Cleanup PartialEq docs.

- Cleanup the `impl PartialEq<BookFormat> for Book` implementation
- Implement `impl PartialEq<Book> for BookFormat` so it’s symmetric
  - Fixes #53844.
- Removes the last example since it appears to be redundant with the
  previous two examples.

src/libcore/cmp.rs

@@ -107,67 +107,29 @@ use self::Ordering::*;
 ///     format: BookFormat,
 /// }
 ///
+/// // Implement <Book> == <BookFormat> comparisons
 /// impl PartialEq<BookFormat> for Book {
 ///     fn eq(&self, other: &BookFormat) -> bool {
-///         match (&self.format, other) {
-///            (BookFormat::Paperback, BookFormat::Paperback) => true,
-///            (BookFormat::Hardback,  BookFormat::Hardback)  => true,
-///            (BookFormat::Ebook,     BookFormat::Ebook)     => true,
-///            (_, _) => false,
-///         }
+///         self.format == *other
 ///     }
 /// }
 ///
-/// let b1 = Book { isbn: 3, format: BookFormat::Paperback };
-///
-/// assert!(b1 == BookFormat::Paperback);
-/// assert!(b1 != BookFormat::Ebook);
-/// ```
-///
-/// By changing `impl PartialEq for Book` to `impl PartialEq<BookFormat> for Book`,
-/// we've changed what type we can use on the right side of the `==` operator.
-/// This lets us use it in the `assert!` statements at the bottom.
-///
-/// You can also combine these implementations to let the `==` operator work with
-/// two different types:
-///
-/// ```
-/// enum BookFormat {
-///     Paperback,
-///     Hardback,
-///     Ebook,
-/// }
-///
-/// struct Book {
-///     isbn: i32,
-///     format: BookFormat,
-/// }
-///
-/// impl PartialEq<BookFormat> for Book {
-///     fn eq(&self, other: &BookFormat) -> bool {
-///         match (&self.format, other) {
-///            (&BookFormat::Paperback, &BookFormat::Paperback) => true,
-///            (&BookFormat::Hardback,  &BookFormat::Hardback)  => true,
-///            (&BookFormat::Ebook,     &BookFormat::Ebook)     => true,
-///            (_, _) => false,
-///         }
-///     }
-/// }
-///
-/// impl PartialEq for Book {
+/// // Implement <BookFormat> == <Book> comparisons
+/// impl PartialEq<Book> for BookFormat {
 ///     fn eq(&self, other: &Book) -> bool {
-///         self.isbn == other.isbn
+///         *other == self.format
 ///     }
 /// }
 ///
 /// let b1 = Book { isbn: 3, format: BookFormat::Paperback };
-/// let b2 = Book { isbn: 3, format: BookFormat::Ebook };
 ///
 /// assert!(b1 == BookFormat::Paperback);
-/// assert!(b1 != BookFormat::Ebook);
-/// assert!(b1 == b2);
+/// assert!(BookFormat::Ebook != b1);
 /// ```
 ///
+/// By changing `impl PartialEq for Book` to `impl PartialEq<BookFormat> for Book`,
+/// we allow `BookFormat`s to be compared with `Book`s.
+///
 /// # Examples
 ///
 /// ```