The proof checker. You verify a proof system by having it produce a proof trace: - Step 3185: Apply rule that a * b = b * a to "length * width" in the current

The proof checker. You verify a proof system by having it produce a proof trace: - Step 3185: Apply rule that a * b = b * a to "length * width" in the current formula. Then you run a proof trace checker which applies each transformation in sequence and checks that the expected result is obtained. Provers are complicated, but proof trace checkers are really dumb.