Rollup merge of #81198 - dtolnay:partialeq, r=m-ou-se

Remove requirement that forces symmetric and transitive PartialEq impls to exist

### Counterexample of symmetry:

If you [have](https://docs.rs/proc-macro2/1.0.24/proc_macro2/struct.Ident.html#impl-PartialEq%3CT%3E) an impl like:

```rust
impl<T> PartialEq<T> for Ident
where
    T: ?Sized + AsRef<str>
```

then Rust will not even allow the symmetric impl to exist.

```console
error[E0210]: type parameter `T` must be covered by another type when it appears before the first local type (`Ident`)
 --> src/main.rs:9:6
  |
9 | impl<T> PartialEq<Ident> for T where T: ?Sized + AsRef<str> {
  |      ^ type parameter `T` must be covered by another type when it appears before the first local type (`Ident`)
  |
  = note: implementing a foreign trait is only possible if at least one of the types for which it is implemented is local, and no uncovered type parameters appear before that first local type
  = note: in this case, 'before' refers to the following order: `impl<..> ForeignTrait<T1, ..., Tn> for T0`, where `T0` is the first and `Tn` is the last
```

<br>

### Counterexample of transitivity:

Consider these two existing impls from `regex` and `clap`:

```rust
// regex

/// An inline representation of `Option<char>`.
pub struct Char(u32);

impl PartialEq<char> for Char {
    fn eq(&self, other: &char) -> bool {
        self.0 == *other as u32
    }
}
```

```rust
// clap

pub(crate) enum KeyType {
    Short(char),
    Long(OsString),
    Position(u64),
}

impl PartialEq<char> for KeyType {
    fn eq(&self, rhs: &char) -> bool {
        match self {
            KeyType::Short(c) => c == rhs,
            _ => false,
        }
    }
}
```

It's nice to be able to add `PartialEq<proc_macro::Punct> for char` in libproc_macro (#80595), but it makes no sense to force an `impl PartialEq<Punct> for Char` and `impl PartialEq<Punct> for KeyType` in `regex` and `clap` in code that otherwise has nothing to do with proc macros.

<br>

`@rust-lang/libs`

Author: jonas-schievink

library/core/src/cmp.rs

@@ -31,14 +31,18 @@ use self::Ordering::*;
 /// equivalence relation. For example, in floating point numbers `NaN != NaN`,
 /// so floating point types implement `PartialEq` but not [`trait@Eq`].
 ///
-/// Formally, the equality must be (for all `a`, `b` and `c`):
+/// Formally, the equality must be (for all `a`, `b`, `c` of type `A`, `B`,
+/// `C`):
 ///
-/// - symmetric: `a == b` implies `b == a`; and
-/// - transitive: `a == b` and `b == c` implies `a == c`.
+/// - **Symmetric**: if `A: PartialEq<B>` and `B: PartialEq<A>`, then **`a == b`
+///   implies `b == a`**; and
+///
+/// - **Transitive**: if `A: PartialEq<B>` and `B: PartialEq<C>` and `A:
+///   PartialEq<C>`, then **`a == b` and `b == c` implies `a == c`**.
 ///
-/// Note that these requirements mean that the trait itself must be implemented
-/// symmetrically and transitively: if `T: PartialEq<U>` and `U: PartialEq<V>`
-/// then `U: PartialEq<T>` and `T: PartialEq<V>`.
+/// Note that the `B: PartialEq<A>` (symmetric) and `A: PartialEq<C>`
+/// (transitive) impls are not forced to exist, but these requirements apply
+/// whenever they do exist.
 ///
 /// ## Derivable
 ///