update in static_2 and basic_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / syntax / toeq_simple.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/toeq_simple.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/toeq_simple.ma
new file mode 100644 (file)
index 0000000..00d9694
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/toeq_simple.ma
@@ -0,0 +1,31 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/term_simple.ma".
+include "static_2/syntax/toeq.ma".
+
+(* SORT-IRRELEVANT OUTER EQUIVALENCE FOR TERMS ******************************)
+
+(* Properies with simple (neutral) terms ************************************)
+
+(* Basic_2A1: was: simple_tsts_repl_dx *)
+lemma simple_toeq_repl_dx: ∀T1,T2. T1 ⩳ T2 → 𝐒⦃T1⦄ → 𝐒⦃T2⦄.
+#T1 #T2 * -T1 -T2 //
+#I #V1 #V2 #T1 #T2 #H
+elim (simple_inv_pair … H) -H #J #H destruct //
+qed-.
+
+(* Basic_2A1: was: simple_tsts_repl_sn *)
+lemma simple_toeq_repl_sn: ∀T1,T2. T1 ⩳ T2 → 𝐒⦃T2⦄ → 𝐒⦃T1⦄.
+/3 width=3 by simple_toeq_repl_dx, toeq_sym/ qed-.