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(* as published by the Free Software Foundation; either version 2.1   *)
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(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the      *)
(* GNU General Public License for more details.                       *)
(*                                                                    *)
(* You should have received a copy of the GNU Lesser General Public   *)
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(* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA *)
(* 02110-1301 USA                                                     *)
(** list. Polymorphic lists with some operations.  @author Olga Caprotti and Martijn Oostdijk @version $Revision$ *)
(** * Polymorphic lists *)
Inductive list (A : Set) : Set :=
| Nil : list A
| Cons : A -> list A -> list A.
(** Length of a list *)
Fixpoint length (A : Set) (l : list A) {struct l} : nat :=
match l with
| Nil => 0
| Cons a r => S (length A r)
end.
(** Map a function over a list *)
Fixpoint map (A B : Set) (f : A -> B) (l : list A) {struct l} :
list B :=
match l with
| Nil => Nil B
| Cons a r => Cons B (f a) (map A B f r)
end.
Notation Map := (map _ _) (only parsing).

Lemma map_length :
forall (A B : Set) (f : A -> B) (l : list A),
length A l = length B (map A B f l).