1. (20 pts) Prove that Vn E Z+, p(n) if and only if p (1) ( yn Z+, p (n) p (n + 1 )) for any given predicate p. (Hints: lfp(1) (Yn E Z+, p(n) p(n + 1)) Z+, p(n). It's explained in a video class how to see this. For the only if part, you can assume , then in E is false and prove Vn too. It's the contrapositive of the only-if part.)