Alphabeta Math
LemmaStatement: AI-adaptedProof: AI-generatedprecheck passaudited 2026-08-01
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.

The set of spanning trees of a finite graph is finite

Statement

Every finite graph has only finitely many spanning trees.

Facts & Assumptions

Given: A finite graph G.

[F1]

A spanning tree of G is determined by its edge set, which is a subset of E(G) (Spanning trees of a graph).

[L1]

The power set of a finite set is finite, and every subset of a finite set is finite (∣P(A)∣=2∣A∣ for finite A, A subset of a finite set is finite, with ∣B∣≤∣A∣, and equality holds if and only if B=A).

[F2]

E(G) is finite (A finite simple graph is a finite vertex set together with a set of two-element vertex subsets).

Proof

technique · direct
1.1

The map sending a spanning tree to its edge set embeds the set of spanning trees into P(E(G)).

F1
2.1

The latter power set is finite, so its subset consisting of spanning-tree edge sets is finite.

F2L1∎

Depends on

Used by

Dependency tree · two levels

24 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