Theorems · Theorem · combinatorics
Finset.biUnion_slice
∀ {α : Type u_1} (𝒜 : Finset (Finset α)) [inst : Fintype α] [inst_1 : DecidableEq α],
(Finset.Iic (Fintype.card α)).biUnion 𝒜.slice = 𝒜- Defined in
- Mathlib.Data.Finset.Slice
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEq
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
- Fintypestatement and proof · cited by 7,736
- Finset.cardproof · cited by 2,327
- Fintype.cardstatement and proof · cited by 1,386
- Finset.Iicstatement and proof · cited by 280
- Finset.biUnionstatement · cited by 217
- Finset.mem_Iicproof · cited by 42
- Finset.card_le_univproof · cited by 32
- Finset.mem_biUnionproof · cited by 26
- Finset.slicestatement · cited by 14
- Finset.Subset.antisymmproof · cited by 12
- Finset.biUnion_subsetproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- Finset.sum_card_sliceproof · cited by 0