theorem
  0++A = A
proof
  let a;
  hereby
    assume a in 0++A;
    then consider c1,c2 such that
A1: a = c1+c2 and
A2: c1 in {0} and
A3: c2 in A;
    c1 = 0 by A2,TARSKI:def 1;
    hence a in A by A1,A3;
  end;
  assume a in A;
  then 0+a in {0+c: c in A};
  hence thesis by Th142;
end;
