reserve R for non empty RelStr,
  N for net of R,
  i for Element of N;

theorem Th36: :: 1.5 Examples (5), p.100
  for L being continuous complete Scott TopLattice, x be Element of L
  holds wayabove x is open
proof
  let L be continuous complete Scott TopLattice, x be Element of L;
  set W = wayabove x;
  W is inaccessible
  proof
    let D be non empty directed Subset of L;
    assume sup D in W;
    then x << sup D by WAYBEL_3:8;
    then consider d being Element of L such that
A1: d in D and
A2: x << d by WAYBEL_4:53;
    d in W by A2;
    hence thesis by A1,XBOOLE_0:3;
  end;
  hence thesis by Def4;
end;
