Apply Zorn's Lemma to deduce maximal elements in Lean 4 proofs.
npx skills add https://github.com/bneb/perqed --skill maximality-zorns-lemma
Please help me install this Agent Skill. Skill: maximality_zorns_lemma Source: https://github.com/bneb/perqed/tree/main/.agents/skills/maximality_zorns_lemma Command: npx skills add https://github.com/bneb/perqed --skill maximality-zorns-lemma
Finds a maximal element in nonempty partially ordered sets using Zorn's Lemma, enabling non-constructive existence proofs in algebra, set theory, and related fields.
Provide a nonempty poset with every chain bounded above, then apply Zorn's Lemma to obtain a maximal element.
High-intent search queries and answers about installing and using this skill.
To prove the existence of a maximal element in Lean 4, you provide a nonempty partially ordered set and show every chain has an upper bound, then apply Zorn's Lemma to deduce the maximal element non-constructively.
Using Zorn's Lemma, you can prove the existence of maximal ideals, maximal linearly independent sets, and maximal cliques. It applies to non-constructive existence proofs in algebra, order theory, and combinatorics.
To apply Zorn's Lemma, you need a nonempty partially ordered set where every chain has an upper bound within the set. You also need access to a formalization context like Lean 4 templates.
Use Zorn's Lemma when you need to guarantee a maximal object non-constructively in algebra or set theory. It is necessary when explicit construction is difficult and you can prove every chain has an upper bound.
Yes, this approach works for proving maximal ideals exist in Lean 4. The Skill provides templates and proof sketches for common maximal-object existence results, including maximal ideals in ring theory.
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