Theorems · Theorem · order theory
iSup_prod
∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : CompleteLattice α] {f : β × γ → α}, ⨆ x, f x = ⨆ i, ⨆ j, f (i, j)- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
- 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
- eq_of_forall_ge_iffproof · cited by 96
Cited by10
Results whose statement or proof uses this declaration.
- biSup_prodproof · cited by 5
- iSup_inf_iSupproof · cited by 3
- iSup_prod'proof · cited by 3
- Set.finite_sdiff_iUnion_Ioo'proof · cited by 3
- SimpleGraph.ediam_defproof · cited by 3
- iSup_unpairproof · cited by 3
- iInf_iSup_eq_of_finiteproof · cited by 2
- Set.Finite.biInf_iSup_eqproof · cited by 1
- Set.iUnion_prod'proof · cited by 1
- LinearMap.IsSymmetric.directSum_isInternal_of_commuteproof · cited by 0