Theorems · Theorem · order theory
biInf_le_biSup
∀ {α : Type u_1} [inst : CompleteLattice α] {ι : Type u_8} {s : Set ι},
s.Nonempty → ∀ {f : ι → α}, ⨅ i ∈ s, f i ≤ ⨆ i ∈ s, f i- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses Classical.choice
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- LE.le.transproof · cited by 3,151
- Set.Nonemptystatement and proof · cited by 2,627
- iSupstatement · cited by 2,415
- iInfstatement · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- le_biSupproof · cited by 20
- biInf_leproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- Set.biInter_subset_biUnionproof · cited by 0