
theorem :: THEOREM 4.7 (1)=(4)
  for L1 be continuous lower-bounded sup-Semilattice for B1 be
with_bottom CLbasis of L1 st card B1 = CLweight L1 holds CLweight L1 = CLweight
  InclPoset Ids subrelstr B1
proof
  let L1 be continuous lower-bounded sup-Semilattice;
  let B1 be with_bottom CLbasis of L1;
  assume
A1: card B1 = CLweight L1;
A2: card the carrier of CompactSublatt InclPoset Ids subrelstr B1 = card the
  carrier of subrelstr B1 by Th26,WAYBEL23:69;
  thus CLweight InclPoset Ids subrelstr B1 = card the carrier of
  CompactSublatt InclPoset Ids subrelstr B1 by Th3
    .= CLweight L1 by A1,A2,YELLOW_0:def 15;
end;
