theorem Th67:
  for a being quasi-adjective of C holds Non Non a = a
proof
  let a be quasi-adjective of C;
  per cases;
  suppose a is positive;
    then reconsider a9 = a as positive expression of C, an_Adj C;
A1: ex b being positive expression of C, an_Adj C st ( Non a9 =
    (non_op C)term b)&( Non Non a9 = b) by Th61;
    Non a9 = (non_op C)term a by Th59;
    hence thesis by A1,Th44;
  end;
  suppose a is negative;
    then reconsider a9 = a as negative expression of C, an_Adj C;
    ex b being positive expression of C, an_Adj C st
    a9 = (non_op C)term b & Non a9 = b by Th61;
    hence thesis by Th59;
  end;
end;
