
theorem
for f be FuzzySet of REAL st
f in {f where f is Function of REAL,REAL :
ex a,b be Real st a<>0 & for th be Real holds f.th= 1/2*cos(a*th+b)+1/2}
holds
f is normalized
proof
 let f be FuzzySet of REAL;
 assume f in {f where f is Function of REAL,REAL :
 ex a,b be Real st a<>0 & for th be Real holds f.th= 1/2*cos(a*th+b)+1/2};
 then
 consider f1 being Function of REAL,REAL such that
 A1:f1=f and
 A2:(ex a,b be Real st a<>0 & for th be Real holds f1.th= 1/2*cos(a*th+b)+1/2);
 thus thesis by A1,TrF22,A2;
end;
