Theorems · Theorem · order theory
le_ciInf
∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompleteLattice α] [Nonempty ι] {f : ι → α} {c : α},
(∀ (x : ι), c ≤ f x) → c ≤ iInf fThe indexed minimum of a function is bounded below by a uniform lower bound
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iInfstatement · cited by 1,690
- ConditionallyCompleteLatticestatement and proof · cited by 364
- ciSup_leproof · cited by 56
Cited by32
Results whose statement or proof uses this declaration.
- EuclideanGeometry.dist_orthogonalProjection_eq_infDistproof · cited by 5
- LipschitzOnWith.extend_realproof · cited by 3
- ProbabilityTheory.IsMeasurableRatCDF.monotone_stieltjesFunctionAuxproof · cited by 2
- Metric.glueDist_glued_pointsproof · cited by 2
- ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunctionAux_nonnegproof · cited by 2
- le_mul_ciInfproof · cited by 2
- le_add_ciInfproof · cited by 2
- PiTensorProduct.norm_eval_le_projectiveSeminormproof · cited by 2
- Real.iInf_Ioi_eq_iInf_rat_gtproof · cited by 2
- ProbabilityTheory.IsRatCondKernelCDFAux.integrable_iInf_rat_gtproof · cited by 2
- EuclideanGeometry.Sphere.IsTangent.infDist_eq_radiusproof · cited by 2
- le_ciInf_addproof · cited by 2