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

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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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/syntax/prototerm.ma".
  16 include "ground/lib/subset_equivalence.ma".
  17
  18 (* EQUIVALENCE FOR PROTOTERM ************************************************)
  19
  20 (* Constructions with prototerm_grafted *************************************)
  21
  22 lemma grafted_empty_dx (t):
  23       t ⇔ t⋔𝐞.
  24 /2 width=1 by conj/
  25 qed.
  26
  27 lemma grafted_incl_repl (t1) (t2) (p):
  28       t1 ⊆ t2 → t1⋔p ⊆ t2⋔p.
  29 #t1 #t2 #p #Ht #q #Hq
  30 /2 width=1 by/
  31 qed.
  32
  33 lemma grafted_eq_repl (t1) (t2) (p):
  34       t1 ⇔ t2 → t1⋔p ⇔ t2⋔p.
  35 #t1 #t2 #p * #H1t #H2t
  36 /3 width=1 by conj, grafted_incl_repl/
  37 qed.
  38
  39 (* Constructions with prototerm_root ****************************************)
  40
  41 lemma prototerm_root_incl_repl:
  42       ∀t1,t2. t1 ⊆ t2 → ▵t1 ⊆ ▵t2.
  43 #t1 #t2 #Ht #p * #q #Hq
  44 /3 width=2 by ex_intro/
  45 qed.
  46
  47 lemma prototerm_root_eq_repl:
  48       ∀t1,t2. t1 ⇔ t2 → ▵t1 ⇔ ▵t2.
  49 #t1 #t2 * #H1 #H2
  50 /3 width=3 by conj, prototerm_root_incl_repl/
  51 qed.