@Empty[xs]: xs = End;

@Element[x, xs]:
  ?xs_: (xs = Node[x, xs_] | (?x_: (xs = Node[x_, xs_] & @Element[x, xs_])));

@Subset[xs, ys]:
  xs = End |
  (?x_: ?xs_: (xs = Node[x_, xs_] & @Element[x_, ys] & @Subset[xs_, ys]));

@Join[xs, ys, zs]:
  (xs = End & ys = zs) |
  (?h: ?xs_: ?zs_: (xs = Node[h, xs_] & zs = Node[h, zs_] & @Join[xs_, ys, zs_]));