maximality_zorns_lemma

What problem does it solve?

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.

Core Features & Use Cases

• Define a partial order on a collection of objects.
• Show that every chain has an upper bound within the set.
• Conclude existence of a maximal element via Zorn's Lemma.
• Lean 4 templates and proof sketches for common maximal-object existence results (e.g., maximal ideal, maximal linearly independent set).

Quick Start

Provide a nonempty poset with every chain bounded above, then apply Zorn's Lemma to obtain a maximal element.