Theorems · Theorem · order theory
biSup_iInter_of_pairwise_disjoint
∀ {α : Type u} [inst : CompletelyDistribLattice α] {ι : Type u_1} {κ : Type u_2} [hκ : Nonempty κ] {f : ι → α},
Pairwise (Function.onFun Disjoint f) → ∀ (s : κ → Set ι), ⨆ i ∈ ⋂ j, s j, f i = ⨅ j, ⨆ i ∈ s j, f i- Defined in
- Mathlib.Order.CompleteBooleanAlgebra
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- iSupstatement and proof · cited by 2,415
- Disjointstatement and proof · cited by 2,201
- le_antisymmproof · cited by 2,068
- iInfstatement and proof · cited by 1,690
- le_rflproof · cited by 1,558
- Set.iInterstatement and proof · cited by 1,084
- Function.onFunstatement and proof · cited by 570
- Pairwisestatement and proof · cited by 516
- bot_leproof · cited by 306
- iSup_congr_Propproof · cited by 247
- le_infproof · cited by 107
Cited by1
Results whose statement or proof uses this declaration.
- Set.biUnion_iInter_of_pairwise_disjointproof · cited by 0