Multiversal OmnidoG Conglomerate

You are designing a story with a multiverse. Or maybe, you are thinking about the possibility of an irl multiverse. Either way, you may want the following to be true:

1. Every conceivable series of events really happens somewhere within this multiverse.

2. Travel between universes is possible.

I would like to inform you that, if these are both true, then the following must also be true:

Somewhere, according to rule 1, there exists a dog*. This dog is, by some (presumably hilarious) string of circumstances, about to travel to another universe. They will be transported to universe U, at position X in space and T in time. This means that there must be a dog at the location (U, X, T).

This is all true regardless of what values are inserted for U, X, and T. Therefore there must be, in every universe, at every point in space, at every moment of time, a dog. There must be a multiversal, space-filling, infinitely dense field of dog matter, spanning across every spacetime of every universe, perpetually crushed by its own density. Capital 'G' doG. The Omnidog.

That is all. I just wanted to make you aware of this.

*This line of reasoning applies for non-dogs too, but I will be sticking to dogs for the purposes of this post.