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 (* PROTOTERM ****************************************************************)
22 (* Note: a prototerm is a subset of complete paths *)
23 definition prototerm: Type[0] ≝ 𝒫❨path❩.
25 definition prototerm_grafted: path → prototerm → prototerm ≝
30 'Pitchfork t p = (prototerm_grafted p t).
32 definition prototerm_root: prototerm → prototerm ≝
37 'UpTriangle t = (prototerm_root t).
39 (* Basic constructions ******************************************************)
41 lemma prototerm_in_comp_root (p) (t):
43 /2 width=2 by ex_intro/
46 (* Basic destructions *******************************************************)
48 lemma prototerm_in_root_append_des_sn (t) (p) (q):
51 /2 width=2 by ex_intro/