% app(L1,L2,L3) <=> list concatenation
app([]     ,L,L   ).
app([E|R],L,[E|RL]) :- app(R,L,RL).

% add an elementat the end of a list:
add_list(L,E,LandE) :- app(L,[E],LandE).

% compute the last element of a list:
last(L,E) :- app(_,[E],L).

% is an element member of a list
elem(E,L) :- app(_,[E|_],L).

% removes an occurrence of an element from a list
remove(E,L,LwithoutE) :- app(Xs,[E|Ys],L), app(Xs,Ys,LwithoutE).

% sublist(T,L) <=> T is a sublist of L
sub(T,L) :- app(_,Zs,L), app(T,_,Zs).