DefinitionDefinition: AI-adaptedProof: Not applicableSession-authored (Fable 5 assisted)judge 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.

Pi-systems

Definition

Let $X$ be a set. A pi-system on $X$ is a nonempty family $P \subseteq P (X)$ closed under binary intersections: if $A, B \in P$ , then $A \cap B \in P$ .

The nonempty-family requirement is the convention used here. It does not require $X \in P$ and it does not add an empty-intersection axiom.

Used by

Dependency tree · next 3 levels

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

Sources

A. Dembo, Probability Theory lecture notes, Definition 1.1.36 (standard reference, not scraped)