Theorems · Theorem · order theory
iInf_le_iInf_of_subset
∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] {f : β → α} {s t : Set β},
s ⊆ t → ⨅ x ∈ t, f x ≤ ⨅ x ∈ s, f x- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses no axioms
- Assumes
- CompleteLattice
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.
- Setstatement and proof · cited by 53,352
- iInfstatement · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- biInf_monoproof · cited by 8
Cited by5
Results whose statement or proof uses this declaration.
- Metric.infEDist_antiproof · cited by 7
- Ideal.comap_jacobson_of_surjectiveproof · cited by 2
- UniformOnFun.monoproof · cited by 2
- ProbabilityTheory.IsPreLocalizingSequence.isLocalizingSequence_biInfproof · cited by 1
- isJacobsonRing_localizationproof · cited by 1