contains([Val|Rest],Val).
contains([Other|Rest],Val)
  :- contains(Rest,Val).


add([],Right,Right).
add([1|MoreLeft],Right,[1|MoreSum])
  :- add(MoreLeft,Right,MoreSum).


multiply([],Right,[]).
multiply([1],Right,Right).
multiply([1|MoreLeft],Right,Product)
  :- le(MoreLeft,Product)
   , le(Right,Product)
   , multiply(MoreLeft,Right,PartialProduct)
   , add(Right,PartialProduct,Product).

le([],X).
le([1|X],[1|Y]) :- le(X,Y).

fact([],[1]).
fact([1|N],F) :- le([1|N],F),fact(N,F2),multiply([1|N],F2,F).