Theorems · Theorem · order theory
iInf_iSup_of_monotone
∀ {ι : Type u_1} {ι' : Type u_2} {α : Type u_3} [Finite ι] [inst : Preorder ι'] [Nonempty ι'] [IsCodirectedOrder ι']
[inst_3 : Order.Coframe 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 · cited by 2,415
- iInfstatement and proof · cited by 1,690
- Monotonestatement and proof · cited by 1,397
- IsCodirectedOrderstatement and proof · cited by 95
- Set.finite_univproof · cited by 52
- Order.Coframestatement and proof · cited by 38
- iSup_univproof · cited by 8
- Set.Finite.iInf_biSup_of_monotoneproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- iInf_iSup_of_antitoneproof · cited by 2
- Set.iInter_iUnion_of_monotoneproof · cited by 0
- Set.iInf_iSup_of_monotoneproof · cited by 0