reserve a,b,c,d for Real;
reserve r,s for Real;

theorem
  a-b <= c+d implies a-d <= c+b
proof
  assume c+d >= a-b;
  then per cases;  ::??? wyzej bylo to samo
  suppose
    c+d >= a-b;
    then c+d+b >= a by Lm19;
    then c+b+d >= a;
    hence thesis by Lm18;
  end;
  suppose
    d+c >= a-b;
    then c+d+b >= a by Lm19;
    then c+b+d >= a;
    hence thesis by Lm18;
  end;
end;
