update in ground_2 static_2 basic_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / etc / tueq / tueq_tueq.etc

diff --git a/matita/matita/contribs/lambdadelta/static_2/etc/tueq/tueq_tueq.etc b/matita/matita/contribs/lambdadelta/static_2/etc/tueq/tueq_tueq.etc
new file mode 100644 (file)
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--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/static_2/etc/tueq/tueq_tueq.etc
@@ -0,0 +1,44 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "static_2/syntax/tueq.ma".
+
+(* TAIL SORT-IRRELEVANT EQUIVALENCE ON TERMS ********************************)
+
+(* Main properties **********************************************************)
+
+theorem tueq_trans: Transitive … tueq.
+#T1 #T #H elim H -T1 -T
+[ #s1 #s #X #H
+  elim (tueq_inv_sort1 … H) -s /2 width=1 by tueq_sort/
+| #i1 #i #H //
+| #l1 #l #H //
+| #p #I #V #T1 #T #_ #IHT #X #H
+  elim (tueq_inv_bind1 … H) -H /3 width=1 by tueq_bind/
+| #V #T1 #T #_ #IHT #X #H
+  elim (tueq_inv_appl1 … H) -H /3 width=1 by tueq_appl/
+| #V1 #V #T1 #T #_ #_ #IHV #IHT #X #H
+  elim (tueq_inv_cast1 … H) -H /3 width=1 by tueq_cast/
+]
+qed-.
+
+theorem tueq_canc_sn: left_cancellable … tueq.
+/3 width=3 by tueq_trans, tueq_sym/ qed-.
+
+theorem tueq_canc_dx: right_cancellable … tueq.
+/3 width=3 by tueq_trans, tueq_sym/ qed-.
+
+theorem tueq_repl: ∀T1,T2. T1 ≅ T2 →
+                   ∀U1. T1 ≅ U1 → ∀U2. T2 ≅ U2 → U1 ≅ U2.
+/3 width=3 by tueq_canc_sn, tueq_trans/ qed-.