reserve i,j,k,n,l for 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
  A is symmetry_circulant & n>0 implies A@ is symmetry_circulant
proof
  assume that
A1: A is symmetry_circulant and
A2: n>0;
  consider p being FinSequence of D such that
A3: len p=width A and
A4: A is_symmetry_circulant_about p by A1;
  width A=n & len A=n by MATRIX_0:24;
  then width (A@)=len p by A2,A3,MATRIX_0:54;
  then consider p being FinSequence of D such that
A5: len p = width (A@) & A@ is_symmetry_circulant_about p by A2,A4,Th6;
  take p;
  thus thesis by A5;
end;
