update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc / cpce / lpce.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/cpce/lpce.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/cpce/lpce.etc
new file mode 100644 (file)
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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 "static_2/relocation/lex.ma".
+include "basic_2/notation/relations/pconveta_4.ma".
+include "basic_2/rt_conversion/cpce_ext.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).
+
+(* Basic properties *********************************************************)
+
+lemma lpce_bind (h) (G):
+      ∀K1,K2. ⦃G,K1⦄ ⊢ ⬌η[h] K2 →
+      ∀I1,I2. ⦃G,K1⦄ ⊢ I1 ⬌η[h] I2 → ⦃G,K1.ⓘ{I1}⦄ ⊢ ⬌η[h] K2.ⓘ{I2}.
+/2 width=1 by lex_bind/ qed.
+
+(* 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_bind_sn (h) (G):
+      ∀I1,L2,K1. ⦃G,K1.ⓘ{I1}⦄ ⊢ ⬌η[h] L2 →
+      ∃∃I2,K2. ⦃G,K1⦄ ⊢ ⬌η[h] K2 & ⦃G,K1⦄ ⊢ I1 ⬌η[h] I2 & L2 = K2.ⓘ{I2}.
+/2 width=1 by lex_inv_bind_sn/ qed-.
+
+lemma lpce_inv_atom_dx (h) (G):
+      ∀L1. ⦃G,L1⦄ ⊢ ⬌η[h] ⋆ → L1 = ⋆.
+/2 width=2 by lex_inv_atom_dx/ qed-.
+
+lemma lpce_inv_bind_dx (h) (G):
+      ∀I2,L1,K2. ⦃G,L1⦄ ⊢ ⬌η[h] K2.ⓘ{I2} →
+      ∃∃I1,K1. ⦃G,K1⦄ ⊢ ⬌η[h] K2 & ⦃G,K1⦄ ⊢ I1 ⬌η[h] I2 & L1 = K1.ⓘ{I1}.
+/2 width=1 by lex_inv_bind_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-.