theorem
  X "/\" (Y \ Z) = X "/\" Y \ X "/\" Z
proof
  X "/\" Y \ X "/\" Z = ((X "/\" Y) \ X) "\/" ((X "/\" Y) \ Z) by Th42
    .= Bottom L "\/" ((X "/\" Y) \ Z) by Th29,LATTICES:6
    .= (X "/\" Y) \ Z;
  hence thesis by LATTICES:def 7;
end;
