member1(Head,[Head|_]).
member1(X,[_|Tail]) :- member1(X,Tail).

concat1([],L2,L2).
concat1([Head|Tail],L2,[Head|L3]) :- concat1(Tail,L2,L3).

delete1(Head,[Head|Tail],Tail).
delete1(E,[Head|Tail],[Head|L1]) :- delete1(E,Tail,L1).

insert1([],L1,L1).
insert1(E,L1,L2) :- delete1(E,L2,L1).

len1([],0).
len1([_|Tail], N) :- len1(Tail, X), N is X+1.

reverse1([],[]).
reverse1([Head|Tail], L2) :- reverse1(Tail, L1), concat1(L1, [Head], L2).

sum([], 0).
sum([Head|Tail], N) :- sum(Tail, X), N is X + Head.

avg(L, N) :- sum(L, X), len1(L, Z), N is X / Z.

count1(_, [], 0).
count1(E, [Head|Tail], N) :- E =\= Head, count1(E, Tail, N).
count1(Head,[Head|Tile], N):- count1(Head, Tile, X), N is X+1.

double([],[]).
double([H|T],Out):-
    double(T,Out1),
    concat1([H],[H|Out1],Out2),
    Out2 = Out.