1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "basic_2/syntax/theq.ma".
17 (* HEAD EQUIVALENCE FOR TERMS ***********************************************)
19 (* Main properties **********************************************************)
21 (* Basic_1: was: iso_trans *)
22 (* Basic_2A1: was: tsts_trans *)
23 theorem theq_trans: ∀h,o. Transitive … (theq h o).
25 [ #s1 #s #d #Hs1 #Hs #X #H
26 elim (theq_inv_sort1_deg … H … Hs) -s /2 width=3 by theq_sort/
27 | #i1 #i #H <(theq_inv_lref1 … H) -H //
28 | #l1 #l #H <(theq_inv_gref1 … H) -H //
29 | #I #V1 #V #T1 #T #X #H
30 elim (theq_inv_pair1 … H) -H #V2 #T2 #H destruct //
34 (* Basic_2A1: was: tsts_canc_sn *)
35 theorem theq_canc_sn: ∀h,o. left_cancellable … (theq h o).
36 /3 width=3 by theq_trans, theq_sym/ qed-.
38 (* Basic_2A1: was: tsts_canc_dx *)
39 theorem theq_canc_dx: ∀h,o. right_cancellable … (theq h o).
40 /3 width=3 by theq_trans, theq_sym/ qed-.