
theorem MM41:
{f where f,g is Function of REAL,REAL :
for x be Real holds f.x= max(0,min(1, g.x))}
 c= Membership_Funcs (REAL)
proof
 let F be object;
 assume F in {f where f,g is Function of REAL,REAL :
 for x be Real holds f.x= max(0,min(1, g.x))};
 then consider f,g being Function of REAL,REAL
 such that
 A1: F=f and A2: for x be Real holds f.x= max(0,min(1, g.x));
 F in {f where f is Function of REAL,REAL :
 for x be Real holds f.x= max(0,min(1, g.x))} by A1,A2;
 hence thesis by MM4,TARSKI:def 3;
end;
