You might be interested in Lean's way of doing things. They have normal types (e.g. numeric types) and subtypes (e.g. numbers less than zero). An element of the subtype "numbers less than zero" can be understood as a tuple containing the actual number (which has a normal numeric type) and a proof that this specific number is indeed less than zero.

https://lean-lang.org/doc/reference/latest/Basic-Types/Subty...