
theorem SYLM2:
  for I be non trivial finite set,
  CPNT be Colored-PT-net-Family of I holds
  union {Funcs(Outbds(CPNT.i), the carrier of CPNT.j)
  where i, j is Element of I : i <> j} is non empty
proof
  let I be non trivial finite set;
  let CPNT be Colored-PT-net-Family of I;
  deffunc F(Element of I, Element of I) =
  Funcs(Outbds(CPNT.$1), the carrier of CPNT.$2);
  consider i0, j0 be Element of I such that
I0J0: i0 <> j0 by LMXorDelta;
  set O12 = the Function of Outbds(CPNT.i0), the carrier of CPNT.j0;
  F(i0, j0) in {F(i, j) where i, j is Element of I:i <> j} by I0J0;
  then F(i0, j0) c= union
  {F(i, j) where i, j is Element of I:i <> j} by ZFMISC_1:74;
  hence thesis;
end;
