This is what is associated with the type itself. So any time you see an `ex`, it will have an `A` and and a `P` and the `ex` will be of type `Prop`. Skipping `A` for the moment, let's focus on `P` ...

Elpi is an extension language that comes as a library to be embedded into host applications such as Coq. Elpi is a variant of λProlog enriched with constraints.