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Theorems · Theorem · order theory

Set.sUnion_subset_sUnion

∀ {α : Type u_1} {S T : Set (Set α)}, S ⊆ T → ⋃₀ S ⊆ ⋃₀ T
Defined in
Mathlib.Data.Set.Lattice
Cited by
1 results in Mathlib
Foundations
Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set.sUnion_mono · cited by 0Set.sUnion_monoSet · cited by 53352SetSet.sUnion · cited by 392Set.sUnionSet.subset_sUnion_of_mem · cited by 39Set.subset_sUnion_of_memSet.sUnion_subset · cited by 9Set.sUnion_subsetSet.sUnion_subset_sUnionCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.