From bbb6dd07ecb430bf06bb52c2506626106449a5af Mon Sep 17 00:00:00 2001
From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Tue, 6 Nov 2018 10:57:00 +0100
Subject: [PATCH] update in basic_2

+ lpce
---
 .../basic_2/notation/relations/pconveta_4.ma  | 19 +++++
 .../lambdadelta/basic_2/rt_conversion/lpce.ma | 69 +++++++++++++++++++
 .../lambdadelta/basic_2/web/basic_2_src.tbl   |  1 +
 3 files changed, 89 insertions(+)
 create mode 100644 matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconveta_4.ma
 create mode 100644 matita/matita/contribs/lambdadelta/basic_2/rt_conversion/lpce.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconveta_4.ma b/matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconveta_4.ma
new file mode 100644
index 000000000..ba25a067b
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/notation/relations/pconveta_4.ma
@@ -0,0 +1,19 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* NOTATION FOR THE FORMAL SYSTEM λδ ****************************************)
+
+notation "hvbox( ⦃ term 46 G, break term 46 L1 ⦄ ⊢ ⬌η[ break term 46 h ] break term 46 L2 )"
+   non associative with precedence 45
+   for @{ 'PConvEta $h $G $L1 $L2 }.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_conversion/lpce.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_conversion/lpce.ma
new file mode 100644
index 000000000..8aca0e26b
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_conversion/lpce.ma
@@ -0,0 +1,69 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "static_2/relocation/lex.ma".
+include "basic_2/notation/relations/pconveta_4.ma".
+include "basic_2/rt_conversion/cpce.ma".
+
+(* PARALLEL ETA-CONVERSION FOR FULL LOCAL ENVIRONMENTS **********************)
+
+definition lpce (h) (G): relation lenv ≝ lex (cpce h G).
+
+interpretation
+  "parallel eta-conversion on all entries (local environment)"
+  'PConvEta h G L1 L2 = (lpce h G L1 L2).
+
+(* Advanced properties ******************************************************)
+
+lemma lpce_pair (h) (G):
+      ∀K1,K2,V1,V2. ⦃G,K1⦄ ⊢ ⬌η[h] K2 → ⦃G,K1⦄ ⊢ V1 ⬌η[h] V2 →
+      ∀I. ⦃G,K1.ⓑ{I}V1⦄ ⊢ ⬌η[h] K2.ⓑ{I}V2.
+/2 width=1 by lex_pair/ qed.
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma lpce_inv_atom_sn (h) (G):
+      ∀L2. ⦃G,⋆⦄ ⊢ ⬌η[h] L2 → L2 = ⋆.
+/2 width=2 by lex_inv_atom_sn/ qed-.
+
+lemma lpce_inv_atom_dx (h) (G):
+      ∀L1. ⦃G,L1⦄ ⊢ ⬌η[h] ⋆ → L1 = ⋆.
+/2 width=2 by lex_inv_atom_dx/ qed-.
+
+(* Advanced inversion lemmas ************************************************)
+
+lemma lpce_inv_unit_sn (h) (G):
+      ∀I,L2,K1. ⦃G,K1.ⓤ{I}⦄ ⊢ ⬌η[h] L2 →
+      ∃∃K2. ⦃G, K1⦄ ⊢ ⬌η[h] K2 & L2 = K2.ⓤ{I}.
+/2 width=1 by lex_inv_unit_sn/ qed-.
+
+lemma lpce_inv_pair_sn (h) (G):
+      ∀I,L2,K1,V1. ⦃G,K1.ⓑ{I}V1⦄ ⊢ ⬌η[h] L2 →
+      ∃∃K2,V2. ⦃G,K1⦄ ⊢ ⬌η[h] K2 & ⦃G,K1⦄ ⊢ V1 ⬌η[h] V2 & L2 = K2.ⓑ{I}V2.
+/2 width=1 by lex_inv_pair_sn/ qed-.
+
+lemma lpce_inv_unit_dx (h) (G):
+      ∀I,L1,K2. ⦃G,L1⦄ ⊢ ⬌η[h] K2.ⓤ{I} →
+      ∃∃K1. ⦃G,K1⦄ ⊢ ⬌η[h] K2 & L1 = K1.ⓤ{I}.
+/2 width=1 by lex_inv_unit_dx/ qed-.
+
+lemma lpce_inv_pair_dx (h) (G):
+      ∀I,L1,K2,V2. ⦃G,L1⦄ ⊢ ⬌η[h] K2.ⓑ{I}V2 →
+      ∃∃K1,V1. ⦃G,K1⦄ ⊢ ⬌η[h] K2 & ⦃G,K1⦄ ⊢ V1 ⬌η[h] V2 & L1 = K1.ⓑ{I}V1.
+/2 width=1 by lex_inv_pair_dx/ qed-.
+
+lemma lpce_inv_pair (h) (G):
+      ∀I1,I2,L1,L2,V1,V2. ⦃G,L1.ⓑ{I1}V1⦄ ⊢ ⬌η[h] L2.ⓑ{I2}V2 →
+      ∧∧ ⦃G,L1⦄ ⊢ ⬌η[h] L2 & ⦃G,L1⦄ ⊢ V1 ⬌η[h] V2 & I1 = I2.
+/2 width=1 by lex_inv_pair/ qed-.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
index 236b4f999..8cd2fd30f 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
+++ b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
@@ -41,6 +41,7 @@ table {
    class "blue"
    [ { "rt-conversion" * } {
         [ { "context-sensitive parallel eta-conversion" * } {
+             [ [ "for lenvs on all entries" ] "lpce ( ⦃?,?⦄ ⊢ ⬌η[?] ? )" * ]
              [ [ "for terms" ] "cpce" + "( ⦃?,?⦄ ⊢ ? ⬌η[?] ? )" * ]
           }
         ]
-- 
2.39.2