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_drops.ma".
16 include "basic_2/rt_transition/cpx_drops.ma".
17 include "basic_2/rt_transition/rpx.ma".
19 (* EXTENDED PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS **********)
21 (* Properties with generic slicing for local environments *******************)
23 lemma rpx_lifts_sn (G): f_dedropable_sn (cpx G).
24 /3 width=6 by rex_liftable_dedropable_sn, cpx_lifts_sn/ qed-.
26 (* Inversion lemmas with generic slicing for local environments *************)
28 lemma rpx_inv_lifts_sn (G): f_dropable_sn (cpx G).
29 /2 width=5 by rex_dropable_sn/ qed-.
31 lemma rpx_inv_lifts_dx (G): f_dropable_dx (cpx G).
32 /2 width=5 by rex_dropable_dx/ qed-.
34 lemma rpx_inv_lifts_bi (G):
35 ∀L1,L2,U. ❪G,L1❫ ⊢ ⬈[U] L2 → ∀b,f. 𝐔❪f❫ →
36 ∀K1,K2. ⇩*[b,f] L1 ≘ K1 → ⇩*[b,f] L2 ≘ K2 →
37 ∀T. ⇧*[f]T ≘ U → ❪G,K1❫ ⊢ ⬈[T] K2.
38 /2 width=10 by rex_inv_lifts_bi/ qed-.