ExampleConstruction: Literature-sourcedVerification: AI-generatedPipeline-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-09-06

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.

Cyclic simple groups of prime order

Example

$C_{p}$ is finite simple for every prime $p$ .

Facts & Assumptions

Given: Let $p$ be prime.

Verification

technique · direct

1.1

The group $C_{p}$ has order $p$ , so Lagrange's theorem leaves only subgroups of orders $1$ and $p$ . Thus it has no nontrivial proper normal subgroup.

givenalgebra

2.1

Hence $C_{p}$ is finite and simple.

step 1.1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

12 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

Stephen D. Smith, CFSG—A User’s Manual (standard reference, not scraped)