Theorems · Theorem · order theory
Finset.set_biInter_insert
∀ {α : Type u_2} {β : Type u_3} [inst : DecidableEq α] (a : α) (s : Finset α) (t : α → Set β),
⋂ x ∈ insert a s, t x = t a ∩ ⋂ x ∈ s, t x- Defined in
- Mathlib.Order.CompleteLattice.Finset
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- Set.iInterstatement · cited by 1,084
- Finset.iInf_insertproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.iIndepSets.iIndepproof · cited by 4
- ProbabilityTheory.Kernel.iIndepSets.indepSetsproof · cited by 3
- Filter.iInf_principal_finsetproof · cited by 3
- ProbabilityTheory.Kernel.iIndepSets.piiUnionInter_of_notMemproof · cited by 3
- TopCat.isTopologicalBasis_cofiltered_limitproof · cited by 1