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 i,l st [i,l] in Indices (1.(K,n)) & l=i holds
    (Line(1.(K,n),i)).l = 1.K
proof
  let i,l;
  assume that
A1: [i,l] in Indices (1.(K,n)) and
A2: l=i;
  l in Seg width (1.(K,n)) by A1,ZFMISC_1:87;
  hence (Line(1.(K,n),i)).l=(1.(K,n))*(i,l) by MATRIX_0:def 7
    .= 1.K by A1,A2,MATRIX_1:def 3;
end;
