Theorems · Theorem · order theory
iInf_iSup_eq_of_finite
∀ {α : Type u} {ι : Sort v} {κ : ι → Sort w} [inst : Order.Frame α] [Finite ι] {f : (a : ι) → κ a → α},
⨅ a, ⨆ b, f a b = ⨆ g, ⨅ a, f a (g a)- Defined in
- Mathlib.Data.Set.Finite.Lattice
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Order.FrameFinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Top.topproof · cited by 9,680
- Equivproof · cited by 8,337
- Fintypeproof · cited by 7,736
- Equiv.symmproof · cited by 3,681
- Finitestatement and proof · cited by 3,029
- iSupstatement and proof · cited by 2,415
- iInfstatement and proof · cited by 1,690
- SupSetproof · cited by 154
- InfSetproof · cited by 145
- Order.Framestatement and proof · cited by 88
- Equiv.piCongrLeftproof · cited by 36
Cited by2
Results whose statement or proof uses this declaration.
- Set.Finite.biInf_iSup_eqproof · cited by 1
- iSup_iInf_eq_of_finiteproof · cited by 0