Inapplicable "add explicit lifetime bound" suggestion for trait with GAT bound

[detly]

Code

pub trait HasGat {
    type Gat<'a>
    where
        Self: 'a;
}

pub trait NoGat: for<'a> HasGat<Gat<'a> = Self::At> {
    type At;
}

Current output

Compiling playground v0.0.1 (/playground)
error[E0311]: the parameter type `Self` may not live long enough
 --> src/lib.rs:7:33
  |
7 | pub trait NoGat: for<'a> HasGat<Gat<'a> = Self::At> {
  |                                 ^^^^^^^^^^^^^^^^^^
  |
note: the parameter type `Self` must be valid for the lifetime `'a` as defined here...
 --> src/lib.rs:7:22
  |
7 | pub trait NoGat: for<'a> HasGat<Gat<'a> = Self::At> {
  |                      ^^
  = help: consider adding an explicit lifetime bound `Self: 'a`...
note: ...so that the type `Self` will meet its required lifetime bounds...
 --> src/lib.rs:7:33
  |
7 | pub trait NoGat: for<'a> HasGat<Gat<'a> = Self::At> {
  |                                 ^^^^^^^^^^^^^^^^^^
note: ...that is required by this bound
 --> src/lib.rs:4:15
  |
4 |         Self: 'a;
  |               ^^

error[E0311]: the parameter type `Self` may not live long enough
 --> src/lib.rs:8:5
  |
8 |     type At;
  |     ^^^^^^^^
  |
note: the parameter type `Self` must be valid for the lifetime `'a` as defined here...
 --> src/lib.rs:7:22
  |
7 | pub trait NoGat: for<'a> HasGat<Gat<'a> = Self::At> {
  |                      ^^
  = help: consider adding an explicit lifetime bound `Self: 'a`...
note: ...so that the type `Self` will meet its required lifetime bounds...
 --> src/lib.rs:8:5
  |
8 |     type At;
  |     ^^^^^^^^
note: ...that is required by this bound
 --> src/lib.rs:4:15
  |
4 |         Self: 'a;
  |               ^^

For more information about this error, try `rustc --explain E0311`.
error: could not compile `playground` (lib) due to 2 previous errors

Desired output

No response

Rationale and extra context

The message contains the suggestion

consider adding an explicit lifetime bound Self: 'a...

...but there is nowhere I can see that would be syntactically valid to do this.

One solution is to have trait NoGat: 'static + for<'a> ..., but I don't know that it should be the suggestion here, because it's potentially stricter than necessary.

This seems related to #96465, but note that this is not about whether this bound is a reasonable one or not, or how to express it if it is, but that the "help" message is not applicable (and quite confusing when more complex types and traits are involved).

Other cases

No response

Anything else?

No response