Prove Theorem 25.10 of the text.

Data from Theorem 25.10

Let R be an ordered ring with set P of positive elements and let ∅ : R → R' be a ring isomorphism. The subset P' = ∅[P] satisfies the requirements of Definition 25.1 for a set of positive elements of R'. Furthermore, in the ordering of R' given by P', we have ∅(a) <' ∅(b) in R' if and only if a < b in R.

We call the ordering of R' described in the preceding theorem the" ordering induced by" ∅ from the ordering of R.