Theorems · Theorem · order theory
Set.iUnion_subset
∀ {α : Type u_1} {ι : Sort u_5} {s : ι → Set α} {t : Set α}, (∀ (i : ι), s i ⊆ t) → ⋃ i, s i ⊆ t- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 51 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
- iSup_leproof · cited by 190
Cited by51
Results whose statement or proof uses this declaration.
- Set.iUnion₂_subsetproof · cited by 48
- Set.iUnion_subset_iffproof · cited by 15
- VitaliFamily.measure_le_of_frequently_leproof · cited by 5
- Set.iUnion₂_subset_iUnionproof · cited by 4
- Subalgebra.coe_iSup_of_directedproof · cited by 4
- ENNReal.iUnion_Iic_coe_natproof · cited by 3
- Submodule.coe_iSup_of_directedproof · cited by 3
- Submodule.iSup_spanproof · cited by 3
- Matroid.IsCircuit.strong_multi_eliminationproof · cited by 2
- Matroid.IsBasis.iUnion_isBasis_iUnionproof · cited by 2
- IntermediateField.coe_iSup_of_directedproof · cited by 2
- MeasureTheory.measure_iUnion_congr_of_subsetproof · cited by 2