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-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
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-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-include "basic_2/notation/relations/predsnstaralt_5.ma".
-include "basic_2/computation/cpxs_cpxs.ma".
-include "basic_2/computation/lpxs.ma".
-
-(* SN EXTENDED PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS *******************)
-
-(* alternative definition *)
-definition lpxsa: ∀h. sd h → relation3 genv lenv lenv ≝
- λh,g,G. lpx_sn … (cpxs h g G).
-
-interpretation "extended parallel computation (local environment, sn variant) alternative"
- 'PRedSnStarAlt h g G L1 L2 = (lpxsa h g G L1 L2).
-
-(* Main properties on the alternative definition ****************************)
-
-theorem lpxsa_lpxs: ∀h,g,G,L1,L2. ⦃G, L1⦄ ⊢ ➡➡*[h, g] L2 → ⦃G, L1⦄ ⊢ ➡*[h, g] L2.
-/2 width=1 by lpx_sn_LTC_TC_lpx_sn/ qed-.
-
-(* Main inversion lemmas on the alternative definition **********************)
-
-theorem lpxs_inv_lpxsa: ∀h,g,G,L1,L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → ⦃G, L1⦄ ⊢ ➡➡*[h, g] L2.
-/3 width=3 by TC_lpx_sn_inv_lpx_sn_LTC, lpx_cpxs_trans/ qed-.
-
-(* Alternative eliminators **************************************************)
-
-lemma lpxs_ind_alt: ∀h,g,G. ∀R:relation lenv.
- R (⋆) (⋆) → (
- ∀I,K1,K2,V1,V2.
- ⦃G, K1⦄ ⊢ ➡*[h, g] K2 → ⦃G, K1⦄ ⊢ V1 ➡*[h, g] V2 →
- R K1 K2 → R (K1.ⓑ{I}V1) (K2.ⓑ{I}V2)
- ) →
- ∀L1,L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → R L1 L2.
-/3 width=4 by TC_lpx_sn_ind, lpx_cpxs_trans/ qed-.