Inherent associated type projections are not normalized after substitution

[fmease]

I tried this code:

#![feature(inherent_associated_types)]
#![allow(incomplete_features)]

struct S<T>(T);
impl<T: O> S<T> {
    type P = <T as O>::P;
}
trait O {
    type P;
}
impl O for i32 {
    type P = String;
}
fn main() {
    let _: S<i32>::P = String::new();
}

I expected to see it compile successfully.
Instead, it was rejected with the following error message:

error[E0308]: mismatched types
  --> p0.rs:15:24
   |
15 |     let _: S<i32>::P = String::new();
   |            ---------   ^^^^^^^^^^^^^ expected associated type, found struct `String`
   |            |
   |            expected due to this
   |
   = note: expected associated type `<i32 as O>::P`
                       found struct `String`
   = help: consider constraining the associated type `<i32 as O>::P` to `String` or calling a method that returns `<i32 as O>::P`
   = note: for more information, visit https://doc.rust-lang.org/book/ch19-03-advanced-traits.html
help: call `Into::into` on this expression to convert `String` into `<i32 as O>::P`
   |
15 |     let _: S<i32>::P = String::new().into();
   |                                     +++++++

Meta

rustc -Vv:

rustc 1.67.0-nightly (53e4b9dd7 2022-12-04)
binary: rustc
commit-hash: 53e4b9dd74c29cc9308b8d0f10facac70bb101a7
commit-date: 2022-12-04
host: x86_64-unknown-linux-gnu
release: 1.67.0-nightly
LLVM version: 15.0.4

@rustbot label F-inherent_associated_types
@rustbot claim