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

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  14
  15 include "delayed_updating/substitution/lift_prototerm_eq.ma".
  16 include "delayed_updating/syntax/prototerm_constructors.ma".
  17
  18 (* LIFT FOR PROTOTERM *******************************************************)
  19
  20 lemma lift_iref_after_sn (f) (t:prototerm) (n:pnat):
  21       ↑[f∘𝐮❨n❩]t ⊆ ↑[f](𝛗n.t).
  22 #f #t #n #p * #q #Hq #H0 destruct
  23 @(ex2_intro … (𝗱n◗𝗺◗q))
  24 /2 width=1 by in_comp_iref/
  25 qed-.
  26
  27 lemma lift_iref_after_dx (f) (t) (n:pnat):
  28       ↑[f](𝛗n.t) ⊆ ↑[f∘𝐮❨n❩]t.
  29 #f #t #n #p * #q #Hq #H0 destruct
  30 elim (in_comp_inv_iref … Hq) -Hq #p #Hp #Ht destruct
  31 /2 width=1 by in_comp_lift_bi/
  32 qed-.
  33
  34 lemma lift_iref_after (f) (t) (n:pnat):
  35       ↑[f∘𝐮❨n❩]t ⇔ ↑[f](𝛗n.t).
  36 /3 width=1 by conj, lift_iref_after_sn, lift_iref_after_dx/
  37 qed.
  38
  39 lemma lift_iref (f) (t) (n:pnat):
  40       ↑[f]↑[𝐮❨n❩]t ⇔ ↑[f](𝛗n.t).
  41 /3 width=3 by lift_term_after, subset_eq_trans/
  42 qed.