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 being Matrix of n,K st 
  M1 is antisymmetric holds -M1 is antisymmetric by Th27;
