theorem Th51:
  for i, j st i in Seg n & j in Seg n & i <> j holds Det RLine(A,i
  ,Line(A,j)) = 0.K
proof
  let i, j such that
A1: i in Seg n and
A2: j in Seg n and
A3: i <> j;
A4: i<j or j<i by A3,XXREAL_0:1;
  len Line(A,j) = width A by MATRIX_0:def 7;
  then
A5: Line(RLine(A,i,Line(A,j)),i)=Line(A,j) by A1,Th28;
  Line(RLine(A,i,Line(A,j)),j)=Line(A,j) by A2,A3,Th28;
  hence thesis by A1,A2,A5,A4,Th50;
end;
