reserve a,b,c,d,e,f for Real,
        g           for positive Real,
        x,y         for Complex,
        S,T         for Element of REAL 2,
        u,v,w       for Element of TOP-REAL 3;
reserve a,b,c for Element of F_Real,
          M,N for Matrix of 3,F_Real;
reserve D        for non empty set;
reserve d1,d2,d3 for Element of D;
reserve A        for Matrix of 1,3,D;
reserve B        for Matrix of 3,1,D;

theorem
  A@ = <* <* A*(1,1) *>, <* A*(1,2) *>, <* A*(1,3) *> *>
  proof
A1: A@ is Matrix of 3,1,D by Th23;
    [1,1] in Indices A & [1,2] in Indices A & [1,3] in Indices A
      by MATRIX_0:31;
    then (A@)*(1,1) = A*(1,1) & (A@)*(2,1) = A*(1,2) & (A@)*(3,1) = A*(1,3)
      by MATRIX_0:def 6;
    hence thesis by A1,Th27;
  end;
