Theorems · Theorem · order theory
ciInf_le_of_le
∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompleteLattice α] {a : α} {f : ι → α},
BddBelow (Set.range f) → ∀ (c : ι), f c ≤ a → iInf f ≤ a- Cited by
- 8 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_ciSup_of_leproof · cited by 22
Cited by8
Results whose statement or proof uses this declaration.
- ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunction_le_oneproof · cited by 2
- ProbabilityTheory.IsRatCondKernelCDFAux.integrable_iInf_rat_gtproof · cited by 2
- tendsto_smoothingFun_of_eq_zeroproof · cited by 1
- ciInf₂_leproof · cited by 0
- PiTensorProduct.projectiveSeminorm_add_leproof · cited by 0
- PiTensorProduct.projectiveSeminorm_smul_leproof · cited by 0
- Finite.ciInf_le_of_leproof · cited by 0
- ciInf_le_of_le'proof · cited by 0