Theorems · Theorem · order theory
Set.singleton_subset_iff
∀ {α : Type u_1} {a : α} {s : Set α}, {a} ⊆ s ↔ a ∈ s- Defined in
- Mathlib.Data.Set.Insert
- Cited by
- 206 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 18 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 and proof · cited by 53,352
Cited by206
Results whose statement or proof uses this declaration.
- Submodule.span_singleton_le_iff_memproof · cited by 21
- Set.eq_singleton_iff_unique_memproof · cited by 20
- Ideal.span_singleton_le_span_singletonproof · cited by 15
- Set.subset_sdiff_singletonproof · cited by 14
- Matroid.indep_singletonproof · cited by 12
- Unitization.quasispectrum_eq_spectrum_inr'proof · cited by 12
- PrimeSpectrum.isTopologicalBasis_basic_opensproof · cited by 11
- MeasureTheory.Measure.dirac_applyproof · cited by 9
- AddSubgroup.zmultiples_leproof · cited by 7
- Set.subset_compl_singleton_iffproof · cited by 7
- Set.zero_subsetproof · cited by 7
- Submodule.mem_span_finite_of_mem_spanproof · cited by 6
Showing the 200 most cited of 206.