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

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   3 (*      ||M||                                                             *)
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  14
  15 include "delayed_updating/substitution/lift_eq.ma".
  16
  17 axiom lift_path_after (p) (f1) (f2):
  18       ↑[f2]↑[f1]p = ↑[f2∘f1]p.
  19 (*
  20 #p @(path_ind_lift … p) -p // [ #n | #n #l #p | #p ] #IH #f1 #f2
  21 [ <lift_path_d_empty_sn <lift_path_d_empty_sn
  22 | <lift_path_d_lcons_sn <lift_path_d_lcons_sn
  23 | <lift_path_L_sn <lift_path_L_sn <lift_path_L_sn
  24 *)
  25 include "delayed_updating/substitution/lift_prototerm.ma".
  26
  27 axiom lift_term_after (t) (f1) (f2):
  28       ↑[f2]↑[f1]t ⇔ ↑[f2∘f1]t.
  29
  30 include "delayed_updating/syntax/prototerm_constructors.ma".
  31
  32 (* LIFT FOR PROTOTERM *******************************************************)
  33
  34 lemma lift_iref_after_sn (f) (t) (n:pnat):
  35       ↑[f∘𝐮❨n❩]t ⊆ ↑[f](𝛗n.t).
  36 #f #t #n #p * #q #Hq #H0 destruct
  37 @(ex2_intro … (𝗱n◗𝗺◗q))
  38 /2 width=1 by in_comp_iref/
  39 qed-.
  40
  41 lemma lift_iref_after_dx (f) (t) (n:pnat):
  42       ↑[f](𝛗n.t) ⊆ ↑[f∘𝐮❨n❩]t.
  43 #f #t #n #p * #q #Hq #H0 destruct
  44 elim (in_comp_inv_iref … Hq) -Hq #p #Hp #Ht destruct
  45 /2 width=1 by in_comp_lift_bi/
  46 qed-.
  47
  48 lemma lift_iref_after (f) (t) (n:pnat):
  49       ↑[f∘𝐮❨n❩]t ⇔ ↑[f](𝛗n.t).
  50 /3 width=1 by conj, lift_iref_after_sn, lift_iref_after_dx/
  51 qed.
  52
  53 lemma lift_iref (f) (t) (n:pnat):
  54       ↑[f]↑[𝐮❨n❩]t ⇔ ↑[f](𝛗n.t).
  55 /3 width=3 by lift_term_after, subset_eq_trans/
  56 qed.