+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||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-.