
theorem Th26:
  for T being Hausdorff TopLattice, N being convergent net of T
  for x being Element of T st x"/\" is continuous holds x "/\" lim N in Lim (x
  "/\" N)
proof
  let T be Hausdorff TopLattice, N be convergent net of T, x be Element of T
  such that
A1: x"/\" is continuous;
  x "/\" lim N = (x"/\").(lim N) by WAYBEL_1:def 18;
  then x "/\" lim N in Lim (x"/\" * N) by A1,Th25;
  hence thesis by Th18;
end;
