Merge branch 'matita-lablgtk3' of ssh://matita.cs.unibo.it:/srv/git/helm into matita...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / cnv_cpes.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpes.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpes.ma
new file mode 100644 (file)
index 0000000..fbf407f
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpes.ma
@@ -0,0 +1,76 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_cpms.ma".
+include "basic_2/rt_equivalence/cpes.ma".
+include "basic_2/dynamic/cnv.ma".
+
+(* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
+
+(* Properties with t-bound rt-equivalence for terms *************************)
+
+lemma cnv_appl_cpes (h) (a) (G) (L):
+      ∀n. ad a n →
+      ∀V. ⦃G,L⦄ ⊢ V ![h,a] → ∀T. ⦃G,L⦄ ⊢ T ![h,a] →
+      ∀W. ⦃G,L⦄ ⊢ V ⬌*[h,1,0] W →
+      ∀p,U. ⦃G,L⦄ ⊢ T ➡*[n,h] ⓛ{p}W.U → ⦃G,L⦄ ⊢ ⓐV.T ![h,a].
+#h #a #G #L #n #Hn #V #HV #T #HT #W *
+/4 width=11 by cnv_appl, cpms_cprs_trans, cpms_bind/
+qed.
+
+lemma cnv_cast_cpes (h) (a) (G) (L):
+      ∀U. ⦃G,L⦄ ⊢ U ![h,a] →
+      ∀T. ⦃G,L⦄ ⊢ T ![h,a] → ⦃G,L⦄ ⊢ U ⬌*[h,0,1] T → ⦃G,L⦄ ⊢ ⓝU.T ![h,a].
+#h #a #G #L #U #HU #T #HT * /2 width=3 by cnv_cast/
+qed.
+
+(* Inversion lemmas with t-bound rt-equivalence for terms *******************)
+
+lemma cnv_inv_appl_cpes (h) (a) (G) (L):
+      ∀V,T. ⦃G,L⦄ ⊢ ⓐV.T ![h,a] →
+      ∃∃n,p,W,U. ad a n & ⦃G,L⦄ ⊢ V ![h,a] & ⦃G,L⦄ ⊢ T ![h,a] &
+                 ⦃G,L⦄ ⊢ V ⬌*[h,1,0] W & ⦃G,L⦄ ⊢ T ➡*[n,h] ⓛ{p}W.U.
+#h #a #G #L #V #T #H
+elim (cnv_inv_appl … H) -H #n #p #W #U #Hn #HV #HT #HVW #HTU
+/3 width=7 by cpms_div, ex5_4_intro/
+qed-.
+
+lemma cnv_inv_cast_cpes (h) (a) (G) (L):
+      ∀U,T. ⦃G,L⦄ ⊢ ⓝU.T ![h,a] →
+      ∧∧ ⦃G,L⦄ ⊢ U ![h,a] & ⦃G,L⦄ ⊢ T ![h,a] & ⦃G,L⦄ ⊢ U ⬌*[h,0,1] T.
+#h #a #G #L #U #T #H
+elim (cnv_inv_cast … H) -H
+/3 width=3 by cpms_div, and3_intro/
+qed-.
+
+(* Eliminators with t-bound rt-equivalence for terms ************************)
+
+lemma cnv_ind_cpes (h) (a) (Q:relation3 genv lenv term):
+      (∀G,L,s. Q G L (⋆s)) →
+      (∀I,G,K,V. ⦃G,K⦄ ⊢ V![h,a] → Q G K V → Q G (K.ⓑ{I}V) (#O)) →
+      (∀I,G,K,i. ⦃G,K⦄ ⊢ #i![h,a] → Q G K (#i) → Q G (K.ⓘ{I}) (#(↑i))) →
+      (∀p,I,G,L,V,T. ⦃G,L⦄ ⊢ V![h,a] → ⦃G,L.ⓑ{I}V⦄⊢T![h,a] →
+                     Q G L V →Q G (L.ⓑ{I}V) T →Q G L (ⓑ{p,I}V.T)
+      ) →
+      (∀n,p,G,L,V,W,T,U. ad a n → ⦃G,L⦄ ⊢ V![h,a] → ⦃G,L⦄ ⊢ T![h,a] →
+                         ⦃G,L⦄ ⊢ V ⬌*[h,1,0]W → ⦃G,L⦄ ⊢ T ➡*[n,h] ⓛ{p}W.U →
+                         Q G L V → Q G L T → Q G L (ⓐV.T)
+      ) →
+      (∀G,L,U,T. ⦃G,L⦄⊢ U![h,a] → ⦃G,L⦄ ⊢ T![h,a] → ⦃G,L⦄ ⊢ U ⬌*[h,0,1] T →
+                 Q G L U → Q G L T → Q G L (ⓝU.T)
+      ) →
+      ∀G,L,T. ⦃G,L⦄⊢ T![h,a] → Q G L T.
+#h #a #Q #IH1 #IH2 #IH3 #IH4 #IH5 #IH6 #G #L #T #H
+elim H -G -L -T [5,6: /3 width=7 by cpms_div/ |*: /2 width=1 by/ ]
+qed-.