Theorems · Theorem · logic and foundations
Set.mem_union
∀ {α : Type u} (x : α) (a b : Set α), x ∈ a ∪ b ↔ x ∈ a ∨ x ∈ b- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 47 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 by47
Results whose statement or proof uses this declaration.
- Matroid.restrict_closure_eq'proof · cited by 9
- iInf_unionproof · cited by 5
- HasSum.of_nat_of_neg_add_oneproof · cited by 5
- iInf_splitproof · cited by 4
- LieAlgebra.Basis.iSup_cartan_borelLower_borelUpper_eq_topproof · cited by 4
- finsum_add_distribproof · cited by 4
- Function.support_prodMkproof · cited by 3
- Metric.ediam_union_le_add_edistproof · cited by 3
- ProbabilityTheory.Kernel.IndepSets.unionproof · cited by 3
- Topology.IsCoinducing.isConnected_preimage_of_isClosedproof · cited by 3
- IsSemilinearSet.unionproof · cited by 3
- Set.Definable.unionproof · cited by 3