Theorems · Theorem · order theory
Set.mem_singleton_iff
∀ {α : Type u_1} {a b : α}, a ∈ {b} ↔ a = b- Defined in
- Mathlib.Data.Set.Insert
- Cited by
- 172 results in Mathlib
- Foundations
- Depth 4 from the axioms, rests on 13 definitions · 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 · cited by 53,352
Cited by172
Results whose statement or proof uses this declaration.
- Submodule.mem_botproof · cited by 55
- Algebra.self_mem_adjoin_singletonproof · cited by 37
- finsum_eq_singleproof · cited by 18
- hasSumUniformlyOn_iff_tendstoUniformlyOnproof · cited by 12
- AddSubmonoid.mem_botproof · cited by 12
- LieSubmodule.mem_botproof · cited by 11
- collinear_pairproof · cited by 8
- lowerClosure_singletonproof · cited by 8
- Set.Icc_sdiff_rightproof · cited by 8
- gauge_le_of_memproof · cited by 8
- Set.insert_sdiff_singleton_commproof · cited by 7
- StieltjesFunction.measure_singletonproof · cited by 6