Theorems · Theorem · order theory
le_biSup
∀ {α : Type u_1} [inst : CompleteLattice α] {ι : Type u_8} {s : Set ι} (f : ι → α) {i : ι}, i ∈ s → f i ≤ ⨆ i ∈ s, f i- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses no axioms
- Assumes
- CompleteLattice
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.
- Setstatement and proof · cited by 53,352
- iSupstatement · cited by 2,415
- le_rflproof · cited by 1,558
- CompleteLatticestatement and proof · cited by 1,048
- le_iSup₂_of_leproof · cited by 52
Cited by20
Results whose statement or proof uses this declaration.
- Submodule.biSup_comap_subtype_eq_topproof · cited by 5
- DirectedOn.inf_sSup_eqproof · cited by 3
- isSemisimpleModule_biSup_of_isSemisimpleModule_submoduleproof · cited by 2
- MeasureTheory.VectorMeasure.semivariation_monoproof · cited by 2
- LieModule.lie_mem_genWeightSpaceChain_of_genWeightSpace_eq_bot_rightproof · cited by 2
- MeasureTheory.VectorMeasure.enorm_apply_le_semivariationproof · cited by 2
- HomogeneousIdeal.irrelevant_eq_closureproof · cited by 1
- LinearMap.trace_eq_sum_trace_restrict_of_eq_biSupproof · cited by 1
- eVariationOn.eq_biSup_inter_Iccproof · cited by 1
- Submodule.biSup_comap_eq_top_of_surjectiveproof · cited by 1
- biInf_le_biSupproof · cited by 1
- ContinuousLinearMap.spectralRadius_eq_nnnormproof · cited by 1