Yeah, reimplementing the solution just to have something to check against is a bad idea.

I find that most tutorials talk about "properties of function `foo`", whereas I prefer to think about "how is function `foo` related to other functions". Those relationships can be expressed as code, by plugging outputs of one function into arguments of another, or by sequencing calls in a particular order, etc. and ultimately making assertions. However, there will usually be gaps; filling in those gaps is what a property's inputs are for.

Another good source of properties is trying to think of ways to change an expression/block which are irrelevant. For example, when we perform a deletion, any edits made beforehand should be irrelevant; boom, that's a property. If something would filter out negative values, then it's a property that sprinkling negative values all over the place has no effect. And so on.