Theorems · Theorem · combinatorics
Finset.card_truncatedSup_union_add_card_truncatedSup_infs
∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : Fintype α] (𝒜 ℬ : Finset (Finset α)) (s : Finset α),
((𝒜 ∪ ℬ).truncatedSup s).card + ((𝒜 ⊼ ℬ).truncatedSup s).card = (𝒜.truncatedSup s).card + (ℬ.truncatedSup s).card- Cited by
- 1 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- Top.topproof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Fintypestatement and proof · cited by 7,736
- Finset.cardstatement and proof · cited by 2,327
- add_commproof · cited by 1,535
- HasInfs.infsstatement and proof · cited by 105
- lowerClosureproof · cited by 83
- Finset.hasInfsstatement · cited by 62
- Finset.truncatedSupstatement and proof · cited by 19
- Finset.card_union_add_card_interproof · cited by 14
- Finset.truncatedSup_of_notMemproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- AhlswedeZhang.supSum_union_add_supSum_infsproof · cited by 1