Theorems · Theorem · logic and foundations
Set.mem_inter_iff
∀ {α : Type u} (x : α) (a b : Set α), x ∈ a ∩ b ↔ x ∈ a ∧ x ∈ b- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 50 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 by50
Results whose statement or proof uses this declaration.
- Summable.hasSumproof · cited by 184
- Set.indicator_indicatorproof · cited by 12
- Set.support_indicatorproof · cited by 10
- Matroid.restrict_closure_eq'proof · cited by 9
- finprod_mem_eq_prod_of_inter_mulSupport_eqproof · cited by 7
- finsum_mem_eq_sum_of_inter_support_eqproof · cited by 7
- MeasureTheory.le_hittingBtwnproof · cited by 6
- Set.Ici_inter_Iciproof · cited by 4
- ProperlyDiscontinuousSMul.exists_nhds_image_smul_eq_selfproof · cited by 3
- ProperlyDiscontinuousVAdd.exists_nhds_image_vadd_eq_selfproof · cited by 3
- Set.zero_mem_sub_iffproof · cited by 3
- SimpleGraph.addCayley_erase_zeroproof · cited by 3