Definition. A Proof Theory is complete if whenever (truth/valid) then (proof).
I am still confused at how these two are related. https://math.stackexchange.com/questions/3536805/what-is-true-about-a-proof-system-that-is-complete-but-not-sound
If a proof system is unsound and complete, then all the semantically valid inferences can be proven, but in addition it proves some sequents that are not actually valid.