Theorems · Theorem · order theory
Set.sUnion_subset
∀ {α : Type u_1} {S : Set (Set α)} {t : Set α}, (∀ t' ∈ S, t' ⊆ t) → ⋃₀ S ⊆ t- 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.sUnionstatement · cited by 392
- sSup_leproof · cited by 35
Cited by9
Results whose statement or proof uses this declaration.
- interior_subsetproof · cited by 171
- IsLindelof.elim_countable_subcoverproof · cited by 10
- TopologicalSpace.isOpen_iUnion_countableproof · cited by 9
- balancedCore_subsetproof · cited by 8
- exists_linearIndepOn_extensionproof · cited by 5
- ChainClosure.succ_fixpointproof · cited by 1
- Set.sUnion_subset_sUnionproof · cited by 1
- ContinuousMap.compactOpen_eq_generateFromproof · cited by 1