One of the observations in programming language semantic proofs is that one doesn't need coinduction. Statements can be proven by good old fashion induction, by

One of the observations in programming language semantic proofs is that one doesn't need coinduction. Statements can be proven by good old fashion induction, by indexing them with the number of steps in the computation, then proving they hold for any finite number of steps. I suspect the same technique applies to analysis. We don't need to prove a statement holds for reals with "infininte" number of digits, but merely for all rationals with finite k digits, where k is a parameter of the proof, thus can be arbitrarily large.