ExampleConstruction: Literature-sourcedVerification: AI-adaptedSession-authored (Fable 5 assisted)precheck passjudge pass (gpt-5.6-terra)audited 2026-08-27

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.

Indicator functions of measurable sets are measurable

Example

If $E$ is measurable, then its indicator $1_{E}$ is measurable.

Facts & Assumptions

Given: A measurable space $(X, A)$ and a measurable set $E \in A$ .

[L1]

An indicator function is measurable exactly when its set is measurable. (An indicator function is measurable exactly when its set is measurable)

Verification

technique · direct

1.1

The set $E$ is measurable by hypothesis.

given

2.1

Therefore [L1] gives that $1_{E}$ is measurable.

step 1.1L1∎

Depends on

An indicator function is measurable exactly when its set is measurable

Used by

Nothing in the library uses this result yet.

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

Sheldon Axler, Measure, Integration and Real Analysis, Section 2B (standard reference, not scraped)