Theorems · Theorem · order theory
iInf_range
∀ {α : Type u_1} {β : Type u_2} {ι : Sort u_4} [inst : CompleteLattice α] {g : β → α} {f : ι → β},
⨅ b ∈ Set.range f, g b = ⨅ i, g (f i)- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
- 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.
- Setstatement · cited by 53,352
- Set.rangestatement and proof · cited by 4,705
- iInfstatement and proof · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- iInf_subtype''proof · cited by 11
- iInf_range'proof · cited by 3
Cited by27
Results whose statement or proof uses this declaration.
- iInf_uniformityproof · cited by 19
- Set.biInter_rangeproof · cited by 17
- iInf_sup_eqproof · cited by 7
- Filter.nhds_eqproof · cited by 6
- HomogeneousIdeal.toIdeal_iInfproof · cited by 3
- IsIntegrallyClosed.of_localization_maximalproof · cited by 2
- MeasureTheory.OuterMeasure.iInf_applyproof · cited by 2
- MeasureTheory.OuterMeasure.iInf_apply'proof · cited by 2
- Filter.isCountablyGenerated_seqproof · cited by 2
- ClosedSubmodule.toSubmodule_iInfproof · cited by 1
- Filter.atTop_eq_generate_Iciproof · cited by 1
- iInf_nat_gt_zero_eqproof · cited by 1