% Alternative form to first fact: member1(X, [H|T]) :- X = H.
member1(X, [X|T]).
member1(X, [H|T]) :- member1(X, T).

% Alternative form for first fact: treesearch(X, node(V, L, R)) :- V = X.
% Alternative form for first fact: treesearch(X, N) :- node(X, L, R) = N.
treesearch(X, node(X, L, R)).
treesearch(X, node(Y, L, R)) :- X < Y, treesearch(X, L).
treesearch(X, node(Y, L, R)) :- X > Y, treesearch(X, R).

% We pick 'leaf' atom to indicate the leaf of a tree
treeinsert(X, leaf, node(X, leaf, leaf)).
treeinsert(X, node(X, L, R), node(X, L, R)).
treeinsert(X, node(Y, L, R), node(Y, L1, R)) :- X < Y, treeinsert(X, L, L1).
treeinsert(X, node(Y, L, R), node(Y, L, R1)) :- X > Y, treeinsert(X, R, R1).

% Try it out in Prolog:

% > swipl
% ?- [test].
% ?- treeinsert(3, leaf, T), treeinsert(2, T, T1), treeinsert(4, T1, T2).