Theorems · Theorem · order theory
iInf_mono
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α] {f g : ι → α}, (∀ (i : ι), g i ≤ f i) → iInf g ≤ iInf f- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 29 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.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iInfstatement · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- le_iInfproof · cited by 102
- iInf_le_of_leproof · cited by 62
Cited by29
Results whose statement or proof uses this declaration.
- iInf_commproof · cited by 12
- iInf_inf_eqproof · cited by 12
- iInf₂_monoproof · cited by 10
- biInf_monoproof · cited by 8
- Set.iInter_monoproof · cited by 7
- Set.MapsTo.egauge_leproof · cited by 5
- Filter.lift_monoproof · cited by 5
- MeasureTheory.OuterMeasure.comap_iInfproof · cited by 3
- Set.iInter_mono''proof · cited by 3
- ProbabilityTheory.bayesRisk_const'proof · cited by 2
- BoxIntegral.IntegrationParams.toFilterDistortion_monoproof · cited by 2
- MeasureTheory.OuterMeasure.map_iInf_comapproof · cited by 2