incomplete ordering trait impls lint

When a user derives or implement PartialOrd<T> for T we can call it a day.

However, when a user implements PartialOrd<U> for T, then for transitivity ("a < b and b < c implies a < c") to hold the user needs to provide more trait implementations (proof below):

• PartialOrd<T> for T
• PartialOrd<U> for U
• PartialOrd<T> for U

All these implementations need to "cooperate" and implement the same semantics for everything to work and I don't think we can check that, not statically at least. But we could at least check that they are provided.

Proof:

Consider: a: T, b: U, c: T

• a < b is ok, since PartialOrd<U> for T is implemented,
• b < c does not type check unless the user also implements PartialOrd<T> for U,
• a < c does not type check unless the user also implements PartialOrd<T> for T,

Consider the opposite case: a: U, b: T, c: U where a < c requires PartialOrd<U> for U.

Start by locating the existing Rust Clippy lint implementations and their tests, then trace how trait implementations are inspected. The intended result is a lint that detects a cross-type PartialOrd for T without the three related PartialOrd implementations described in the issue.