update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / lprs_lpr.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs_lpr.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs_lpr.ma
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs_lpr.ma
@@ -0,0 +1,48 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "basic_2/relocation/lex_tc.ma".
+include "basic_2/rt_computation/cprs_lpr.ma".
+include "basic_2/rt_computation/lprs.ma".
+
+(* PARALLEL R-COMPUTATION FOR FULL LOCAL ENVIRONMENTS ***********************)
+
+(* Eliminators with r-transition for full local environments ****************)
+
+(* Basic_2A1: was: lprs_ind_dx *)
+lemma lprs_ind_sn (h) (G) (L2): ∀R:predicate lenv. R L2 →
+                                (∀L1,L. ⦃G, L1⦄ ⊢ ➡[h] L → ⦃G, L⦄ ⊢ ➡*[h] L2 → R L → R L1) →
+                                ∀L1. ⦃G, L1⦄ ⊢ ➡*[h] L2 → R L1.
+/3 width=7 by lpr_cprs_trans, cpr_refl, lex_CTC_ind_sn/ qed-.
+
+(* Basic_2A1: was: lprs_ind *)
+lemma lprs_ind_dx (h) (G) (L1): ∀R:predicate lenv. R L1 →
+                                (∀L,L2. ⦃G, L1⦄ ⊢ ➡*[h] L → ⦃G, L⦄ ⊢ ➡[h] L2 → R L → R L2) →
+                                ∀L2. ⦃G, L1⦄ ⊢ ➡*[h] L2 → R L2.
+/3 width=7 by lpr_cprs_trans, cpr_refl, lex_CTC_ind_dx/ qed-.
+
+(* Properties with unbound rt-transition for full local environments ********)
+
+lemma lpr_lprs (h) (G): ∀L1,L2. ⦃G, L1⦄ ⊢ ➡[h] L2 → ⦃G, L1⦄ ⊢ ➡*[h] L2.
+/3 width=3 by lpr_cprs_trans, lex_CTC_inj/ qed.
+
+(* Basic_2A1: was: lprs_strap2 *)
+lemma lprs_step_sn (h) (G): ∀L1,L. ⦃G, L1⦄ ⊢ ➡[h] L →
+                            ∀L2.⦃G, L⦄ ⊢ ➡*[h] L2 → ⦃G, L1⦄ ⊢ ➡*[h] L2.
+/3 width=3 by lpr_cprs_trans, lex_CTC_step_sn/ qed-.
+
+(* Basic_2A1: was: lpxs_strap1 *)
+lemma lprs_step_dx (h) (G): ∀L1,L. ⦃G, L1⦄ ⊢ ➡*[h] L →
+                            ∀L2. ⦃G, L⦄ ⊢ ➡[h] L2 → ⦃G, L1⦄ ⊢ ➡*[h] L2.
+/3 width=3 by lpr_cprs_trans, lex_CTC_step_dx/ qed-.