reserve x, X, Y for set;
reserve L for complete LATTICE,
  a for Element of L;

theorem
  for L being with_infima Poset for x, y being Element of InclPoset(Ids
  L) holds x "/\" y = x /\ y
proof
  let L be with_infima Poset;
  let x, y be Element of InclPoset(Ids L);
  reconsider x9= x, y9= y as Ideal of L by Th41;
  x9 /\ y9 is Ideal of L by Th40;
  then x9 /\ y9 in the set of all X where X is Ideal of L;
  hence thesis by YELLOW_1:9;
end;
