Theorems · Theorem · order theory
Set.subset_sUnion_of_mem
∀ {α : Type u_1} {S : Set (Set α)} {t : Set α}, t ∈ S → t ⊆ ⋃₀ S- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 39 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
- le_sSupproof · cited by 79
Cited by39
Results whose statement or proof uses this declaration.
- interior_maximalproof · cited by 29
- TopologicalSpace.nhds_generateFromproof · cited by 15
- exists_linearIndepOn_extensionproof · cited by 5
- MonotoneOn.convexOn_of_derivproof · cited by 4
- StrictMonoOn.strictConvexOn_of_derivproof · cited by 4
- Vitali.exists_disjoint_subfamily_covering_enlargementproof · cited by 3
- isPreconnected_sUnionproof · cited by 3
- ultrafilterBasis_is_basisproof · cited by 3
- Convex.mul_sub_le_image_sub_of_le_derivproof · cited by 3
- Convex.mul_sub_lt_image_sub_of_lt_derivproof · cited by 3
- isStationary_sUnion_iff_of_cof_le_oneproof · cited by 3
- exists_sSupIndep_disjoint_sSup_atomsproof · cited by 2