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

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   3 (*      ||M||                                                             *)
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  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/functions/class_p_0.ma".
  17 include "ground/lib/subset.ma".
  18 include "ground/xoa/ex_1_2.ma".
  19
  20 (* PROPER CONDITION FOR PATH ************************************************)
  21
  22 definition ppc: predicate path ≝
  23            λp. 𝐞 = p → ⊥
  24 .
  25
  26 interpretation
  27   "proper condition (path)"
  28   'ClassP = (ppc).
  29
  30 (* Basic constructions ******************************************************)
  31
  32 lemma ppc_lcons (l) (q): l◗q ϵ 𝐏.
  33 #l #p #H destruct
  34 qed.
  35
  36 (* Basic inversions ********************************************************)
  37
  38 lemma ppc_inv_empty:
  39       (𝐞) ϵ 𝐏 → ⊥.
  40 #H0 @H0 -H0 //
  41 qed-.
  42
  43 lemma ppc_inv_lcons (p):
  44       p ϵ 𝐏 → ∃∃l,q. l◗q = p.
  45 *
  46 [ #H0 elim (ppc_inv_empty … H0)
  47 | #l #q #_ /2 width=3 by ex1_2_intro/
  48 ]
  49 qed-.