Theorems · Theorem · order theory
Set.mem_singleton
∀ {α : Type u_1} (a : α), a ∈ {a}- Defined in
- Mathlib.Data.Set.Insert
- Cited by
- 183 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 by187
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.zeta_specproof · cited by 29
- Set.Nonempty.image_constproof · cited by 26
- Ideal.span_singleton_oneproof · cited by 21
- mem_connectedComponentproof · cited by 21
- IntermediateField.mem_adjoin_simple_selfproof · cited by 19
- Set.Subsingleton.eq_singleton_of_memproof · cited by 16
- MeasureTheory.SimpleFunc.inductionproof · cited by 14
- right_mem_affineSpan_pairproof · cited by 12
- Submodule.IsPrincipal.generator_memproof · cited by 9
- nhdsWithin_insert_of_neproof · cited by 9
- AddSubgroup.mem_closure_singletonproof · cited by 6
- specializes_TFAEproof · cited by 6