syntactic components detached from basic_2 become static_2

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

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/theq_theq.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/theq_theq.ma
new file mode 100644 (file)
index 0000000..e9e586d
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/theq_theq.ma
@@ -0,0 +1,40 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/theq.ma".
+
+(* HEAD EQUIVALENCE FOR TERMS ***********************************************)
+
+(* Main properties **********************************************************)
+
+(* Basic_1: was: iso_trans *)
+(* Basic_2A1: was: tsts_trans *)
+theorem theq_trans: ∀h,o. Transitive … (theq h o).
+#h #o #T1 #T * -T1 -T
+[ #s1 #s #d #Hs1 #Hs #X #H
+  elim (theq_inv_sort1_deg … H … Hs) -s /2 width=3 by theq_sort/
+| #i1 #i #H <(theq_inv_lref1 … H) -H //
+| #l1 #l #H <(theq_inv_gref1 … H) -H //
+| #I #V1 #V #T1 #T #X #H
+  elim (theq_inv_pair1 … H) -H #V2 #T2 #H destruct //
+]
+qed-.
+
+(* Basic_2A1: was: tsts_canc_sn *)
+theorem theq_canc_sn: ∀h,o. left_cancellable … (theq h o).
+/3 width=3 by theq_trans, theq_sym/ qed-.
+
+(* Basic_2A1: was: tsts_canc_dx *)
+theorem theq_canc_dx: ∀h,o. right_cancellable … (theq h o).
+/3 width=3 by theq_trans, theq_sym/ qed-.