matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_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 (**) (* reverse include *)
  16 include "ground/lib/subset_ext_equivalence.ma".
  17 include "delayed_updating/substitution/lift_path_eq.ma".
  18 include "delayed_updating/substitution/lift_prototerm.ma".
  19
  20 (* LIFT FOR PROTOTERM *******************************************************)
  21
  22 (* Constructions with subset_equivalence ************************************)
  23
  24 lemma lift_term_eq_repl_sn (f1) (f2) (t):
  25       f1 ≗ f2 → ↑[f1]t ⇔ ↑[f2]t.
  26 /3 width=1 by subset_equivalence_ext_f1_exteq, lift_path_eq_repl/
  27 qed.
  28
  29 lemma lift_term_eq_repl_dx (f) (t1) (t2):
  30       t1 ⇔ t2 → ↑[f]t1 ⇔ ↑[f]t2.
  31 /2 width=1 by subset_equivalence_ext_f1_bi/
  32 qed.
  33
  34 lemma lift_term_grafted_sn (f) (t) (p):
  35       ↑[↑[p]f](t⋔p) ⊆ (↑[f]t)⋔(↑[f]p).
  36 #f #t #p #q * #r #Hr #H0 destruct
  37 /2 width=3 by ex2_intro/
  38 qed-.
  39
  40 lemma lift_term_grafted_dx (f) (t) (p):
  41       (↑[f]t)⋔(↑[f]p) ⊆ ↑[↑[p]f](t⋔p).
  42 #f #t #p #q * #r #Hr #H0
  43 elim (lift_path_inv_append_sn … (sym_eq … H0)) -H0
  44 #p0 #q0 #Hp0 #Hq0 #H0 destruct
  45 lapply (lift_path_inj … Hp0) -Hp0 #Hp0 destruct
  46 /2 width=1 by in_comp_lift_path_term/
  47 qed-.
  48
  49 lemma lift_term_grafted (f) (t) (p):
  50       ↑[↑[p]f](t⋔p) ⇔ (↑[f]t)⋔(↑[f]p).
  51 /3 width=1 by lift_term_grafted_sn, lift_term_grafted_dx, conj/ qed.
  52
  53 lemma lift_term_grafted_S (f) (t) (p):
  54       ↑[↑[p]f](t⋔(p◖𝗦)) ⇔ (↑[f]t)⋔((↑[f]p)◖𝗦).
  55 // qed.