milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / etc / xpr / xpr_lift.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/etc/xpr/xpr_lift.etc b/matita/matita/contribs/lambdadelta/basic_2A/etc/xpr/xpr_lift.etc
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/basic_2A/etc/xpr/xpr_lift.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/static/ssta_lift.ma".
+include "basic_2/reducibility/cpr_lift.ma".
+include "basic_2/reducibility/xpr.ma".
+
+(* EXTENDED PARALLEL REDUCTION ON TERMS *************************************)
+
+(* Advanced inversion lemmas ************************************************)
+
+lemma xpr_inv_abst1: ∀h,g,a,L,V1,T1,U2. ⦃h, L⦄ ⊢ ⓛ{a}V1.T1 •➡[g] U2 →
+                     ∃∃V2,T2. L ⊢ V1 ➡ V2 & ⦃h, L. ⓛV1⦄ ⊢ T1 •➡[g] T2 &
+                              U2 = ⓛ{a}V2. T2.
+#h #g #a #L #V1 #T1 #U2 *
+[ #H elim (cpr_inv_abst1 … H Abst V1) /3 width=5/
+| #l #H elim (ssta_inv_bind1 … H) /3 width=5/
+]
+qed-.
+
+(* Relocation properties ****************************************************)
+
+lemma xpr_lift: ∀L,K,d,e. ⇩[d, e] L ≡ K →
+                ∀T1,U1. ⇧[d, e] T1 ≡ U1 → ∀T2,U2. ⇧[d, e] T2 ≡ U2 →
+                ∀h,g. ⦃h, K⦄ ⊢ T1 •➡[g] T2 → ⦃h, L⦄ ⊢ U1 •➡[g] U2.
+#L #K #d #e #HLK #T1 #U1 #HTU1 #T2 #U2 #HTU2 #h #g *
+/3 width=9/ /3 width=10/
+qed.
+
+lemma xpr_inv_lift1: ∀L,K,d,e. ⇩[d, e] L ≡ K →
+                     ∀T1,U1. ⇧[d, e] T1 ≡ U1 → ∀h,g,U2. ⦃h, L⦄ ⊢ U1 •➡[g] U2 →
+                     ∃∃T2. ⇧[d, e] T2 ≡ U2 & ⦃h, K⦄ ⊢ T1 •➡[g] T2.
+#L #K #d #e #HLK #T1 #U1 #HTU1 #h #g #U2 * [ #HU12 | #l #HU12 ]
+[ elim (cpr_inv_lift1 … HLK … HTU1 … HU12) -L -U1 /3 width=3/
+| elim (ssta_inv_lift1 … HU12 … HLK … HTU1) -L -U1 /3 width=4/
+]
+qed-.