milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / etc / cpr / ltpr.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/etc/cpr/ltpr.etc b/matita/matita/contribs/lambdadelta/basic_2A/etc/cpr/ltpr.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/grammar/lenv_px.ma".
+include "basic_2/reducibility/tpr.ma".
+
+(* CONTEXT-FREE PARALLEL REDUCTION ON LOCAL ENVIRONMENTS ********************)
+
+definition ltpr: relation lenv ≝ lpx tpr.
+
+interpretation
+  "context-free parallel reduction (environment)"
+  'PRed L1 L2 = (ltpr L1 L2).
+
+(* Basic properties *********************************************************)
+
+lemma ltpr_refl: reflexive … ltpr.
+/2 width=1/ qed.
+
+lemma ltpr_append: ∀K1,K2. K1 ➡ K2 → ∀L1,L2:lenv. L1 ➡ L2 → K1 @@ L1 ➡ K2 @@ L2.
+/2 width=1/ qed.
+
+(* Basic inversion lemmas ***************************************************)
+
+(* Basic_1: was: wcpr0_gen_sort *)
+lemma ltpr_inv_atom1: ∀L2. ⋆ ➡ L2 → L2 = ⋆.
+/2 width=2 by lpx_inv_atom1/ qed-.
+
+(* Basic_1: was: wcpr0_gen_head *)
+lemma ltpr_inv_pair1: ∀K1,I,V1,L2. K1. ⓑ{I} V1 ➡ L2 →
+                      ∃∃K2,V2. K1 ➡ K2 & V1 ➡ V2 & L2 = K2. ⓑ{I} V2.
+/2 width=1 by lpx_inv_pair1/ qed-.
+
+lemma ltpr_inv_atom2: ∀L1. L1 ➡ ⋆ → L1 = ⋆.
+/2 width=2 by lpx_inv_atom2/ qed-.
+
+lemma ltpr_inv_pair2: ∀L1,K2,I,V2. L1 ➡ K2. ⓑ{I} V2 →
+                      ∃∃K1,V1. K1 ➡ K2 & V1 ➡ V2 & L1 = K1. ⓑ{I} V1.
+/2 width=1 by lpx_inv_pair2/ qed-.
+
+(* Basic forward lemmas *****************************************************)
+
+lemma ltpr_fwd_length: ∀L1,L2. L1 ➡ L2 → |L1| = |L2|.
+/2 width=2 by lpx_fwd_length/ qed-.
+
+(* Advanced inversion lemmas ************************************************)
+
+lemma ltpr_inv_append1: ∀K1,L1. ∀L:lenv. K1 @@ L1 ➡ L →
+                        ∃∃K2,L2. K1 ➡ K2 & L1 ➡ L2 & L = K2 @@ L2.
+/2 width=1 by lpx_inv_append1/ qed-.
+
+lemma ltpr_inv_append2: ∀L:lenv. ∀K2,L2. L ➡ K2 @@ L2 →
+                        ∃∃K1,L1. K1 ➡ K2 & L1 ➡ L2 & L = K1 @@ L1.
+/2 width=1 by lpx_inv_append2/ qed-.
+
+(* Basic_1: removed theorems 2: wcpr0_getl wcpr0_getl_back *)