Default trait method implementation for all trait

I have a trait MyTrait, and I want all trait objects &MyTrait to be comparable to each other and to nothing else. I have that now based on How to test for equality between trait objects?.

The problem is that I need to use MyTraitComparable everywhere, instead of MyTrait. Is there a way to get around this?

use std::any::Any;

trait MyTrait {}

trait MyTraitComparable: MyTrait {
    fn as_any(&self) -> &Any;

    fn equals(&self, other: &MyTraitComparable) -> bool;
}

impl<S: 'static + MyTrait + PartialEq> MyTraitComparable for S {
    fn as_any(&self) -> &Any {
        return self as &Any;
    }

    fn equals(&self, other: &MyTraitComparable) -> bool {
        return match other.as_any().downcast_ref::<S>() {
            None => false,
            Some(a) => self == a,
        };
    }
}

#[derive(PartialEq)]
struct MyObj {
    a: i32,
}
impl MyObj {
    fn new(a: i32) -> MyObj {
        return MyObj { a };
    }
}

impl MyTrait for MyObj {}

fn main() {
    assert!(as_trait_obj_and_compare(&MyObj::new(1), &MyObj::new(1)));
}

fn as_trait_obj_and_compare(obj: &MyTraitComparable, another_obj: &MyTraitComparable) -> bool {
    obj.equals(another_obj)
}

I tried moving as_any and equals to MyTrait and providing a default implementation, but

I don't think I can use self in that case, so it doesn't work.
If I use trait MyTrait: PartialEq then I can't create trait objects anymore.

If you're willing to use a nightly compiler and unstable features, you can use specialization to avoid having two traits:

#![feature(specialization)]

use std::any::Any;

trait MyTrait {
    fn as_any(&self) -> &Any;
    fn equals(&self, other: &MyTrait) -> bool;
}

default impl<S: 'static + PartialEq> MyTrait for S {
    default fn as_any(&self) -> &Any {
        return self as &Any;
    }

    default fn equals(&self, other: &MyTrait) -> bool {
        match other.as_any().downcast_ref::<S>() {
            None => false,
            Some(a) => self == a,
        }
    }
}

#[derive(PartialEq)]
struct MyObj {
    a: i32,
}
impl MyObj {
    fn new(a: i32) -> MyObj {
        return MyObj { a };
    }
}

impl MyTrait for MyObj {}

fn main() {
    assert!(as_trait_obj_and_compare(&MyObj::new(1), &MyObj::new(1)));
}

fn as_trait_obj_and_compare(obj: &MyTrait, another_obj: &MyTrait) -> bool {
    obj.equals(another_obj)
}