reserve x,y,z,x1,x2,y1,y2,z1,z2 for object,
  i,j,k,l,n,m for Nat,
  D for non empty set,
  K for Ring;

theorem
  for l,j st [l,j] in Indices (1.(K,n)) & l<>j holds
    (Col(1.(K,n),j)).l = 0.K
proof
  let l,j;
  assume that
A1: [l,j] in Indices (1.(K,n)) and
A2: l<>j;
  l in dom (1.(K,n)) by A1,ZFMISC_1:87;
  hence (Col(1.(K,n),j)).l=(1.(K,n))*(l,j) by MATRIX_0:def 8
    .= 0.K by A1,A2,MATRIX_1:def 3;
end;
