matita/matita/contribs/lambda_delta/Basic_2/unfold/lifts_lift.ma

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  14
  15 include "Basic_2/substitution/lift_lift.ma".
  16 include "Basic_2/unfold/lifts.ma".
  17
  18 (* GENERIC TERM RELOCATION **************************************************)
  19
  20 (* Properties concerning basic term relocation ******************************)
  21
  22 (* Basic_1: was: lift1_xhg *)
  23 lemma lifts_lift_trans_le: ∀T1,T,des. ⇧*[des] T1 ≡ T → ∀T2. ⇧[0, 1] T ≡ T2 →
  24                            ∃∃T0. ⇧[0, 1] T1 ≡ T0 & ⇧*[des + 1] T0 ≡ T2.
  25 #T1 #T #des #H elim H -T1 -T -des
  26 [ /2 width=3/
  27 | #T1 #T3 #T #des #d #e #HT13 #_ #IHT13 #T2 #HT2
  28   elim (IHT13 … HT2) -T #T #HT3 #HT2
  29   elim (lift_trans_le … HT13 … HT3 ?) -T3 // /3 width=5/
  30 ]
  31 qed-.
  32
  33 (* Basic_1: was: lift1_free (right to left) *)
  34 axiom lifts_lift_trans: ∀T1,T0,des0. ⇧*[des0] T1 ≡ T0 →
  35                         ∀T2,i0. ⇧[O, i0 + 1] T0 ≡ T2 →
  36                         ∀des,i. @[i] des ≡ i0 → des + 1 ▭ i + 1 ≡ des0 + 1 →
  37                         ∃∃T. ⇧[0, i + 1] T1 ≡ T & ⇧*[des] T ≡ T2.