
theorem Th43:
  for L be sup-Semilattice holds the carrier of CompactSublatt L
  is join-closed Subset of L
proof
  let L be sup-Semilattice;
  reconsider C = the carrier of CompactSublatt L as Subset of L by
YELLOW_0:def 13;
  subrelstr C = CompactSublatt L by YELLOW_0:def 15;
  hence thesis by Def2;
end;
