reserve FT for non empty RelStr;
reserve x, y, z for Element of FT;
reserve A for Subset of FT;

theorem
  x in A^n iff x in A & U_FT x \ {x} meets A
proof
  thus x in A^n implies x in A & U_FT x \ {x} meets A
  proof
    assume x in A^n;
    then x in A & not x in A^s by XBOOLE_0:def 5;
    hence thesis;
  end;
  assume that
A1: x in A and
A2: U_FT x \ {x} meets A;
  not x in A^s by A2,Th9;
  hence thesis by A1,XBOOLE_0:def 5;
end;
