You're mistranslating 'is' as =, really, it reflects a unary function, a property, in the very least the implication is not bidirectional so you can't use `friendship⊆magic` to connect the other two in the order you want to.
We'll meet for review next week and I'll see if you've made any progress. Look over that bostrom I assigned you, and don't forget you'll have to defend your thesis in september.