Theorems · Theorem · combinatorics
Finset.singleton_subset_iff
∀ {α : Type u_1} {s : Finset α} {a : α}, {a} ⊆ s ↔ a ∈ s- Defined in
- Mathlib.Data.Finset.Insert
- Cited by
- 38 results in Mathlib
- Foundations
- Depth 57 from the axioms · 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 and proof · cited by 13,712
- Finset.singleton_subset_set_iffproof · cited by 5
Cited by38
Results whose statement or proof uses this declaration.
- Finset.disjoint_leftproof · cited by 50
- Finset.single_le_sumproof · cited by 34
- Finset.SupIndep.pairwiseDisjointproof · cited by 7
- Polynomial.support_trinomial_subsetproof · cited by 5
- AddMonoidAlgebra.support_coeff_mul_subsetproof · cited by 5
- MonoidAlgebra.support_coeff_mul_subsetproof · cited by 3
- Finset.single_le_prod'proof · cited by 3
- Finpartition.equitabilise_auxproof · cited by 3
- hasProd_zero_of_exists_eq_zeroproof · cited by 3
- PairReduction.pairSet_subsetproof · cited by 2
- Polynomial.support_binomial_subsetproof · cited by 2
- Finset.single_lt_sumproof · cited by 2