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