
theorem Th6:
  for L be non empty reflexive transitive RelStr for x be Element
  of L holds compactbelow x c= waybelow x
proof
  let L be non empty reflexive transitive RelStr;
  let x be Element of L;
  now
    let z be object;
    assume z in compactbelow x;
    then consider z9 be Element of L such that
A1: z9 = z and
A2: x >= z9 and
A3: z9 is compact;
    z9 << z9 by A3,WAYBEL_3:def 2;
    then z9 << x by A2,WAYBEL_3:2;
    hence z in waybelow x by A1,WAYBEL_3:7;
  end;
  hence thesis;
end;
