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
  for M being Matrix of 1,D holds M@ = M
  proof
    let M be Matrix of 1,D;
A1: M = <* <* M*(1,1) *> *> by MATRIX13:20;
    Indices M = [: {1},{1} :] by MATRIX_0:24,FINSEQ_1:2;
    then [1,1] in Indices M by ZFMISC_1:28;
    then (M@)*(1,1) = M*(1,1) by MATRIX_0:def 6;
    hence thesis by A1,MATRIX13:20;
  end;
