Theorems · Theorem · logic and foundations
Set.union_subset
∀ {α : Type u} {s t r : Set α}, s ⊆ r → t ⊆ r → s ∪ t ⊆ r- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 71 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
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
Cited by71
Results whose statement or proof uses this declaration.
- IntermediateField.adjoin_le_iffproof · cited by 28
- Set.sdiff_union_of_subsetproof · cited by 18
- Algebra.gcproof · cited by 7
- Submodule.mem_span_finite_of_mem_spanproof · cited by 6
- IntermediateField.adjoin_adjoin_leftproof · cited by 6
- TopologicalSpace.isTopologicalBasis_of_subbasisproof · cited by 6
- MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iffproof · cited by 5
- UniqueDiffWithinAt.prodproof · cited by 4
- StarAlgebra.gcproof · cited by 4
- Algebra.adjoin_algebraMap_image_union_eq_adjoin_adjoinproof · cited by 3
- NonUnitalStarAlgebra.gcproof · cited by 3
- Set.exists_superset_subset_encard_eqproof · cited by 3