Theorems · Theorem · logic and foundations
Set.union_subset_union_left
∀ {α : Type u} {s₁ s₂ : Set α} (t : Set α), s₁ ⊆ s₂ → s₁ ∪ t ⊆ s₂ ∪ t- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, 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.Subset.rflproof · cited by 255
- Set.union_subset_unionproof · cited by 29
Cited by7
Results whose statement or proof uses this declaration.
- Algebra.adjoin_algebraMap_image_union_eq_adjoin_adjoinproof · cited by 3
- MeasureTheory.setToFun_of_le_map_of_stronglyMeasurableproof · cited by 2
- Set.Ici_subset_Icc_union_Iciproof · cited by 1
- Set.Ioi_subset_Ioc_union_Iciproof · cited by 1
- IntermediateField.Lifts.union_isExtendibleproof · cited by 1
- Matroid.IsCircuit.strong_multi_elimination_insertproof · cited by 1
- Matroid.Indep.union_isBasis_union_of_contract_isBasisproof · cited by 0