reserve x for set,
  i,j,k,n for Nat,
  K for Field;
reserve a,b,c,d for Element of K;
reserve D for non empty set;

theorem
  for M being Matrix of n, K st (ex i being Element of NAT st i in Seg n
& for k being Element of NAT st k in Seg n holds Col(M,i).k = 0.K) holds Per M
  = 0.K by Lm18;
