theorem Th01:
  1.(F_Real,3) = <* <* 1,0,0 *>,
                    <* 0,1,0 *>,
                    <* 0,0,1 *> *>
  proof
A1: len 1.(F_Real,3) = 3 by MATRIX_0:23;
    1 in Seg 3 & 2 in Seg 3 & 3 in Seg 3 by FINSEQ_1:1;
    then (1.(F_Real,3)).1 = Line(1.(F_Real,3),1) &
         (1.(F_Real,3)).2 = Line(1.(F_Real,3),2) &
         (1.(F_Real,3)).3 = Line(1.(F_Real,3),3) by MATRIX_0:52;
    hence thesis by A1,FINSEQ_1:45,ANPROJ_8:68;
  end;
