theorem
  l in Seg n implies Det(RLine(A,l,a*Line(A,l))) = a*Det(A)
proof
A1: len Line(A,l)=width A by MATRIX_0:def 7;
  assume l in Seg n;
  then Det(RLine(A,l,a*Line(A,l)))=a*Det(RLine(A,l,Line(A,l))) by A1,Th34,
MATRIX_0:24;
  hence thesis by Th30;
end;
