reserve i,j,k,n,l for Element of NAT,
  K for Field,
  a,b,c for Element of K,
  p ,q for FinSequence of K,
  M1,M2,M3 for Matrix of n,K;
reserve D for non empty set,
  t for FinSequence of D,
  A for Matrix of n,D;

theorem Th27:
  M1 is col_circulant & M2 is col_circulant implies a*M1 - b*M2 is
  col_circulant
proof
  assume that
A1: M1 is col_circulant and
A2: M2 is col_circulant;
  b*M2 is col_circulant by A2,Th20;
  then
A3: -(b*M2) is col_circulant by Th25;
  a*M1 is col_circulant by A1,Th20;
  hence thesis by A3,Th21;
end;
