theorem Th151:
  a ++ (A \+\ B) = (a++A) \+\ (a++B)
proof
  thus a ++ (A \+\ B) = (a++(A\B)) \/ (a++(B\A)) by Th48
    .= ((a++A)\(a++B)) \/ (a++(B\A)) by Th150
    .= (a++A) \+\ (a++B) by Th150;
end;
