matita/matita/contribs/lambdadelta/static_2/syntax/fold.ma

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  14
  15 include "static_2/syntax/lenv.ma".
  16
  17 (* FOLD FOR RESTRICTED CLOSURES *********************************************)
  18
  19 rec definition fold L T on L ≝ match L with
  20 [ LAtom     ⇒ T
  21 | LBind L I ⇒ match I with
  22   [ BUnit _   ⇒ fold L (-ⓛ⋆𝟎.T)
  23   | BPair I V ⇒ fold L (-ⓑ[I]V.T)
  24   ]
  25 ].
  26
  27 interpretation "fold (restricted closure)" 'plus L T = (fold L T).
  28
  29 (* Basic properties *********************************************************)
  30
  31 lemma fold_atom: ∀T. ⋆ + T = T.
  32 // qed.
  33
  34 lemma fold_unit: ∀I,L,T. L.ⓤ[I]+T = L+(-ⓛ⋆𝟎.T).
  35 // qed.
  36
  37 lemma fold_pair: ∀I,L,V,T. (L.ⓑ[I]V)+T = L+(-ⓑ[I]V.T).
  38 // qed.