Theorems · Theorem · order theory
iSup_iInf_of_monotone
∀ {ι : Type u_1} {ι' : Type u_2} {α : Type u_3} [Finite ι] [inst : Preorder ι'] [Nonempty ι'] [IsDirectedOrder ι']
[inst_3 : Order.Frame α] {f : ι → ι' → α}, (∀ (i : ι), Monotone (f i)) → ⨆ j, ⨅ i, f i j = ⨅ i, ⨆ j, f i j- Defined in
- Mathlib.Data.Set.Finite.Lattice
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- Set.univproof · cited by 3,945
- Finitestatement and proof · cited by 3,029
- iSupstatement and proof · cited by 2,415
- iInfstatement · cited by 1,690
- Monotonestatement and proof · cited by 1,397
- IsDirectedOrderstatement and proof · cited by 316
- Order.Framestatement and proof · cited by 88
- Set.finite_univproof · cited by 52
- iInf_univproof · cited by 8
- Set.Finite.iSup_biInf_of_monotoneproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- iSup_iInf_of_antitoneproof · cited by 2
- Set.iUnion_iInter_of_monotoneproof · cited by 1
- Set.iSup_iInf_of_monotoneproof · cited by 0