Theorems · Theorem · order theory
le_iSup_of_le
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α] {f : ι → α} {a : α} (i : ι), a ≤ f i → a ≤ iSup f- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 79 results in Mathlib
- Foundations
- Depth 11 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.
- LE.le.transproof · cited by 3,151
- iSupstatement · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- le_iSupproof · cited by 207
Cited by79
Results whose statement or proof uses this declaration.
- le_iSup₂proof · cited by 56
- iSup_monoproof · cited by 37
- Finset.sup_eq_iSupproof · cited by 30
- iSup_mono'proof · cited by 17
- Set.subset_iUnion_of_subsetproof · cited by 16
- MeasureTheory.Measure.measurable_coeproof · cited by 14
- ENNReal.mul_iSupproof · cited by 13
- MeasurableEmbedding.lintegral_mapproof · cited by 10
- FormalMultilinearSeries.le_radius_of_boundproof · cited by 8
- MeasureTheory.SimpleFunc.iSup_eapprox_applyproof · cited by 8
- eVariationOn.sum_leproof · cited by 6
- Order.height_top_eq_krullDimproof · cited by 6