theorem
  M1 is line_circulant & M2 is line_circulant & M3 is line_circulant
  implies a*M1+b*M2+c*M3 is line_circulant
proof
  assume that
A1: M1 is line_circulant & M2 is line_circulant and
A2: M3 is line_circulant;
A3: c*M3 is line_circulant by A2,Th6;
  a*M1 is line_circulant & b*M2 is line_circulant by A1,Th6;
  hence thesis by A3,Th8;
end;
