theorem Th15:
  (a*x + b*y).|.z = a * x.|.z + b * y.|.z
proof
  (a*x+b*y) .|. z = (a*x) .|. z + (b*y) .|. z by Def11
    .= a * x .|. z + (b*y) .|. z by Def11;
  hence thesis by Def11;
end;
