
theorem
for f,g be Function of REAL,REAL st
(for x be Real holds f.x= min(1,max(0, g.x)))
holds f is FuzzySet of REAL
proof
 let f,g be Function of REAL,REAL;
 assume for x be Real holds f.x= min(1,max(0, g.x)); then
 f in {f where f is Function of REAL,REAL :
 for x be Real holds f.x= min(1,max(0, g.x))}; then
 f in Membership_Funcs (REAL) by TARSKI:def 3,MM3;
 hence thesis by Def1;
end;
