reserve i,j,n for Nat,
  K for Field,
  a for Element of K,
  M,M1,M2,M3,M4 for Matrix of n,K;
reserve A for Matrix of K;

theorem
  for K being Field,n being Nat,M1,M2 being Matrix of n,K st 
  M1 is symmetric & M2 is symmetric holds M1-M2 is symmetric
proof
  let K,n,M1,M2;
  assume that
A1: M1 is symmetric and
A2: M2 is symmetric;
  (M1-M2)@=M1@+(-M2)@ by Th24
    .=M1+(-M2)@ by A1
    .=M1+-(M2@) by Th27
    .=M1-M2 by A2;
  hence thesis;
end;
