ExampleConstruction: AI-generatedVerification: AI-generatedSession-authored (Fable 5 assisted)precheck 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

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

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 · next 3 levels

Direct dependencies and their dependencies through the next three levels: 9 results over 7 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.