Theorems · Theorem · order theory
Set.iUnion_inter_of_monotone
∀ {ι : Type u_12} {α : Type u_13} [inst : Preorder ι] [IsDirectedOrder ι] {s t : ι → Set α},
Monotone s → Monotone t → ⋃ i, s i ∩ t i = (⋃ i, s i) ∩ ⋃ i, t i- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderIsDirectedOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Preorderstatement and proof · cited by 7,952
- Set.iUnionstatement · cited by 2,483
- Monotonestatement and proof · cited by 1,397
- IsDirectedOrderstatement and proof · cited by 316
- iSup_inf_of_monotoneproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- exists_spanning_measurableSet_leproof · cited by 1
- iUnion_Ioo_of_mono_of_isGLB_of_isLUBproof · cited by 1