Theorems · Theorem · order theory
iSup_iSup_eq_left
∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] {b : β} {f : (x : β) → x = b → α},
⨆ x, ⨆ (h : x = b), f x h = f b ⋯- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iSupstatement · cited by 2,415
- le_antisymmproof · cited by 2,068
- le_rflproof · cited by 1,558
- CompleteLatticestatement and proof · cited by 1,048
- iSup₂_leproof · cited by 96
- le_iSup₂proof · cited by 56
Cited by15
Results whose statement or proof uses this declaration.
- Set.iUnion_iUnion_eq_leftproof · cited by 27
- iSup_insertproof · cited by 10
- iSup_singletonproof · cited by 7
- iSup_split_singleproof · cited by 3
- LieAlgebra.Basis.iSupIndep_rootSpaceproof · cited by 3
- MeasureTheory.isTightMeasureSet_range_of_tendsto_limsup_innerproof · cited by 2
- MeasureTheory.Measure.LebesgueDecomposition.iSup_mem_measurableLEproof · cited by 2
- Metric.ediam_pairproof · cited by 2
- MeasureTheory.isTightMeasureSet_range_of_tendsto_limsup_measure_norm_gtproof · cited by 1
- spectrum.spectralRadius_oneproof · cited by 1
- Finset.iSup_singletonproof · cited by 1
- Metric.exists_set_encard_eq_packingNumberproof · cited by 0