
theorem
Membership_Funcs (REAL)
= {f where f is Function of REAL,REAL : f is FuzzySet of REAL}
proof
 A1:Membership_Funcs (REAL)
 c={f where f is Function of REAL,REAL : f is FuzzySet of REAL}
 proof
  let f be object;
  assume f in Membership_Funcs (REAL);
  then ex f0 being Membership_Func of REAL st f0=f & dom f0 =REAL by LM1;
  hence thesis;
 end;
 {f where f is Function of REAL,REAL : f is FuzzySet of REAL}
 c=Membership_Funcs (REAL)
 proof
  let f be object;
  assume f in {f where f is Function of REAL,REAL : f is FuzzySet of REAL};
  then
  consider f1 being Function of REAL,REAL such that
  B1:f=f1 and B2: f1 is FuzzySet of REAL;
  thus thesis by B1,B2,Def1;
 end;
 hence thesis by XBOOLE_0:def 10,A1;
end;
