Checked fact 180218 Oct 2026Research

The Axioms page says Lean has four standard axioms: Classical.choice, propext and Quot.sound, which it calls important parts of how mathematics is done in Lean and says are known to be consistent, and sorryAx, which implements sorry and is not intended to occur in finished proofs.

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There are four standard axioms in Lean. The first three axioms are important parts of how mathematics is done in Lean: Classical.choice ... propext ... Quot.sound ... The axiom sorryAx is used as part of the implementation of the sorry tactic ... Lean itself provides three such axioms that are known to be consistent.

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Lean reference: Axioms
Lean FRO / Lean project

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Checked by the notis newsroom on 18 Oct 2026, against the source above.

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How Lean checks an AI-written proof, and where that stops 18 Oct 2026

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“The Axioms page says Lean has four standard axioms: Classical.choice, propext and Quot.sound, which it calls important parts of how mathematics is done in Lean and says are known to be consistent, and sorryAx, which implements sorry and is not intended to occur in finished proofs.” ai notis, checked 18 Oct 2026. Source: Lean reference: Axioms (Lean FRO / Lean project). https://ainotis.com/c/1802

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ai notis. (2026, October 18). The Axioms page says Lean has four standard axioms: Classical.choice, propext and Quot.sound, which it calls important parts of how mathematics is done in Lean and says are known to be consistent, and sorryAx, which implements sorry and is not intended to occur in finished proofs [Checked claim 1802]. ai notis. https://ainotis.com/c/1802

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