Theorems · Theorem · order theory
iInf_subtype
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α] {p : ι → Prop} {f : Subtype p → α},
iInf f = ⨅ i, ⨅ (h : p i), f ⟨i, h⟩- 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iInfstatement and proof · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- iInf_leproof · cited by 104
- le_iInfproof · cited by 102
- le_iInf₂proof · cited by 67
- ge_antisymmproof · cited by 51
- iInf₂_leproof · cited by 45
Cited by12
Results whose statement or proof uses this declaration.
- iInf_subtype'proof · cited by 34
- iInf_subtype''proof · cited by 11
- Set.iInter_subtypeproof · cited by 9
- SimpleGraph.vertexCoverNum_existsproof · cited by 3
- LinearMap.mem_span_iff_continuousproof · cited by 1
- MeasureTheory.OuterMeasure.trim_eq_iInf'proof · cited by 0
- Metric.exists_set_encard_eq_coveringNumberproof · cited by 0
- iInf_valuationSubring_supersetproof · cited by 0
- UniformSpace.Completion.uniformity_distproof · cited by 0
- SimpleGraph.chromaticNumber_eq_iInfproof · cited by 0
- UniformOnFun.isUniformInducing_pi_restrictproof · cited by 0
- MeasureTheory.measure_eq_iInf'proof · cited by 0