Theorems · Theorem · order theory
le_iSup
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α] (f : ι → α) (i : ι), f i ≤ iSup f- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 207 results in Mathlib
- Foundations
- Depth 10 from the axioms, rests on 44 definitions · uses no axioms
- Assumes
- CompleteLattice
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.
- iSupstatement · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- le_sSupproof · cited by 79
Cited by209
Results whose statement or proof uses this declaration.
- Set.subset_iUnionproof · cited by 81
- le_iSup_of_leproof · cited by 79
- iSup_posproof · cited by 61
- le_iSup₂proof · cited by 56
- Finset.sup_eq_iSupproof · cited by 30
- iSup_subtypeproof · cited by 26
- Submodule.mem_iSup_of_memproof · cited by 20
- iSup_commproof · cited by 17
- Set.iUnion_subset_iffproof · cited by 15
- iSup_andproof · cited by 13
- iSup_existsproof · cited by 13
- MeasurableEmbedding.lintegral_mapproof · cited by 10
Showing the 200 most cited of 209.