Theorems · Theorem · order theory
iInf_of_empty
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α] [IsEmpty ι] (f : ι → α), iInf f = ⊤- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
- Assumes
- CompleteLatticeIsEmpty
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.
- Top.topstatement · cited by 9,680
- iInfstatement · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- IsEmptystatement and proof · cited by 759
- sInf_emptyproof · cited by 12
- iInf_of_isEmptyproof · cited by 10
Cited by12
Results whose statement or proof uses this declaration.
- Set.iInter_of_emptyproof · cited by 23
- InfClosed.iInf_memproof · cited by 4
- Filter.iInf_neBot_of_directedproof · cited by 3
- iInf_iSup_eq_of_finiteproof · cited by 2
- ENat.mul_iInf'proof · cited by 2
- ENNReal.toNNReal_iInfproof · cited by 2
- Filter.lift_iInf_of_map_univproof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.emultiplicity_iSupproof · cited by 1
- SimpleGraph.radius_eq_top_of_isEmptyproof · cited by 1
- MeasureTheory.lintegral_iInf_directed_of_measurableproof · cited by 1
- MeasureTheory.inducedOuterMeasure_union_of_false_of_nonempty_interproof · cited by 0
- DividedPowers.isSubDPIdeal_iInfproof · cited by 0