Theorems · Theorem · combinatorics
Finset.mem_singleton
∀ {α : Type u_1} {a b : α}, b ∈ {a} ↔ b = a- Defined in
- Mathlib.Data.Finset.Insert
- Cited by
- 103 results in Mathlib
- Foundations
- Depth 54 from the axioms, rests on 818 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Multiset.mem_singletonproof · cited by 14
Cited by103
Results whose statement or proof uses this declaration.
- Finsupp.sum_single_indexproof · cited by 130
- Finset.univ_uniqueproof · cited by 94
- Finset.mem_singleton_selfproof · cited by 44
- Finset.sum_eq_single_of_memproof · cited by 33
- Finsupp.prod_single_indexproof · cited by 26
- tsum_eq_singleproof · cited by 19
- Finset.singleton_injectiveproof · cited by 14
- Finset.notMem_singletonproof · cited by 13
- hasSum_singleproof · cited by 10
- Finset.mem_sym_iffproof · cited by 9
- Finset.HasAntidiagonal.antidiagonal_zeroproof · cited by 8
- Polynomial.cyclotomic_primeproof · cited by 7