Theorems · Theorem · order theory
sup_sInf_le_iInf_sup
∀ {α : Type u_1} [inst : CompleteLattice α] {a : α} {s : Set α}, a ⊔ sInf s ≤ ⨅ b ∈ s, a ⊔ bThis is a weaker version of sup_sInf_eq
- Defined in
- Mathlib.Order.CompleteLattice.Lemmas
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- iInfstatement · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- InfSet.sInfstatement · cited by 935
- sInf_leproof · cited by 110
- le_iInf₂proof · cited by 67
- sup_le_sup_leftproof · cited by 20
Cited by1
Results whose statement or proof uses this declaration.
- codisjoint_sInf_rightproof · cited by 0