Theorem 5.6. Let x and y be real numbers. If xy > 1/2, then x + y > 1. Your mission is to fill in the gaps and blanks, leaving no detail omitted. Proof. The proof will proceed by (insert name of proof technique or description of proof strategy here). So suppose that x + y2 1. Now we know that (x-y)2 0. (Insert missing steps of proof here.) Therefore xy 1/2, and the proof is complete.