theorem Th98:
  for x, y, z holds (x '&' y) '&' z = x '&' (y '&' z)
proof
  let x, y, z;
  consider t, u such that
    A1: x = LD-EqClassOf t and
    A2: y = LD-EqClassOf u and
    A3: x '&' y = LD-EqClassOf (t '&' u) by Def92;
  consider v such that
    A5: z = LD-EqClassOf v by Th88;
  A10: (t '&' (u '&' v)) '=' ((t '&' u) '&' v) is LD-provable;
  thus (x '&' y) '&' z = LD-EqClassOf ((t '&' u) '&' v) by A3, A5, Def92
      .= LD-EqClassOf (t '&' (u '&' v)) by A10, Th80, Def76
      .= (LD-EqClassOf t) '&' (LD-EqClassOf (u '&' v)) by Def92
      .= x '&' (y '&' z) by A1, A2, A5, Def92;
end;
