Theorems · Theorem · order theory
Set.subset_iUnion_of_subset
∀ {α : Type u_1} {ι : Sort u_5} {s : Set α} {t : ι → Set α} (i : ι), s ⊆ t i → s ⊆ ⋃ i, t iThis rather trivial consequence of subset_iUnion is convenient with apply, and has i
explicit for this purpose.
- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 16 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.iUnionstatement · cited by 2,483
- le_iSup_of_leproof · cited by 79
Cited by16
Results whose statement or proof uses this declaration.
- Topology.RelCWComplex.Subcomplex.closedCell_subset_of_memproof · cited by 4
- Algebra.Presentation.coeffs_relation_subset_coeffsproof · cited by 2
- IsLindelof.indexed_countable_subcoverproof · cited by 2
- Topology.RelCWComplex.iUnion_skeletonLT_eq_complexproof · cited by 1
- Topology.RelCWComplex.iUnion_skeleton_eq_complexproof · cited by 1
- exists_clopen_partition_of_clopen_coverproof · cited by 1
- HahnSeries.SummableFamily.isPWO_iUnion_support_prod_smulproof · cited by 1
- Valued.integer.totallyBounded_iff_finite_residueFieldproof · cited by 1
- MeasureTheory.MeasurablySeparable.iUnionproof · cited by 1
- IsLindelof.elim_nhds_subcover'proof · cited by 1
- differentiableOn_iUnion_iff_of_isOpenproof · cited by 0
- mdifferentiableOn_iUnion_iff_of_isOpenproof · cited by 0