milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / etc / llpr / llpr.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/etc/llpr/llpr.etc b/matita/matita/contribs/lambdadelta/basic_2A/etc/llpr/llpr.etc
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/notation/relations/lazypredsn_5.ma".
+include "basic_2/relocation/llpx_sn.ma".
+include "basic_2/reduction/cpr.ma".
+
+(* LAZY SN PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS ************************)
+
+definition llpr: genv → relation4 ynat term lenv lenv ≝ λG. llpx_sn (cpr G).
+
+interpretation "lazy parallel reduction (local environment, sn variant)"
+   'LazyPRedSn G L1 L2 T d = (llpr G d T L1 L2).
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma llpr_inv_flat: ∀I,G,L1,L2,V,T,d. ⦃G, L1⦄ ⊢ ➡[ⓕ{I}V.T, d] L2 →
+                     ⦃G, L1⦄ ⊢ ➡[V, d] L2 ∧ ⦃G, L1⦄ ⊢ ➡[T, d] L2.
+/2 width=2 by llpx_sn_inv_flat/ qed-.
+
+(* Basic forward lemmas *****************************************************)
+
+lemma llpr_fwd_length: ∀G,L1,L2,T,d. ⦃G, L1⦄ ⊢ ➡[T, d] L2 → |L1| = |L2|.
+/2 width=4 by llpx_sn_fwd_length/ qed-.
+
+(* Basic properties *********************************************************)
+
+lemma llpr_lref: ∀I,G,L1,L2,K1,K2,V1,V2,d,i. d ≤ yinj i →
+                 ⇩[i] L1 ≡ K1.ⓑ{I}V1 → ⇩[i] L2 ≡ K2.ⓑ{I}V2 →
+                 ⦃G, K1⦄ ⊢ ➡[V1, 0] K2 → ⦃G, K1⦄ ⊢ V1 ➡ V2 → ⦃G, L1⦄ ⊢ ➡[#i, d] L2.
+/2 width=9 by llpx_sn_lref/ qed.
+
+(* Note: lemma 250 *)
+lemma llpr_refl: ∀G,T,d. reflexive … (llpr G d T).
+/2 width=1 by llpx_sn_refl/ qed.
+
+(* Basic_1: removed theorems 5: wcpr0_gen_sort wcpr0_gen_head
+                                wcpr0_getl wcpr0_getl_back
+                                pr0_subst1_back
+*)