single word requests - Is there a noun for something being contained in something?

In a mathematical context: Let's say x is contained in an interval I. How can I express this as a noun equivalent (but correct) to the "containedness"? I found things like "inherence", "immanence", but they don't seem to fit perfectly

Answer

Speaking in mathematical terms, inclusion sounds like a good candidate.

In your example, you could be writing a "proof of inclusion of x in I"

Relevant Wikipedia page:

https://en.wikipedia.org/wiki/Subset