theorem Th13:
  M1 is line_circulant & M2 is line_circulant implies a*M1 - b*M2
  is line_circulant
proof
  assume that
A1: M1 is line_circulant and
A2: M2 is line_circulant;
  b*M2 is line_circulant by A2,Th6;
  then
A3: -(b*M2) is line_circulant by Th11;
  a*M1 is line_circulant by A1,Th6;
  hence thesis by A3,Th7;
end;
