milestone update in ground_2 and basic_2A

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/etc/fpr/fpr.etc b/matita/matita/contribs/lambdadelta/basic_2A/etc/fpr/fpr.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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+notation "hvbox( ⦃ term 46 L1, break term 46 T1 ⦄ ➡ break ⦃ term 46 L2 , break term 46 T2 ⦄ )"
+   non associative with precedence 45
+   for @{ 'FocalizedPRed $L1 $T1 $L2 $T2 }.
+
+include "basic_2/reducibility/tpr.ma".
+
+(* CONTEXT-FREE PARALLEL REDUCTION ON CLOSURES ******************************)
+
+definition fpr: bi_relation lenv term ≝
+                λL1,T1,L2,T2. |L1| = |L2| ∧ L1 @@ T1 ➡ L2 @@ T2.
+
+interpretation
+   "context-free parallel reduction (closure)"
+   'FocalizedPRed L1 T1 L2 T2 = (fpr L1 T1 L2 T2).
+
+(* Basic properties *********************************************************)
+
+lemma fpr_refl: bi_reflexive … fpr.
+/2 width=1/ qed.
+
+lemma fpr_shift: ∀I1,I2,L1,L2,V1,V2,T1,T2.
+                 ⦃L1, -ⓑ{I1}V1.T1⦄ ➡ ⦃L2, -ⓑ{I2}V2.T2⦄ →
+                 ⦃L1.ⓑ{I1}V1, T1⦄ ➡ ⦃L2.ⓑ{I2}V2, T2⦄.
+#I1 #I2 #L1 #L2 #V1 #V2 #T1 #T2 * #HL12 #HT12
+@conj // normalize // (**) (* explicit constructor *)
+qed.
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma fpr_inv_atom1: ∀L2,T1,T2. ⦃⋆, T1⦄ ➡ ⦃L2, T2⦄ → T1 ➡ T2 ∧ L2 = ⋆.
+#L2 #T1 #T2 * #H
+lapply (length_inv_zero_sn … H) -H #H destruct /2 width=1/
+qed-.
+
+lemma fpr_inv_atom3: ∀L1,T1,T2. ⦃L1,T1⦄ ➡ ⦃⋆,T2⦄ → T1 ➡ T2 ∧ L1 = ⋆.
+#L1 #T1 #T2 * #H
+lapply (length_inv_zero_dx … H) -H #H destruct /2 width=1/
+qed-.
+
+(* Basic forward lemmas *****************************************************)
+
+lemma fpr_fwd_pair1: ∀I1,K1,L2,V1,T1,T2. ⦃K1.ⓑ{I1}V1, T1⦄ ➡ ⦃L2, T2⦄ →
+                     ∃∃I2,K2,V2. ⦃K1, -ⓑ{I1}V1.T1⦄ ➡ ⦃K2, -ⓑ{I2}V2.T2⦄  &
+                                 L2 = K2.ⓑ{I2}V2.
+#I1 #K1 #L2 #V1 #T1 #T2 * #H
+elim (length_inv_pos_sn … H) -H #I2 #K2 #V2 #HK12 #H destruct /3 width=5/
+qed-.
+
+lemma fpr_fwd_pair3: ∀I2,L1,K2,V2,T1,T2. ⦃L1, T1⦄ ➡ ⦃K2.ⓑ{I2}V2, T2⦄ →
+                     ∃∃I1,K1,V1. ⦃K1, -ⓑ{I1}V1.T1⦄ ➡ ⦃K2, -ⓑ{I2}V2.T2⦄  &
+                                 L1 = K1.ⓑ{I1}V1.
+#I2 #L1 #K2 #V2 #T1 #T2 * #H
+elim (length_inv_pos_dx … H) -H #I1 #K1 #V1 #HK12 #H destruct /3 width=5/
+qed-.