> But if you consider deeply, both of these proofs are implicitly encoding same information about the space between your house and the local store That is only

> But if you consider deeply, both of these proofs are implicitly encoding same information about the space between your house and the local store That is only _some_ of the informations that they encode, and particularly informations shared by both proofs, but that it not the only information they encode! The exact way to reach the local food store is also some information, and they encode different ways, hence different informations. > What I wanted to opine was merely the fact that since all proofs use logic Note that there's no single logic! There are at least two big logics, classical and constructive/intuitionistic, each with their own variants. For example a proof by contradiction is valid in classical logic but not in constructive one. It would give you a proof that there must be a way to reach the local store without giving you the way to reach it. Would it still count as the same proof as the other two for you? It doesn't encode how to reach it, so for some it's not even a valid proof.