Theorems · Theorem · order theory
iInf_iSup_eq
∀ {α : Type u} {ι : Sort w} {κ : ι → Sort w'} [inst : CompletelyDistribLattice α] {f : (a : ι) → κ a → α},
⨅ a, ⨆ b, f a b = ⨆ g, ⨅ a, f a (g a)- Defined in
- Mathlib.Order.CompleteBooleanAlgebra
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompletelyDistribLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iSupstatement · cited by 2,415
- iInfstatement · cited by 1,690
- CompletelyDistribLatticestatement and proof · cited by 9
- CompletelyDistribLattice.MinimalAxioms.ofproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- biSup_iInter_of_pairwise_disjointproof · cited by 1