theorem Th19:
  x in A^Fodelta iff for W st W in U_FMT x holds W meets A & W meets A`
proof
  thus x in A^Fodelta implies for W st W in U_FMT x holds W meets A & W meets
  A`
  proof
    assume x in A^Fodelta;
    then ex y st y=x & for W st W in U_FMT y holds W meets A & W meets A`;
    hence thesis;
  end;
  assume for W st W in U_FMT x holds W meets A & W meets A`;
  hence thesis;
end;
