let f, g be Function of REAL,REAL; :: thesis: ( ( for x being Real holds f . x = max (0,(min (1,(g . x)))) ) implies f is FuzzySet of REAL )

assume for x being Real holds f . x = max (0,(min (1,(g . x)))) ; :: thesis: f is FuzzySet of REAL

then f in { f where f is Function of REAL,REAL : for x being Real holds f . x = max (0,(min (1,(g . x)))) } ;

then f in Membership_Funcs REAL by TARSKI:def 3, MM4;

hence f is FuzzySet of REAL by Def1; :: thesis: verum

assume for x being Real holds f . x = max (0,(min (1,(g . x)))) ; :: thesis: f is FuzzySet of REAL

then f in { f where f is Function of REAL,REAL : for x being Real holds f . x = max (0,(min (1,(g . x)))) } ;

then f in Membership_Funcs REAL by TARSKI:def 3, MM4;

hence f is FuzzySet of REAL by Def1; :: thesis: verum