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

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  10 (*       \ /        This file is distributed under the terms of the       *)
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  14
  15 include "delayed_updating/substitution/lift_prototerm_id.ma".
  16 include "delayed_updating/substitution/lift_path_uni.ma".
  17 include "delayed_updating/syntax/prototerm_constructors.ma".
  18
  19 (* LIFT FOR PROTOTERM *******************************************************)
  20
  21 lemma lift_iref_bi (t1) (t2) (n):
  22       t1 ⇔ t2 → 𝛗n.t1 ⇔ 𝛗n.t2.
  23 /2 width=1 by subset_equivalence_ext_f1_bi/
  24 qed.
  25
  26 lemma lift_iref_sn (f) (t:prototerm) (n:pnat):
  27       (𝛗f＠⧣❨n❩.↑[⇂*[n]f]t) ⊆ ↑[f](𝛗n.t).
  28 #f #t #n #p * #q * #r #Hr #H1 #H2 destruct
  29 @(ex2_intro … (𝗱n◗𝗺◗r))
  30 /2 width=1 by in_comp_iref/
  31 qed-.
  32
  33 lemma lift_iref_dx (f) (t) (n:pnat):
  34       ↑[f](𝛗n.t) ⊆ 𝛗f＠⧣❨n❩.↑[⇂*[n]f]t.
  35 #f #t #n #p * #q #Hq #H0 destruct
  36 elim (in_comp_inv_iref … Hq) -Hq #p #H0 #Hp destruct
  37 /3 width=1 by in_comp_iref, in_comp_lift_bi/
  38 qed-.
  39
  40 lemma lift_iref (f) (t) (n:pnat):
  41       (𝛗f＠⧣❨n❩.↑[⇂*[n]f]t) ⇔ ↑[f](𝛗n.t).
  42 /3 width=1 by conj, lift_iref_sn, lift_iref_dx/
  43 qed.
  44
  45 lemma lift_iref_uni (t) (m) (n):
  46       (𝛗(n+m).t) ⇔ ↑[𝐮❨m❩](𝛗n.t).
  47 #t #m #n
  48 @(subset_eq_trans … (lift_iref …))
  49 <tr_uni_pap >nsucc_pnpred <tr_tls_succ_uni
  50 /3 width=1 by lift_iref_bi, lift_term_id/
  51 qed.