To address the last couple posts...
I think you're tending to overlook the real point. It seems maybe you are looking at the story too literally. It is highly symbolic. Plus, I actually like the idea of Catherine being somewhat unsure of herself. In reality, people are often unsure of even their own actions, plus Catherine was genuinely dealing with the fear that she was becoming delusional. She was not at all certain she hadn't actually imagined the whole thing. And, as has been stated, explaining the proof doesn't accomplish anything concrete.
I think you're tending to overlook the real point. It seems maybe you are looking at the story too literally. It is highly symbolic. Plus, I actually like the idea of Catherine being somewhat unsure of herself. In reality, people are often unsure of even their own actions, plus Catherine was genuinely dealing with the fear that she was becoming delusional. She was not at all certain she hadn't actually imagined the whole thing. And, as has been stated, explaining the proof doesn't accomplish anything concrete.