- main proof case closed in the 4th component of preservation

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc / lsubss / lsubss_lsubss.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/lsubss/lsubss_lsubss.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/lsubss/lsubss_lsubss.etc
new file mode 100644 (file)
index 0000000..d9f9496
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/etc/lsubss/lsubss_lsubss.etc
@@ -0,0 +1,36 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/lsubss_ssta.ma".
+
+(* LOCAL ENVIRONMENT REFINEMENT FOR STATIC TYPE ASSIGNMENT ******************)
+
+(* Main properties **********************************************************)
+
+theorem lsubss_trans: ∀h,g,L1,L. h ⊢ L1 •⊑[g] L → ∀L2. h ⊢ L •⊑[g] L2 →
+                      h ⊢ L1 •⊑[g] L2.
+#h #g #L1 #L #H elim H -L1 -L
+[ #X #H >(lsubss_inv_atom1 … H) -H //
+| #I #L1 #L #W #HL1 #IHL1 #X #H
+  elim (lsubss_inv_pair1 … H) -H * #L2
+  [ #HL2 #H destruct /3 width=1/
+  | #V #l #H1WV #H2WV #HL2 #H1 #H2 destruct /3 width=3/
+  ]
+| #L1 #L #V1 #W1 #l #H1VW1 #H2VW1 #HL1 #IHL1 #X #H
+  elim (lsubss_inv_pair1 … H) -H * #L2
+  [ #HL2 #H destruct /3 width=5/
+  | #V #l0 #_ #_ #_ #_ #H destruct
+  ]
+]
+qed.