I'm reading the new HoTT book and I'm wondering about a potential equivalent form of the Univalence Axiom: $(A \simeq B) \simeq (A = B)$. For simplicity, I'm tacitly working in a fixed universe. It ...
Less tongue in cheek, is it known what the relative consistency is for theorems proved with an automatic theorem prover? Of course this depends somewhat on what assumptions one makes with respect to ...