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

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  14
  15 include "delayed_updating/substitution/lift_prototerm_eq.ma".
  16 include "delayed_updating/substitution/lift_path_id.ma".
  17
  18 (* LIFT FOR PROTOTERM *******************************************************)
  19
  20 (* Constructions with tr_id *************************************************)
  21
  22 lemma lift_term_id_sn (t):
  23       t ⊆ ↑[𝐢]t.
  24 #t #p #Hp
  25 >(lift_path_id p)
  26 /2 width=1 by in_comp_lift_path_term/
  27 qed-.
  28
  29 lemma lift_term_id_dx (t):
  30       ↑[𝐢]t ⊆ t.
  31 #t #p * #q #Hq #H destruct //
  32 qed-.
  33
  34 lemma lift_term_id (t):
  35       t ⇔ ↑[𝐢]t.
  36 /3 width=2 by lift_term_id_dx, lift_term_id_sn, conj/
  37 qed.