Theorems · Theorem · order theory
iInf_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
- 12 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.
- iInfstatement · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- iInf_leproof · cited by 104
- le_iInfproof · cited by 102
- ge_antisymmproof · cited by 51
- iInf_monoproof · cited by 29
Cited by12
Results whose statement or proof uses this declaration.
- Filter.prod_atTop_atTop_eqproof · cited by 20
- nhds_eq_orderproof · cited by 9
- MeasureTheory.OuterMeasure.trim_eq_iInfproof · cited by 6
- Set.iInter_commproof · cited by 6
- biInf_prodproof · cited by 4
- iInf₂_commproof · cited by 2
- Finset.iInf_biUnionproof · cited by 1
- UniformOnFun.iInf_eqproof · cited by 1
- ContinuousMap.hasBasis_nhdsproof · cited by 1
- Filter.prod_defproof · cited by 1
- Filter.nhds_nhdsproof · cited by 1
- iInf_extend_topproof · cited by 0