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Anatomy of a Formal Proof
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It also contains dozens of user-contributed automated reasoning procedures that help with the formalization process, as well as notation declarations and configuration information, all of which codify different aspects of our mathematical understanding. Tactics thus play an important role in bridging the gap between the kind of reasoning that is intuitively clear and natural to mathematicians and the stringent axiomatic rules embodied by a formal system. Note that DeepMind’s AlphaProof, which was deemed to have performed at the level of a silver medalist at the most recent International Mathematical Olympiad, Footnote 14 was trained to find formal proofs in Lean.
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