Find a element of a list in a another list in Prolog

i try to solve a problem about lists but i can't... :(

PLAYER(TEAM,[PLAYERS WHO PLAY IN THAT TEAM]).

player(milan,[seedorf,zambrotta,gattuso]).
player(inter,[seedorf,ronaldo,zambrotta]).
player(realmadrid,[seedorf,zidane,ronaldo开发者_高级运维]).

and i try to write predicates that returns 2 Lists; P1 and P2...

find(P1,P2).

For example; if my goal is:

find([milan,inter],X). returns X:[seedorf,zambrotta]. 
                     players who played juventus and also inter 
find([inter,realmadrid],X). returns X:[seedorf,ronaldo]  
                    players who played inter and also realmadrid
find(X,[seedorf]). returns X:[juventus,inter,realmadrid]
                     teams that seedorf played
find(X,[seedorf,ronaldo]). returns X:[inter,realmadrid]
                     teams that seedorf and ronaldo played.

i try to solve this but i can't go further than that (and it is not even enough to try P2 list members find in player facts :( ) : MOREOVER I CANNOT USE "!" because of lecture restrictions.

find(P1,[P2|P2s]):-findall(X,player(X,P2),P1),find(P1,P2s).

Thanks A Lot....

As you accept both P1 and P2 as inputs, I suggest to break down both P1 and P2 by their structures to do recursion. One solution could be finding all team of a specific player and finding all players playing for a specific team:

find1([T], L) :- player(T, L).
find1([T|Ts], L) :- player(T, L0), find1(Ts, L1), intersection(L0, L1, L).

find2(L, [P]) :- findall(X, (player(X, Y), member(P, Y)), L).
find2(L, [P|Ps]) :- findall(X, (player(X, Y), member(P, Y)), L0), find2(L1, Ps), intersection(L0, L1, L).

find(X, Y) :- is_list(X), find1(X, Y).
find(X, Y) :- is_list(Y), find2(X, Y).

Hope it helps you somehow.