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

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  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".
  19
  20 (* PROTOTERM ****************************************************************)
  21
  22 (* Note: a prototerm is a subset of complete paths *)
  23 definition prototerm: Type[0] ≝ 𝒫❨path❩.
  24
  25 definition prototerm_grafted: path → prototerm → prototerm ≝
  26            λp,t,q. p●q ϵ t.
  27
  28 interpretation
  29   "grafted (prototerm)"
  30   'Pitchfork t p = (prototerm_grafted p t).
  31
  32 definition prototerm_root: prototerm → prototerm ≝
  33            λt,q. ∃r. r ϵ t⋔q.
  34
  35 interpretation
  36   "root (prototerm)"
  37   'UpTriangle t = (prototerm_root t).
  38
  39 (* Basic inversions *********************************************************)
  40
  41 lemma prototerm_grafted_inv_gen (t) (p) (q):
  42       q ϵ t⋔p → p●q ϵ t.
  43 // qed-.
  44
  45 (* Basic constructions ******************************************************)
  46
  47 lemma prototerm_in_comp_root (p) (t):
  48       p ϵ t → p ϵ ▵t.
  49 /2 width=2 by ex_intro/
  50 qed.
  51
  52 (* Basic destructions *******************************************************)
  53
  54 lemma prototerm_in_root_append_des_sn (t) (p) (q):
  55       p●q ϵ ▵t → p ϵ ▵t.
  56 #t #p #q * #r #Hr
  57 /2 width=2 by ex_intro/
  58 qed-.