theorem Th5:
  (a*x+b*y) .|. z = a * x .|. z + b * y .|. z
proof
  (a*x+b*y) .|. z = (a*x) .|. z + (b*y) .|. z by Def2
    .= a * x .|. z + (b*y) .|. z by Def2;
  hence thesis by Def2;
end;
