
theorem
  for L being non empty Poset, x being Element of L holds
  ex_inf_of uparrow x, L & inf uparrow x = x
proof
  let L be non empty Poset, x be Element of L;
  ex_inf_of {x}, L by YELLOW_0:38;
  hence ex_inf_of uparrow x, L by Th37;
  thus inf uparrow x = inf {x} by Th38,YELLOW_0:38
    .= x by YELLOW_0:39;
end;
