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

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 include "delayed_updating/syntax/path.ma".
  16 include "delayed_updating/notation/relations/predicate_p_tail_1.ma".
  17 include "ground/xoa/ex_1_2.ma".
  18
  19 (* PROPER CONDITION FOR PATH ************************************************)
  20
  21 definition ppc: predicate path ≝
  22            λp. 𝐞 = p → ⊥
  23 .
  24
  25 interpretation
  26   "proper condition (path)"
  27   'PredicatePTail p = (ppc p).
  28
  29 (* Basic constructions ******************************************************)
  30
  31 lemma ppc_lcons (l) (q): Ꝕ(l◗q).
  32 #l #p #H destruct
  33 qed.
  34
  35 (* Basic inversions ********************************************************)
  36
  37 lemma ppc_inv_lcons (p):
  38       Ꝕp → ∃∃l,q. l◗q = p.
  39 *
  40 [ #H elim H -H //
  41 | #l #q #_ /2 width=3 by ex1_2_intro/
  42 ]
  43 qed-.