Theorems · Theorem · order theory
iInf_apply
∀ {α : Type u_8} {β : α → Type u_9} {ι : Sort u_10} [inst : (i : α) → InfSet (β i)] {f : ι → (a : α) → β a} {a : α},
(⨅ i, f i) a = ⨅ i, f i a- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses propext, Quot.sound
- Assumes
- InfSet
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Set.Elemproof · cited by 7,166
- Set.rangeproof · cited by 4,705
- iInfstatement and proof · cited by 1,690
- InfSet.sInfproof · cited by 935
- Set.range_compproof · cited by 223
- InfSetstatement and proof · cited by 145
- Set.image_eq_rangeproof · cited by 57
- sInf_applyproof · cited by 1
Cited by15
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.sInf_iffproof · cited by 4
- AddCon.coe_sInfproof · cited by 1
- CategoryTheory.ObjectProperty.preservesLimitsOfShape_eq_iSupproof · cited by 1
- RingCon.coe_sInfproof · cited by 1
- Con.coe_sInfproof · cited by 1
- CategoryTheory.MorphismProperty.isLocal_iSupproof · cited by 1
- MeasureTheory.lintegral_iInf'proof · cited by 1
- binary_relation_sInf_iffproof · cited by 0
- Setoid.sInf_defproof · cited by 0
- Set.mulIndicator_iInter_applyproof · cited by 0
- CategoryTheory.ObjectProperty.preservesColimitsOfShape_eq_iSupproof · cited by 0
- CategoryTheory.MorphismProperty.isColocal_iSupproof · cited by 0