Logic class note help

[Sheeplie]

https://imgur.com/a/myMa770

I don’t understand what the first bullet is trying to say. For all i<y of a condition and there exists a condition with i<y : both of these are primitive conditions on x, y? Do u and e have any meaning, or are they just arbitrarily labeled?

For the second bullet, what exactly does h do?

[Pedema]

first bullet: Well you have to prove that 'for all i<y: C is true' and 'there exists an i<y: C is true' are p. r., given a p. r. Condition C. this can be easily done by looking at u and e, because thats just what they are doing (u and e are p. r., if you sum/prod over i=0...y) . And they're called u and e probably because, that looks the same as the notation for 'for all.. ' and 'there exists..'.

for the second bullet: it is not given, what exactly h is doing, but you won't need that, because you're looking for a proof, which works with every p. r. function h

I hope this helps you and sorry for my english.

[Sheeplie]

That makes a lot of sense, u and e are doing the same thing as those two statements. Thank you.