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 "delayed_updating/syntax/prototerm.ma".
16 include "delayed_updating/syntax/path_structure.ma".
17 include "delayed_updating/notation/functions/class_t_0.ma".
19 (* PRETERM ******************************************************************)
21 (* Note: a preterm is a prototerm satislying the condition below *)
22 (* Note: different root paths have different structure *)
23 definition structure_injective: predicate prototerm ≝
24 λt. ∀p1,p2. p1 ϵ ▵t → p2 ϵ ▵t → ⊗p1 = ⊗p2 → p1 = p2
29 'ClassT = (structure_injective).
31 (* Basic inversions *********************************************************)
33 lemma preterm_in_root_append_inv_structure_empty_dx (t) (p) (q):
34 p●q ϵ ▵t → t ϵ 𝐓 → 𝐞 = ⊗q → 𝐞 = q.
36 lapply (Ht p ?? Hpq ?)
37 [ <structure_append //
38 | /2 width=2 by prototerm_in_root_append_des_sn/
39 | /2 width=3 by eq_inv_list_append_dx_dx_refl/