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

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "delayed_updating/syntax/prototerm_constructors.ma".
  16 include "ground/lib/subset_ext_equivalence.ma".
  17
  18 (* CONSTRUCTORS FOR PROTOTERM ***********************************************)
  19
  20 (* Constructions with equivalence for prototerm *****************************)
  21
  22 lemma iref_eq_repl (t1) (t2) (k):
  23       t1 ⇔ t2 → 𝛕k.t1 ⇔ 𝛕k.t2.
  24 /2 width=1 by subset_equivalence_ext_f1_bi/
  25 qed.
  26
  27 lemma abst_eq_repl (t1) (t2):
  28       t1 ⇔ t2 → 𝛌.t1 ⇔ 𝛌.t2.
  29 /2 width=1 by subset_equivalence_ext_f1_bi/
  30 qed.
  31
  32 lemma appl_eq_repl (u1) (u2) (t1) (t2):
  33       u1 ⇔ u2 → t1 ⇔ t2 → ＠u1.t1 ⇔ ＠u2.t2.
  34 /2 width=1 by subset_equivalence_ext_f1_1_bi/
  35 qed.
  36
  37 (* Constructions with prototerm_grafted *************************************)
  38
  39 lemma grafted_abst_hd (t) (p):
  40       t⋔p ⇔ (𝛌.t)⋔(𝗟◗p).
  41 #t #p @conj #r #Hr
  42 [ /2 width=3 by ex2_intro/
  43 | lapply (prototerm_grafted_inv_gen … Hr) -Hr
  44   /2 width=1 by in_comp_inv_abst_hd/
  45 ]
  46 qed.
  47
  48 lemma grafted_appl_sd (v) (t) (p):
  49       v⋔p ⇔ (＠v.t)⋔(𝗦◗p).
  50 #v #t #p @conj #r #Hr
  51 [ /3 width=3 by ex2_intro, or_introl/
  52 | lapply (prototerm_grafted_inv_gen … Hr) -Hr
  53   /2 width=2 by in_comp_inv_appl_sd/
  54 ]
  55 qed.
  56
  57 lemma grafted_appl_hd (v) (t) (p):
  58       t⋔p ⇔ (＠v.t)⋔(𝗔◗p).
  59 #v #t #p @conj #r #Hr
  60 [ /3 width=3 by ex2_intro, or_intror/
  61 | lapply (prototerm_grafted_inv_gen … Hr) -Hr
  62   /2 width=2 by in_comp_inv_appl_hd/
  63 ]
  64 qed.