LemmaStatement: Literature-sourcedProof: 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.

Every finite group is finitely presented

Statement

Every finite group has finitely many generators and relators.

Proof

Given: Let $G$ be finite.

1.1

Use one generator $x_{g}$ for each $g \in G$ and the finitely many relations $x_{g} x_{h} = x_{g h}$ and $x_{1} = 1$ .

given

2.1

Every word reduces to one $x_{g}$ , so the presented group maps bijectively to $G$ and is a finite presentation.

step 1.1algebra∎

Depends on

Free-presentation kernel data

Used by

Multiplier of a finite group is finite Lemma
Existence of Schur covering groups Theorem

Dependency tree · two levels

3 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

Clara Löh, Group Cohomology (standard reference, not scraped)