AnnihilationNumber.lean`

Explanation legend Lean4 Domain Explanation Language (L4DEL)

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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 (4)

Imported by 1 file

FormalConjecturesForMathlib.lean

def SimpleGraph.annihilationNumber The annihilation number of a graph line 31 source
Source documentation
The annihilation number of a graph. This is the largest number of degrees that can be added together without going over the total number of edges of that graph.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Fintype, SimpleGraph, DecidableRel, SimpleGraph.Adj, Nat
Proof uses: Finset.sup, Multiset, Finset.filter, LE.le, Multiset.sum, Finset.card, Sym2, SimpleGraph.edgeFinset, Finset.Iic, SimpleGraph.degreeMultiset, Multiset.card
14 instances, coercions and auxiliary constants left out.
```
def annihilationNumber (G : SimpleGraph α) [DecidableRel G.Adj] : ℕ :=
…
```
def SimpleGraph.annihilationNumber' Computes the annihilation number of a graph G line 46 source
Source documentation
Computes the annihilation number of a graph G.
It calculates the degree sequence, sorts it ascendingly, and finds the largest prefix length 'k' (where 0 ≤ k ≤ |V(G)|) such that the sum of the prefix is less than or equal to the sum of the corresponding suffix.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Fintype, SimpleGraph, DecidableRel, SimpleGraph.Adj, Nat
Proof uses: List.getLast!, List.filter, Decidable.decide, LE.le, List.sum, List.take, Multiset.sort, Multiset.map, SimpleGraph.degree, Membership.mem, Set, SimpleGraph.neighborSet, Finset.val, Finset.univ, List.drop, List.range, HAdd.hAdd, Fintype.card, OfNat.ofNat
16 instances, coercions and auxiliary constants left out.
```
noncomputable def annihilationNumber' (G : SimpleGraph α) [DecidableRel G.Adj] : ℕ :=
…
```