update in ground_2 static_2 basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc / cpue / cnv_cpue.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/cpue/cnv_cpue.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/cpue/cnv_cpue.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 "basic_2/rt_computation/cpms_cnu.ma".
+include "basic_2/rt_computation/cpue.ma".
+include "basic_2/dynamic/cnv_preserve.ma".
+
+(* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
+
+(* Properties with evaluation for t-unbound rt-transition on terms **********)
+
+lemma cnv_cpue_trans (a) (h) (G) (L):
+      ∀T1. ⦃G,L⦄ ⊢ T1 ![a,h] →
+      ∀T2. ⦃G,L⦄ ⊢ T1 ⥲*[h] 𝐍⦃T2⦄ → ⦃G,L⦄ ⊢ T2 ![a,h].
+#a #h #G #L #T1 #HT1 #T2 * #n #HT12 #_
+/2 width=4 by cnv_cpms_trans/
+qed-.
+
+lemma cnv_cpue_cpms_conf (a) (h) (n) (G) (L):
+      ∀T0. ⦃G,L⦄ ⊢ T0 ![a,h] → ∀T1. ⦃G,L⦄ ⊢ T0 ➡*[n,h] T1 →
+      ∀T2. ⦃G,L⦄ ⊢ T0 ⥲*[h] 𝐍⦃T2⦄ →
+      ∃∃T. ⦃G,L⦄ ⊢ T1 ⥲*[h] 𝐍⦃T⦄ & T2 ≅ T.
+#a #h #n1 #G #L #T0 #HT0 #T1 #HT01 #T2 * #n2 #HT02 #HT2
+elim (cnv_cpms_conf … HT0 … HT01 … HT02) -T0 #T0 #HT10 #HT20
+lapply (cpms_inv_cnu_sn … HT20 HT2) -HT20 #HT20
+/4 width=8 by cnu_tueq_trans, ex2_intro/
+qed-.
+
+(* Main properties with evaluation for t-unbound rt-transition on terms *****)
+
+theorem cnv_cpue_mono (a) (h) (G) (L):
+        ∀T0. ⦃G,L⦄ ⊢ T0 ![a,h] → ∀T1. ⦃G,L⦄ ⊢ T0 ⥲*[h] 𝐍⦃T1⦄ →
+        ∀T2. ⦃G,L⦄ ⊢ T0 ⥲*[h] 𝐍⦃T2⦄ → T1 ≅ T2.
+#a #h #G #L #T0 #HT0 #T1 * #n1 #HT01 #HT1 #T2 * #n2 #HT02 #HT2
+elim (cnv_cpms_conf … HT0 … HT01 … HT02) -T0 #T0 #HT10 #HT20
+/3 width=8 by cpms_inv_cnu_sn, tueq_canc_dx/
+qed-.