 reserve i,n for Nat;
 reserve r for Real;
 reserve ra for Element of F_Real;
 reserve a,b,c for non zero Element of F_Real;
 reserve u,v for Element of TOP-REAL 3;
 reserve p1 for FinSequence of (1-tuples_on REAL);
 reserve pf,uf for FinSequence of F_Real;
 reserve N for Matrix of 3,F_Real;
 reserve K for Field;
 reserve k for Element of K;

theorem Th05:
  for a11,a12,a13,a21,a22,a23,a31,a32,a33 being Element of F_Real
  for A being Matrix of 3,F_Real st
  A = <* <* a11,a12,a13 *>, <* a21,a22,a23 *>, <* a31,a32,a33 *> *> holds
  Line(A,1) = <* a11,a12,a13 *> & Line(A,2) = <* a21,a22,a23 *> &
  Line(A,3) = <* a31,a32,a33 *>
  proof
    let a11,a12,a13,a21,a22,a23,a31,a32,a33 be Element of F_Real;
    let A be Matrix of 3,F_Real;
    assume A = <* <* a11,a12,a13 *>, <* a21,a22,a23 *>, <* a31,a32,a33 *> *>;
    then
A1: A.1 = <* a11,a12,a13 *> & A.2 = <* a21,a22,a23 *> &
      A.3 = <* a31,a32,a33 *>;
    1 in Seg 3 & 2 in Seg 3 & 3 in Seg 3 by FINSEQ_1:1;
    hence thesis by A1,MATRIX_0:52;
  end;
