update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / syntax / prototerm_eq.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/prototerm_eq.ma b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/prototerm_eq.ma
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/prototerm_eq.ma
@@ -0,0 +1,32 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "delayed_updating/syntax/prototerm.ma".
+include "ground/lib/subset_equivalence.ma".
+
+(* EQUIVALENCE FOR PROTOTERM ************************************************)
+
+(* Constructions with prototerm_root ****************************************)
+
+lemma prototerm_root_incl_repl:
+      ∀t1,t2. t1 ⊆ t2 → ▵t1 ⊆ ▵t2.
+#t1 #t2 #Ht #p * #q #Hq
+/3 width=2 by ex_intro/
+qed.
+
+lemma prototerm_root_eq_repl:
+      ∀t1,t2. t1 ⇔ t2 → ▵t1 ⇔ ▵t2.
+#t1 #t2 * #H1 #H2
+/3 width=3 by conj, prototerm_root_incl_repl/
+qed.