Theorems · Theorem · order theory
iSup_exists
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α] {p : ι → Prop} {f : Exists p → α},
⨆ (x : Exists p), f x = ⨆ i, ⨆ (h : p i), f ⋯- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 13 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iSupstatement and proof · cited by 2,415
- le_antisymmproof · cited by 2,068
- CompleteLatticestatement and proof · cited by 1,048
- le_iSupproof · cited by 207
- iSup_leproof · cited by 190
- iSup₂_leproof · cited by 96
- le_iSup₂proof · cited by 56
Cited by13
Results whose statement or proof uses this declaration.
- Set.iUnion_existsproof · cited by 45
- iSup_iUnionproof · cited by 5
- ProbabilityTheory.Kernel.indep_iSup_limsupproof · cited by 3
- LieAlgebra.Basis.iSupIndep_rootSpaceproof · cited by 3
- iSup_extend_botproof · cited by 2
- Finset.iSup_biUnionproof · cited by 1
- Finset.iSup_finset_imageproof · cited by 1
- UniformOnFun.edist_def'proof · cited by 1
- Set.iUnion_nonempty_indexproof · cited by 1
- SpectrumRestricts.nnreal_iff_spectralRadius_leproof · cited by 1
- LieAlgebra.Basis.root_mem_or_mem_negproof · cited by 0
- UniformOnFun.edist_continuousRestrictproof · cited by 0