theorem
  M1 is col_circulant &M2 is col_circulant implies a*M1+b*M2 is col_circulant
proof
  assume M1 is col_circulant & M2 is col_circulant;
  then a*M1 is col_circulant & b*M2 is col_circulant by Th20;
  hence thesis by Th21;
end;
