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 Th21:
  x in A^Foi iff ex V st V in U_FMT x & V c= A
proof
  thus x in A^Foi implies ex V st V in U_FMT x & V c= A
  proof
    assume x in A^Foi;
    then ex y st y=x & ex V st V in U_FMT y & V c= A;
    hence thesis;
  end;
  assume ex V st V in U_FMT x & V c= A;
  hence thesis;
end;
