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Copyright 2026 The Formal Conjectures Authors.
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you may not use this file except in compliance with the License.
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-/
module
public import Mathlib.Data.Set.Card@[expose] public sectionSunflowers
This file defines sunflowers of set families.
variable {α : Type*}
A sunflower F with kernel S is a collection of sets in which all possible distinct pairs of sets
share the same intersection S.
def IsSunflowerWithKernel (F : Set (Set α)) (S : Set α) : Prop :=
F.Pairwise (fun A B => A ∩ B = S)theorem isSunflowerWithKernel_empty (S : Set α) : IsSunflowerWithKernel {} S := α:Type u_1S:Set α⊢ IsSunflowerWithKernel ∅ S
All goals completed! 🐙theorem isSunflowerWithKernel_singleton (S : Set α) (A : Set α) :
IsSunflowerWithKernel {A} S := α:Type u_1S:Set αA:Set α⊢ IsSunflowerWithKernel {A} S
All goals completed! 🐙
A sunflower F is a collection of sets in which all possible distinct pairs of sets share the
same intersection.
def IsSunflower (F : Set (Set α)) : Prop := ∃ S, IsSunflowerWithKernel F Stheorem isSunflower_empty : IsSunflower (∅ : Set (Set α)) := α:Type u_1⊢ IsSunflower ∅
All goals completed! 🐙theorem isSunflower_singleton (A : Set α) : IsSunflower {A} := α:Type u_1A:Set α⊢ IsSunflower {A}
All goals completed! 🐙