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 *)
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15 include "static_2/static/reqx_req.ma".
16 include "basic_2/rt_transition/rpx_reqx.ma".
17 include "basic_2/rt_transition/rpx_lpx.ma".
19 (* EXTENDED PARALLEL RT-TRANSITION FOR FULL LOCAL ENVIRONMENTS **************)
21 (* Properties with sort-irrelevant equivalence for local environments *******)
23 (**) (* to update as reqx_rpx_trans *)
24 (* Basic_2A1: uses: lleq_lpx_trans *)
25 lemma reqx_lpx_trans (G):
26 ∀L2,K2. ❪G,L2❫ ⊢ ⬈ K2 → ∀L1. ∀T:term. L1 ≛[T] L2 →
27 ∃∃K1. ❪G,L1❫ ⊢ ⬈ K1 & K1 ≛[T] K2.
28 #G #L2 #K2 #HLK2 #L1 #T #HL12
29 lapply (lpx_rpx … T HLK2) -HLK2 #HLK2
30 lapply (reqx_rpx_trans … HL12 … HLK2) -L2 #H
31 elim (rpx_inv_lpx_req … H) -H #K1 #HLK1 #HK12
32 /3 width=3 by req_reqx, ex2_intro/