matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_constructors.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/unwind/unwind2_prototerm_eq.ma".
  16 include "delayed_updating/unwind/unwind2_path_append.ma".
  17 include "delayed_updating/syntax/prototerm_constructors.ma".
  18
  19 (* TAILED UNWIND FOR PROTOTERM **********************************************)
  20
  21 (* Constructions with constructors ******************************************)
  22
  23 lemma unwind2_term_iref_sn (f) (t) (k:pnat):
  24       ▼[f∘𝐮❨k❩]t ⊆ ▼[f](𝛕k.t).
  25 #f #t #k #p * #q #Hq #H0 destruct
  26 @(ex2_intro … (𝗱k◗𝗺◗q))
  27 /2 width=1 by in_comp_iref/
  28 qed-.
  29
  30 lemma unwind2_term_iref_dx (f) (t) (k:pnat):
  31       ▼[f](𝛕k.t) ⊆ ▼[f∘𝐮❨k❩]t.
  32 #f #t #k #p * #q #Hq #H0 destruct
  33 elim (in_comp_inv_iref … Hq) -Hq #p #Hp #Ht destruct
  34 /2 width=1 by in_comp_unwind2_path_term/
  35 qed-.
  36
  37 lemma unwind2_term_iref (f) (t) (k:pnat):
  38       ▼[f∘𝐮❨k❩]t ⇔ ▼[f](𝛕k.t).
  39 /3 width=2 by conj, unwind2_term_iref_sn, unwind2_term_iref_dx/
  40 qed.