Prove ∃x(P(x) → ∀y(P(y))).
Obviously, we have that ∃x(P(x) → ∀y(P(y))) is equivalent to ∃x(¬P(x) ∨ ∀y(P(y))).
This exercise is found in a section on "proofs involving disjunctions." I have tried many different ways to solve this and have a feeling I am not approaching it the right way (why I"m not including any attempts above). Perhaps I am not considering clever enough exhaustive cases? Can anyone direct me in the proper way to begin?