matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_preterm_eq.ma

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   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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  14
  15 include "ground/lib/subset_equivalence.ma".
  16 include "delayed_updating/syntax/preterm.ma".
  17 include "delayed_updating/substitution/lift_structure.ma".
  18 include "delayed_updating/substitution/lift_prototerm.ma".
  19
  20 (* LIFT FOR PRETERM *********************************************************)
  21
  22 (* Constructions with subset_equivalence ************************************)
  23
  24 lemma lift_grafted_S_sn (f) (t) (p):
  25       ↑[↑[p]f](t⋔(p◖𝗦)) ⊆ (↑[f]t)⋔((⊗p)◖𝗦).
  26 #f #t #p #q * #r #Hr #H0 destruct
  27 @(ex2_intro … Hr) -Hr
  28 <list_append_rcons_sn <list_append_rcons_sn
  29 <lift_append_proper_dx //
  30 qed-.
  31
  32 lemma lift_grafted_S_dx (f) (t) (p): p ϵ ▵t → t ϵ 𝐓 →
  33       (↑[f]t)⋔((⊗p)◖𝗦) ⊆ ↑[↑[p]f](t⋔(p◖𝗦)).
  34 #f #t #p #Hp #Ht #q * #r #Hr
  35 <list_append_rcons_sn #H0
  36 elim (lift_inv_append_proper_dx … (sym_eq … H0)) -H0 //
  37 #p0 #q0 #Hp0 #Hq0 #H0 destruct
  38 <(Ht … Hp0) [|*: /2 width=2 by ex_intro/ ] -p
  39 elim (lift_path_inv_S_sn … (sym_eq … Hq0)) -Hq0
  40 #r1 #r2 #Hr1 #Hr2 #H0 destruct
  41 lapply (preterm_in_root_append_inv_structure_empty_dx … p0 … Ht Hr1)
  42 [ /2 width=2 by ex_intro/ ] -Hr1 #Hr1 destruct
  43 /2 width=1 by in_comp_lift_bi/
  44 qed-.
  45
  46 lemma lift_grafted_S (f) (t) (p): p ϵ ▵t → t ϵ 𝐓 →
  47       ↑[↑[p]f](t⋔(p◖𝗦)) ⇔ (↑[f]t)⋔((⊗p)◖𝗦).
  48 /3 width=1 by lift_grafted_S_sn, conj, lift_grafted_S_dx/ qed.