theorem Th12:
  symmetric_3(a,b,c,d,e,f) is symmetric
  proof
    reconsider a,b,c,d,e,f as Element of F_Real by XREAL_0:def 1;
    (symmetric_3(a,b,c,d,e,f))@ = <* <* a, d, e *>,
                                     <* d, b, f *>,
                                     <* e, f, c *> *> by Th05;
    hence thesis by MATRIX_6:def 5;
  end;
