Sunflower.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

6 declarations, 0 contain sorry, 0 declared as axioms

Sunflowers

This file defines sunflowers of set families.

Imports (1)

Mathlib.Data.Set.Card

Imported by 1 file

FormalConjecturesForMathlib.lean

def IsSunflowerWithKernel A sunflower F with kernel S is a collection of sets in which all possible distinct pairs of sets share the same intersection S line 34 source
Source documentation
A sunflower F with kernel S is a collection of sets in which all possible distinct pairs of sets share the same intersection S.

no axioms what this means
Statement uses: Set
Proof uses: Set.Pairwise, Eq, Inter.inter
1 instances, coercions and auxiliary constants left out.
```
def IsSunflowerWithKernel (F : Set (Set α)) (S : Set α) : Prop :=
…
```
theorem isSunflowerWithKernel_empty line 37 source
standard axioms: propext what this means
Statement uses: Set, IsSunflowerWithKernel, EmptyCollection.emptyCollection
Proof uses: of_eq_true, Set.Pairwise, Eq, Inter.inter
4 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem isSunflowerWithKernel_singleton line 40 source
standard axioms: propext what this means
Statement uses: Set, IsSunflowerWithKernel, Singleton.singleton
Proof uses: of_eq_true, Set.Pairwise, Eq, Inter.inter
4 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
def IsSunflower A sunflower F is a collection of sets in which all possible distinct pairs of sets share the same intersection line 48 source
Source documentation
A sunflower F is a collection of sets in which all possible distinct pairs of sets share the same intersection.

no axioms what this means
Statement uses: Set
Proof uses: Exists, IsSunflowerWithKernel
```
def IsSunflower (F : Set (Set α)) : Prop := ∃ S, IsSunflowerWithKernel F S
```
Mentions: IsSunflowerWithKernel
theorem isSunflower_empty line 50 source
standard axioms: Quot.sound, propext what this means
Statement uses: IsSunflower, EmptyCollection.emptyCollection, Set
Proof uses: of_eq_true, Exists, IsSunflowerWithKernel, Eq.trans, True, congrArg, funext
6 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem isSunflower_singleton line 53 source
standard axioms: Quot.sound, propext what this means
Statement uses: Set, IsSunflower, Singleton.singleton
Proof uses: of_eq_true, Exists, IsSunflowerWithKernel, Eq.trans, True, congrArg, funext
6 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.