Theorems · Theorem · logic and foundations
Set.union_subset_union
∀ {α : Type u} {s₁ s₂ t₁ t₂ : Set α}, s₁ ⊆ s₂ → t₁ ⊆ t₂ → s₁ ∪ t₁ ⊆ s₂ ∪ t₂- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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
- sup_le_supproof · cited by 48
Cited by29
Results whose statement or proof uses this declaration.
- Set.union_subset_union_rightproof · cited by 19
- Set.image2_inter_union_subset_unionproof · cited by 10
- Set.image2_union_inter_subset_unionproof · cited by 9
- Set.union_subset_union_leftproof · cited by 7
- Subalgebra.spectrum_sUnion_connectedComponentInproof · cited by 2
- MeasureTheory.Measure.haar.index_union_leproof · cited by 2
- connectedComponent_eq_iInter_isClopenproof · cited by 2
- MeasureTheory.Measure.haar.addIndex_union_leproof · cited by 2
- IsLinearTopology.hasBasis_subbimoduleproof · cited by 2
- Topology.IsOpenEmbedding.baireSpaceproof · cited by 1
- MeasureTheory.LocallyIntegrable.integrableOn_nhds_isCompactproof · cited by 1
- Set.ite_monoproof · cited by 1