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.

Every induced subgraph of an F-free graph is F-free

Statement

If G is F-free and J is an induced subgraph of G, then J is F-free.

Facts & Assumptions

Given: An F-free graph G and an induced embedding ι:J→G.

[F1]

F-free means that no H∈F has an induced embedding into G (H-free and F-free graphs under the induced-subgraph convention).

[L1]

Induced embeddings compose (Induced embeddings compose, and the induced-subgraph relation is transitive up to isomorphism).

Proof

technique · contradiction
1.1

Suppose J is not F-free. Then some H∈F has an induced embedding φ:H→J.

assume-contraF1
2.1

The composite ι∘φ:H→G is an induced embedding.

step 1.1L1
3.1

This contradicts that G is F-free. Hence J is F-free.

step 2.1F1discharge-contradiction∎

Depends on

Used by

Dependency tree · two levels

6 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