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_lex.ma".
16 include "basic_2/rt_transition/rpx_fsle.ma".
17 include "basic_2/rt_transition/lpx.ma".
19 (* UNBOUND PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS ***********)
21 (* Properties with syntactic equivalence for referred local environments ****)
23 lemma fleq_rpx (h) (G): ∀L1,L2,T. L1 ≡[T] L2 → ⦃G, L1⦄ ⊢ ⬈[h, T] L2.
24 /2 width=1 by req_fwd_rex/ qed.
26 (* Properties with unbound parallel rt-transition for full local envs *******)
28 lemma lpx_rpx: ∀h,G,L1,L2,T. ⦃G, L1⦄ ⊢ ⬈[h] L2 → ⦃G, L1⦄ ⊢ ⬈[h, T] L2.
29 /2 width=1 by rex_lex/ qed.
31 (* Inversion lemmas with unbound parallel rt-transition for full local envs *)
33 lemma rpx_inv_lpx_req: ∀h,G,L1,L2,T. ⦃G, L1⦄ ⊢ ⬈[h, T] L2 →
34 ∃∃L. ⦃G, L1⦄ ⊢ ⬈[h] L & L ≡[T] L2.
35 /3 width=3 by rpx_fsge_comp, rex_inv_lex_req/ qed-.