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 "ground/lib/subset.ma".
16 include "delayed_updating/syntax/path.ma".
17 include "delayed_updating/notation/functions/pitchfork_2.ma".
18 include "delayed_updating/notation/functions/uptriangle_1.ma".
20 (* PRETERM ******************************************************************)
22 (* Note: preterms are subsets of complete paths *)
23 definition preterm: Type[0] ≝ 𝒫❨path❩.
25 definition preterm_grafted: path → preterm → preterm ≝
30 'Pitchfork t p = (preterm_grafted p t).
32 definition preterm_root: preterm → preterm ≝
37 'UpTriangle t = (preterm_root t).
39 (* Basic constructions ******************************************************)
41 lemma preterm_in_comp_root (p) (t):
43 /2 width=2 by ex_intro/