reserve T for TopSpace;
reserve T for non empty TopSpace;
reserve F for Subset-Family of T;
reserve T for non empty TopSpace;

theorem Th66:
  for F being Subset-Family of T holds F is domains-family implies
  Int Cl(meet F) c= meet F & Int Cl Int(meet F) = Int(meet F)
proof
  let F be Subset-Family of T;
  assume
A1: F is domains-family;
  now
    let A be Subset of T;
    reconsider B = A as Subset of T;
    assume A in F;
    then B is condensed by A1;
    hence Int Cl A c= A by TOPS_1:def 6;
  end;
  hence thesis by Th57;
end;
