theorem Th28:
  x in A + g iff ex h st x = h + g & h in A
proof
  thus x in A + g implies ex h st x = h + g & h in A
  proof
    assume x in A + g;
    then consider g1,g2 such that
A1: x = g1 + g2 & g1 in A and
A2: g2 in {g};
    g2 = g by A2,TARSKI:def 1;
    hence thesis by A1;
  end;
  given h such that
A3: x = h + g & h in A;
  g in {g} by TARSKI:def 1;
  hence thesis by A3;
end;
