Theorems · Theorem · order theory
ciInf_le
∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompleteLattice α] {f : ι → α},
BddBelow (Set.range f) → ∀ (c : ι), iInf f ≤ f cThe indexed infimum of a function is bounded above by the value taken at one point
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses no axioms
- Assumes
- ConditionallyCompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.rangestatement and proof · cited by 4,705
- iInfstatement · cited by 1,690
- BddBelowstatement and proof · cited by 401
- ConditionallyCompleteLatticestatement and proof · cited by 364
- le_ciSupproof · cited by 57
Cited by25
Results whose statement or proof uses this declaration.
- ciInf_le'proof · cited by 6
- LipschitzOnWith.extend_realproof · cited by 3
- Real.iInf_Ioi_eq_iInf_rat_gtproof · cited by 2
- ProbabilityTheory.IsMeasurableRatCDF.monotone_stieltjesFunctionAuxproof · cited by 2
- Metric.glueDist_glued_pointsproof · cited by 2
- schnirelmannDensity_le_divproof · cited by 2
- PiTensorProduct.projectiveSeminorm_tprod_leproof · cited by 2
- ProbabilityTheory.iInf_rat_gt_defaultRatCDFproof · cited by 1
- norm_eq_iInf_iff_real_inner_le_zeroproof · cited by 1
- smoothingFun_leproof · cited by 1
- GromovHausdorff.hausdorffDist_optimalproof · cited by 1
- Submodule.starProjection_tendsto_closure_iSupproof · cited by 1