DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (deepseek-v4-pro + claude-sonnet-5)audited 2026-08-17

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.

Lambda-systems, or Dynkin systems

Let $X$ be a set. A lambda-system, or Dynkin system, on $X$ is a family $D \subseteq P (X)$ such that:

$X \in D$ ;
if $A, B \in D$ and $A \subseteq B$ , then $B ∖ A \in D$ ;
if $A_{0} \subseteq A_{1} \subseteq \dots$ and every $A_{n} \in D$ , then $⋃_{n \in N} A_{n} \in D$ .

Used by

Nothing. This result depends on no other item in the library.