matita/matita/contribs/lambda_delta/Ground_2/list.ma

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  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 include "Ground_2/arith.ma".
  16 include "Ground_2/notation.ma".
  17
  18 (* LISTS ********************************************************************)
  19
  20 inductive list (A:Type[0]) : Type[0] :=
  21   | nil : list A
  22   | cons: A -> list A -> list A.
  23
  24 interpretation "nil (list)" 'Nil = (nil ?).
  25
  26 interpretation "cons (list)" 'Cons hd tl = (cons ? hd tl).
  27
  28 let rec all A (R:predicate A) (l:list A) on l ≝
  29   match l with
  30   [ nil        ⇒ True
  31   | cons hd tl ⇒ R hd ∧ all A R tl
  32   ].