theorem
  M1 is line_circulant & M2 is line_circulant implies a*M1+b*M2 is
  line_circulant
proof
  assume M1 is line_circulant & M2 is line_circulant;
  then a*M1 is line_circulant & b*M2 is line_circulant by Th6;
  hence thesis by Th7;
end;
