Theorems · Theorem · combinatorics
Set.Intersecting.exists_card_eq
∀ {α : Type u_1} [inst : BooleanAlgebra α] [Nontrivial α] [inst_2 : Fintype α] {s : Finset α},
(↑s).Intersecting → ∃ t, s ⊆ t ∧ 2 * t.card = Fintype.card α ∧ (↑t).Intersecting- Cited by
- 1 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Fintypestatement and proof · cited by 7,736
- LE.le.transproof · cited by 3,151
- Nontrivialstatement and proof · cited by 2,416
- Finset.cardstatement and proof · cited by 2,327
- Fintype.cardstatement and proof · cited by 1,386
- BooleanAlgebrastatement and proof · cited by 300
- Set.Subset.rflproof · cited by 255
- Set.Intersectingstatement and proof · cited by 22
- ssubset_iff_subset_neproof · cited by 7
- Set.Intersecting.card_leproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Finset.card_biUnion_le_of_intersectingproof · cited by 0