DefinitionDefinition: Literature-sourcedProof: Not applicablejudge 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

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