matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_prototerm_constructors.ma

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   3 (*      ||M||                                                             *)
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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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  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 for prototerm ****************************)
  22
  23 lemma unwind2_term_oref_pap (f) (k):
  24       (⧣(f＠⧣❨k❩)) ⇔ ▼[f]⧣k.
  25 #f #k @conj #p *
  26 [ /2 width=1 by in_comp_unwind2_path_term/
  27 | #q * #H0 destruct //
  28 ]
  29 qed.
  30
  31 lemma unwind2_term_iref (f) (t) (k:pnat):
  32       ▼[f∘𝐮❨k❩]t ⇔ ▼[f](𝛕k.t).
  33 #f #t #k @conj
  34 #p * #q #Hq #H0 destruct
  35 [ @(ex2_intro … (𝗱k◗𝗺◗q))
  36   /2 width=1 by in_comp_iref_hd/
  37 | elim (in_comp_inv_iref … Hq) -Hq #p #Hp #Ht destruct
  38   /2 width=1 by in_comp_unwind2_path_term/
  39 ]
  40 qed.
  41
  42 lemma unwind2_term_abst (f) (t):
  43       (𝛌.▼[⫯f]t) ⇔ ▼[f]𝛌.t.
  44 #f #t @conj #p #Hp
  45 [ elim (in_comp_inv_abst … Hp) -Hp #q #H1 * #r #Hr #H2 destruct
  46   /3 width=1 by in_comp_unwind2_path_term, in_comp_abst_hd/
  47 | elim Hp -Hp #q #Hq #H0 destruct
  48   elim (in_comp_inv_abst … Hq) -Hq #r #H0 #Hr destruct
  49   /3 width=1 by in_comp_unwind2_path_term, in_comp_abst_hd/
  50 ]
  51 qed.
  52
  53 lemma unwind2_term_appl (f) (v) (t):
  54       ＠▼[f]v.▼[f]t ⇔ ▼[f]＠v.t.
  55 #f #v #t @conj #p #Hp
  56 [ elim (in_comp_inv_appl … Hp) -Hp * #q #H1 * #r #Hr #H2 destruct
  57   /3 width=1 by in_comp_unwind2_path_term, in_comp_appl_sd, in_comp_appl_hd/
  58 | elim Hp -Hp #q #Hq #H0 destruct
  59   elim (in_comp_inv_appl … Hq) -Hq * #r #H0 #Hr destruct
  60   /3 width=1 by in_comp_unwind2_path_term, in_comp_appl_sd, in_comp_appl_hd/
  61 ]
  62 qed.