matita/matita/contribs/lambdadelta/delayed_updating/etc/lift_k/lift_prototerm_eq.etc

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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 "ground/lib/subset_ext_equivalence.ma".
  16 include "delayed_updating/substitution/lift_path_after.ma".
  17 include "delayed_updating/substitution/lift_prototerm.ma".
  18
  19 (* LIFT FOR PROTOTERM *******************************************************)
  20
  21 (* Constructions with subset_equivalence ************************************)
  22
  23 lemma lift_term_eq_repl_sn (f1) (f2) (t):
  24       f1 ≗ f2 → ↑[f1]t ⇔ ↑[f2]t.
  25 /3 width=1 by subset_equivalence_ext_f1_exteq, lift_path_eq_repl/
  26 qed.
  27
  28 lemma lift_term_eq_repl_dx (f) (t1) (t2):
  29       t1 ⇔ t2 → ↑[f]t1 ⇔ ↑[f]t2.
  30 /2 width=1 by subset_equivalence_ext_f1_bi/
  31 qed.
  32
  33 lemma lift_term_after (f1) (f2) (t):
  34       ↑[f2]↑[f1]t ⇔ ↑[f2∘f1]t.
  35 #f1 #f2 #t @subset_eq_trans
  36 [
  37 | @subset_inclusion_ext_f1_compose
  38 | @subset_equivalence_ext_f1_exteq /2 width=5/
  39 ]
  40 qed.