matita/matita/contribs/lambdadelta/basic_2A/etc/append/cl_shift.etc

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  14
  15 include "basic_2/grammar/lenv_append.ma".
  16
  17 (* SHIFT OF A CLOSURE *******************************************************)
  18
  19 let rec shift L T on L ≝ match L with
  20 [ LAtom       ⇒ T
  21 | LPair L I V ⇒ shift L (-ⓑ{I} V. T)
  22 ].
  23
  24 interpretation "shift (closure)" 'Append L T = (shift L T).
  25
  26 (* Basic properties *********************************************************)
  27
  28 lemma shift_append_assoc: ∀L,K. ∀T:term. (L @@ K) @@ T = L @@ K @@ T.
  29 #L #K elim K -K // normalize //
  30 qed.
  31
  32 (* Basic inversion lemmas ***************************************************)
  33
  34 lemma shift_inj: ∀L1,L2. ∀T1,T2:term. L1 @@ T1 = L2 @@ T2 → |L1| = |L2| →
  35                  L1 = L2 ∧ T1 = T2.
  36 #L1 elim L1 -L1
  37 [ * normalize /2 width=1/
  38   #L2 #I2 #V2 #T1 #T2 #_ <plus_n_Sm #H destruct
  39 | #L1 #H1 #V1 #IH * normalize
  40   [ #T1 #T2 #_ <plus_n_Sm #H destruct
  41   | #L2 #I2 #V2 #T1 #T2 #H1 #H2
  42     elim (IH … H1) -IH -H1 /2 width=1/ -H2 #H1 #H2 destruct /2 width=1/
  43   ]
  44 ]
  45 qed-.