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

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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_eq.ma".
  18
  19 (* LIFT FOR PROTOTERM *******************************************************)
  20
  21 lemma lift_iref_sn (f) (t:prototerm) (n:pnat):
  22       (𝛗f＠⧣❨n❩.↑[⇂*[n]f]t) ⊆ ↑[f](𝛗n.t).
  23 #f #t #n #p * #q * #r #Hr #H1 #H2 destruct
  24 @(ex2_intro … (𝗱n◗𝗺◗r))
  25 /2 width=1 by in_comp_iref/
  26 qed-.
  27
  28 lemma lift_iref_dx (f) (t) (n:pnat):
  29       ↑[f](𝛗n.t) ⊆ 𝛗f＠⧣❨n❩.↑[⇂*[n]f]t.
  30 #f #t #n #p * #q #Hq #H0 destruct
  31 elim (in_comp_inv_iref … Hq) -Hq #p #H0 #Hp destruct
  32 /3 width=1 by in_comp_iref, in_comp_lift_path_term/
  33 qed-.
  34
  35 lemma lift_iref (f) (t) (n:pnat):
  36       (𝛗f＠⧣❨n❩.↑[⇂*[n]f]t) ⇔ ↑[f](𝛗n.t).
  37 /3 width=1 by conj, lift_iref_sn, lift_iref_dx/
  38 qed.
  39
  40 lemma lift_iref_uni (t) (m) (n):
  41       (𝛗(n+m).t) ⇔ ↑[𝐮❨m❩](𝛗n.t).
  42 #t #m #n
  43 @(subset_eq_trans … (lift_iref …))
  44 <tr_uni_pap >nsucc_pnpred <tr_tls_succ_uni
  45 /3 width=1 by iref_eq_repl, lift_term_id/
  46 qed.