DefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge pass (gpt-5.6-terra)audited 2026-08-28

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Modular lattice

Definition

A lattice $L$ (Lattices, distributive lattices, and order ideals) is modular when for every $x, y, z \in L$ with $x \leq z$ one has

$x \lor (y \land z) = (x \lor y) \land z .$

The hypothesis $x \leq z$ is part of the law. Without it, the displayed identity need not hold.

Depends on

Lattices, distributive lattices, and order ideals

Used by

The subobject lattice of an abelian category is modular Theorem

Dependency tree · two levels

2 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Daniel Murfet, Abelian Categories, Section 4.1 (standard reference, not scraped)