Theorems · Theorem · order theory
iSup_comm
∀ {α : Type u_1} {ι : Sort u_4} {ι' : Sort u_5} [inst : CompleteLattice α] {f : ι → ι' → α},
⨆ i, ⨆ j, f i j = ⨆ j, ⨆ i, f i j- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 17 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
- CompleteLatticestatement and proof · cited by 1,048
- le_iSupproof · cited by 207
- iSup_leproof · cited by 190
- iSup_monoproof · cited by 37
Cited by17
Results whose statement or proof uses this declaration.
- MeasureTheory.lintegral_sum_measureproof · cited by 16
- Set.iUnion_commproof · cited by 6
- biSup_prodproof · cited by 5
- iSup_iUnionproof · cited by 5
- Encodable.iSup_decode₂proof · cited by 3
- ProbabilityTheory.Kernel.indep_iSup_limsupproof · cited by 3
- iSupIndep_comp_coe_iff_supIndepproof · cited by 3
- LieAlgebra.Basis.iSupIndep_rootSpaceproof · cited by 3
- Module.End.iSup_iInf_maxGenEigenspace_eq_top_of_forall_mapsToproof · cited by 2
- iSup_extend_botproof · cited by 2
- iSup₂_commproof · cited by 1
- MeasureTheory.setLIntegral_iUnion_of_directedproof · cited by 1