
theorem
for f being Function of REAL,REAL, a,b,c,d being Real st
for x be Real holds f.x= max(0,min(1, c*arctan(a*x+b)+d))
holds f is FuzzySet of REAL
proof
 let f be Function of REAL,REAL;
 let a,b,c,d be Real;
 assume for x be Real holds f.x= max(0,min(1, c*arctan(a*x+b)+d)); then
 f in {f where f is Function of REAL,REAL, a,b,c,d is Real:
 for x be Real holds f.x= max(0,min(1, c*arctan(a*x+b)+d))} ;
 then
 f in Membership_Funcs (REAL) by MM60,MM41;
 hence thesis by Def1;
end;
