Add mut declarations and mutable-place checks

[bit-aloo]

What does this PR do?

closes: #419

took me sometime but i do understand borrow check a bit better now

How does it work, what questions do you have?

AI disclosure

• I did not use any AI tools

[rustbot]

Thanks for contributing to formality! :)
A reviewer will take a look at your PR within a week or two. If not, come talk to us on https://rust-lang.zulipchat.com/#narrow/channel/402470-t-types.2Fformality