reserve FT for non empty RelStr;
reserve A for Subset of FT;
reserve T for non empty TopStruct;
reserve FMT for non empty FMT_Space_Str;
reserve x, y for Element of FMT;
reserve A, B, W, V for Subset of FMT;

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;
