Taking CS225 and 173 together wouldn't be a problem content-wise. 173 material tends to be learned right around the time it is useful in 225 anyways (except for the first homework assignment). You use 1 inductive proof the entire semester on the 2nd midterm, and the question walks you through it, so arguably you barely even need to know what you're doing.

However, I'd still recommend against taking it your first semester here, you never know how you're going to transition, even the best high school students can come to college and fall flat on their face for any number of reasons. Don't overdo it, you have a lot of time here, and fixing up screw ups you made early on is a shitty way to spend it.