = L2.ⓤ[I].
33 /2 width=1 by rex_inv_zero_length/ qed-.