Theorems · Theorem · order theory
Set.biUnion_subset_biUnion_left
∀ {α : Type u_1} {β : Type u_2} {s s' : Set α} {t : α → Set β}, s ⊆ s' → ⋃ x ∈ s, t x ⊆ ⋃ x ∈ s', t x- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Set.iUnion₂_subsetproof · cited by 48
- Set.subset_biUnion_of_memproof · cited by 24
Cited by18
Results whose statement or proof uses this declaration.
- IsCompact.elim_finite_subcoverproof · cited by 28
- Set.monotone_accumulateproof · cited by 10
- Set.biUnion_monoproof · cited by 3
- IsPreconnected.biUnion_of_reflTransGenproof · cited by 3
- convexJoin_monoproof · cited by 2
- TopologicalSpace.Compacts.isCompact_biUnion_coe_of_isCompactproof · cited by 2
- IsCountablyCompact.elim_finite_subcoverproof · cited by 2
- Set.biUnion_sdiff_biUnion_subsetproof · cited by 2
- Besicovitch.exists_disjoint_closedBall_covering_ae_of_finiteMeasure_auxproof · cited by 1
- MeasureTheory.Measure.restrict_iUnion_congrproof · cited by 1
- indicator_biUnion_finset_eventuallyEqproof · cited by 1