theorem Th22:
  x in A^Fos iff x in A & ex V st V in U_FMT x & V \ {x} misses A
proof
  thus x in A^Fos implies x in A & ex V st V in U_FMT x & V \ {x} misses A
  proof
    assume x in A^Fos;
    then ex y st y=x & y in A & ex V st V in U_FMT y & (V \ {y}) misses A;
    hence thesis;
  end;
  assume x in A & ex V st V in U_FMT x & V \ {x} misses A;
  hence thesis;
end;
