matita/matita/contribs/lambdadelta/delayed_updating/syntax/prototerm_eq.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       *)
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  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 (* Constructions with prototerm_root ****************************************)
  28
  29 lemma prototerm_root_incl_repl:
  30       ∀t1,t2. t1 ⊆ t2 → ▵t1 ⊆ ▵t2.
  31 #t1 #t2 #Ht #p * #q #Hq
  32 /3 width=2 by ex_intro/
  33 qed.
  34
  35 lemma prototerm_root_eq_repl:
  36       ∀t1,t2. t1 ⇔ t2 → ▵t1 ⇔ ▵t2.
  37 #t1 #t2 * #H1 #H2
  38 /3 width=3 by conj, prototerm_root_incl_repl/
  39 qed.