Theorems · Theorem · order theory
Set.iInter_subset_of_subset
∀ {α : Type u_1} {ι : Sort u_5} {s : ι → Set α} {t : Set α} (i : ι), s i ⊆ t → ⋂ i, s i ⊆ tThis rather trivial consequence of iInter_subset is convenient with apply, and has i
explicit for this purpose.
- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.iInterstatement · cited by 1,084
- iInf_le_of_leproof · cited by 62
Cited by9
Results whose statement or proof uses this declaration.
- uniformity_hasBasis_closedproof · cited by 4
- isPiSystem_piiUnionInterproof · cited by 3
- Set.iInter_mono'proof · cited by 1
- MeasureTheory.Measure.exists_null_set_measure_lt_of_disjointproof · cited by 1
- MeasureTheory.Measure.mutuallySingular_of_disjointproof · cited by 1
- isExtreme_iInterproof · cited by 1
- Disjoint.hasSeparatingCover_closed_gdelta_rightproof · cited by 0
- Set.iInter_subset_dissipateproof · cited by 0