Theorems · Theorem · logic and foundations
Set.union_subset_iff
∀ {α : Type u} {s t u : Set α}, s ∪ t ⊆ u ↔ s ⊆ u ∧ t ⊆ u- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 21 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 by21
Results whose statement or proof uses this declaration.
- AddSubgroup.closure_toAddSubmonoidproof · cited by 6
- Matroid.Indep.contract_dep_iffproof · cited by 4
- Set.BijOn.exists_extend_of_subsetproof · cited by 2
- TopologicalSpace.NoetherianSpace.exists_finite_set_closeds_irreducibleproof · cited by 2
- PrimeSpectrum.exists_mul_eq_zero_add_eq_one_basicOpen_eq_of_isClopenproof · cited by 2
- Set.mem_Ici_Ioi_of_subset_of_subsetproof · cited by 1
- Set.mem_Iic_Iio_of_subset_of_subsetproof · cited by 1
- Matroid.contract_closure_eqproof · cited by 1
- RootPairing.Base.exists_root_eq_sum_nat_or_negproof · cited by 1
- Equiv.Perm.support_closure_subset_unionproof · cited by 1
- AddSubgroup.closure_image_isAddIndecomposable_baseOfproof · cited by 1
- Algebra.etaleLocus_eq_univ_iffproof · cited by 1