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 "delayed_updating/syntax/path.ma".
16 include "delayed_updating/notation/relations/up_down_arrow_epsilon_2.ma".
17 include "delayed_updating/notation/relations/up_arrow_epsilon_2.ma".
19 (* PRETERM ******************************************************************)
21 definition preterm: Type[0] ≝ predicate path.
23 definition preterm_in_comp: relation2 path preterm ≝
27 "belongs to complete (preterm)"
28 'UpDownArrowEpsilon p t = (preterm_in_comp p t).
30 definition preterm_in_root: relation2 path preterm ≝
34 "belongs to root (preterm)"
35 'UpArrowEpsilon p t = (preterm_in_root p t).
37 (* Basic constructions ******************************************************)
39 lemma preterm_in_comp_root (p) (t):
41 /2 width=2 by ex_intro/