matita/matita/contribs/lambdadelta/delayed_updating/syntax/preterm.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  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".
  18
  19 (* PRETERM ******************************************************************)
  20
  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
  25 .
  26
  27 interpretation
  28   "preterm (prototerm)"
  29   'ClassT = (structure_injective).
  30
  31 (* Basic inversions *********************************************************)
  32
  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.
  35 #t #p #q #Hpq #Ht #Hq
  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/
  40 ]
  41 qed-.