SubgraphIsomorphism.lean`

Explanation legend Lean4 Domain Explanation Language (L4DEL)

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L4DEL: Lean4 Domain Explanation Language

Annotation provenance. This overlay contains 10 curated AI-written annotations and 7190 mechanical source-derived annotations. They have not been human-reviewed as explanations; treat them as unverified and not mathematical authority. Retained generation history: The 71 original curated annotations were produced in a Claude Sonnet 5.5 session at medium effort; Claude Opus 5.5 is recorded in that session as the advisor model, not the direct author. The bulk source-derived expansion was generated mechanically from pinned source comments by tooling developed in a GPT-5.6 Sol session at ultra reasoning; GPT-5.6 Sol did not originate the quoted source prose. On 2026-10-17 the mechanically generated source-comment annotations of the Formal Conjectures, Carleson, FLT, PFR, CompFiles, Mathematics in Lean and Theorem Proving in Lean overlays were regenerated by the same generator after three corrections made in a Claude Sonnet 5.5 session: titles no longer cut a sentence inside mathematics or end on a dangling word, workflow markers are removed from the quoted prose, and declaration names follow the scanner's namespace resolution. The boilerplate step line was dropped, and comments that were only a row of dashes no longer yield annotations. No new prose was written and no human review is claimed.

Credit: The upstream authors and contributors retain credit for the project and mathematics. lean4-explainer only renders their pinned source and adds the separately disclosed explanation layer.

Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

2 declarations, 0 contain sorry, 0 declared as axioms

Imports (2)

Imported by 1 file

FormalConjecturesForMathlib.lean

def SimpleGraph.IsUniqueSubgraph G is a unique subgraph of H if there is exactly one subgraph of H isomorphic to G line 30 source
Source documentation
G is a unique subgraph of H if there is exactly one subgraph of H isomorphic to G. Subgraphs of H are taken in the spanning sense: elements G' ≤ H of the lattice SimpleGraph V, i.e. subsets of the edges of H (not necessarily induced).

standard axioms: Quot.sound what this means
Statement uses: SimpleGraph
Proof uses: ExistsUnique, And, LE.le, Nonempty, SimpleGraph.Iso
1 instances, coercions and auxiliary constants left out.
```
def IsUniqueSubgraph (G H : SimpleGraph V) : Prop :=
…
```
def SimpleGraph.uniqueSubgraphCount The number of distinct unique subgraphs of H: the number of isomorphism classes of graphs that occur exactly once as a subgraph of H line 37 source
Source documentation
The number of distinct unique subgraphs of H: the number of isomorphism classes of graphs that occur exactly once as a subgraph of H. Each such class contains exactly one subgraph G ≤ H (uniqueness forbids a second isomorphic copy), so counting those representatives counts the classes.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: SimpleGraph, Nat
Proof uses: Set.ncard, Set.ofPred, And, LE.le, SimpleGraph.IsUniqueSubgraph
1 instances, coercions and auxiliary constants left out.
```
noncomputable def uniqueSubgraphCount (H : SimpleGraph V) : ℕ :=
…
```