As of this morning I had a huge multi-case definition that teetered and tottered around, breaking down at the least provocation. It was ugly. It was alarming. It had two halves and six subsubsections, and mumbled provisos, and side-conditions that stuck out like warts. But it pointed a finger forward. I felt sure it was pointing in the right direction.
Now the definition (with the thing I'm trying to prove about it) is this:
So pretty! Just one unified definition over lists of signed, labelled propositions, and such a symmetric one! Just break Γ in half at world v, shove in whatever A^i wants to do there, and glue everything back together. I ♥ math!
Oh, shit, I found a problem with it already with implies-right. I think I can fix it, still.