Comment by xelxebar

The really interesting aspect of this, IMHO, is discovering what theorem formulations combine together well as a whole. It's much akin to a software architecture problem.

Metamath has done quite a bit or primary research into this. Theorems often have a slightly non-standard, but more general form.

One can ask things like, "what is the equivalent of functional programming?" Or, "is there global state?" It's a perspective on reverse mathematics.