ExampleConstruction: AI-generatedVerification: AI-generatedprecheck passaudited 2026-07-31

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.

Four explicit petals with a common two-element core form a sunflower

Example

The four sets

${1, 2, 3, 4}, {1, 2, 5, 6}, {1, 2, 7, 8}, {1, 2, 9, 10}$

form a $4$ -petal sunflower. Their common core is ${1, 2}$ and their petals are the pairwise disjoint sets ${3, 4}$ , ${5, 6}$ , ${7, 8}$ , and ${9, 10}$ .

Facts & Assumptions

Given: The four sets displayed in the Example.

[F1]

Distinct sets form a sunflower when all pairwise intersections equal one common core (Sunflowers, petals, and their common core).

Verification

technique · direct

1.1

Every displayed set contains ${1, 2}$ , and outside this pair their elements lie in disjoint two-element blocks.

given

2.1

Therefore the intersection of any two distinct displayed sets is exactly ${1, 2}$ .

step 1.1

3.1

By [F1], the four sets form a sunflower with the stated core and petals.

step 2.1F1∎

Depends on

Sunflowers, petals, and their common core

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

2 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.