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This alternate formula makes much more sense, thanks! Does it suffice to prove what the old formula was claimed to -- i.e. that (𝐴⊠𝐵)^𝐾 → 𝐴 is a Kan fibration for all K?
Free theorems as I understand it were given based on logical relations not natural transformations (I'm aware of some work sort of relating the two). Do you have a reference for free theorems as natural transformations directly?