Impl coherence false negative for associated types.

I tried this code:

use std::ops::{Add, Mul};

pub struct Generic<A>(A);

impl<A, B> Mul<Generic<B>> for Generic<A>
where
    A: Add<B>,
{
    type Output = Generic<<A as Add<B>>::Output>;

    fn mul(self, rhs: Generic<B>) -> Self::Output {
        Generic(self.0.add(rhs.0))
    }
}

type A = <Generic<i32> as Mul<Generic<i32>>>::Output;
type B = <Generic<u32> as Mul<Generic<u32>>>::Output;

trait Trait {}

impl Trait for A {}

impl Trait for B {}

playground

I expected to see this happen: code to compile.

Associated type Mul::Output should expand to different concrete types - Generic<i32> and Generic<u32>, and as such impls should be coherent.

Instead, this happened: compiler reports conflicting implementations of Trait

error[E0119]: conflicting implementations of trait `Trait` for type `<Generic<i32> as Mul>::Output`
  --> src/mini.rs:23:1
   |
21 | impl Trait for A {}
   | ---------------- first implementation here
22 |
23 | impl Trait for B {}
   | ^^^^^^^^^^^^^^^^ conflicting implementation for `<Generic<i32> as Mul>::Output`

I've looked for similar bug reports, most similar one I've found was #99940. Discussion there however takes place in the context of intercrate interactions, here everything happens locally.

Here's a reduced version of the code in which I originally encountered this problem, playground.

Meta

The issue persists on beta and nightly.

rustc --version --verbose:

rustc 1.89.0 (29483883e 2025-08-04)
binary: rustc
commit-hash: 29483883eed69d5fb4db01964cdf2af4d86e9cb2
commit-date: 2025-08-04
host: aarch64-apple-darwin
release: 1.89.0
LLVM version: 20.1.7

Start by reproducing the reduced example from the issue and compare the compiler's behavior on stable, beta, and nightly. Trace the coherence check for the two associated-type implementations; done means the compiler accepts the impls because their associated outputs resolve to distinct concrete types.