I came across this proof today and I can't figure out what the second restriction is supposed to mean (marked in red) - does it mean, that for every Turing machine, that if it stops for an input after s steps then it stops for infinity many steps after that? But wouldn't that be obvious, since halting means that all steps after the halting point are just ignored? :)
I'd be very thankful for any reply that can tell me, why this is a restriction for sets.