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 *)
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15 include "basic_2/syntax/tsts.ma".
17 (* SAME TOP TERM STRUCTURE **************************************************)
19 (* Main properties **********************************************************)
21 (* Basic_1: was: iso_trans *)
22 theorem tsts_trans: ∀h,o. Transitive … (tsts h o).
24 [ #s1 #s #d #Hs1 #Hs #X #H
25 elim (tsts_inv_sort1_deg … H … Hs) -s /2 width=3 by tsts_sort/
26 | #i1 #i #H <(tsts_inv_lref1 … H) -H //
27 | #l1 #l #H <(tsts_inv_gref1 … H) -H //
28 | #I #V1 #V #T1 #T #X #H
29 elim (tsts_inv_pair1 … H) -H #V2 #T2 #H destruct //
33 theorem tsts_canc_sn: ∀h,o. left_cancellable … (tsts h o).
34 /3 width=3 by tsts_trans, tsts_sym/ qed-.
36 theorem tsts_canc_dx: ∀h,o. right_cancellable … (tsts h o).
37 /3 width=3 by tsts_trans, tsts_sym/ qed-.