[V__]

Ah, thank you, that makes more sense. Maybe a weird follow-up question: Is it possible (or does it make sense) to find a proof in an inconsistent system and to try to "transform" it into a consistent one?

[koyanisqatsi]

Yes, paraconsistent logic could be considered an instance of such a system: https://en.wikipedia.org/wiki/Paraconsistent_logic.