Auto merge of rust-lang#118247 - spastorino:type-equality-subtyping, r=<try>

Fix for TypeId exposes equality-by-subtyping vs normal-form-syntactic-equality unsoundness

Fixes rust-lang#97156

This PR revives rust-lang#97427 idea, it sits on top of rust-lang#118118 because the idea uncovered some problems with IATs.

r? `@lcnr`

This is ICEing yet for `tests/ui/traits/new-solver/escaping-bound-vars-in-writeback-normalization.rs` using the new trait solver.
After rust-lang#118118 and this ICE is fixed, we would need a rebase and a crater run.

Opening as a WIP for now.

Author: bors

tests/ui/coherence/coherence-fn-implied-bounds.stderr

@@ -9,17 +9,11 @@
 //
 // * `'c` can be the intersection of `'a` and `'b` (and there is always an intersection)
 // * `'a` and `'b` can both be equal to `'c`
+//
+// check-pass
 
 trait Trait {}
 impl Trait for for<'a, 'b> fn(&'a u32, &'b u32) {}
-impl Trait for for<'c> fn(&'c u32, &'c u32) {
-    //~^ ERROR conflicting implementations
-    //
-    // Note in particular that we do NOT get a future-compatibility warning
-    // here. This is because the new leak-check proposed in [MCP 295] does not
-    // "error" when these two types are equated.
-    //
-    // [MCP 295]: https://github.com/rust-lang/compiler-team/issues/295
-}
+impl Trait for for<'c> fn(&'c u32, &'c u32) {}
 
 fn main() {}