Theorems · Theorem · combinatorics
Multiset.singleton_le
∀ {α : Type u_1} {a : α} {s : Multiset α}, {a} ≤ s ↔ a ∈ s- Defined in
- Mathlib.Data.Multiset.ZeroCons
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Multisetstatement and proof · cited by 2,627
- Multiset.consproof · cited by 313
- Multiset.mem_of_leproof · cited by 17
- Multiset.exists_cons_of_memproof · cited by 15
- Multiset.zero_leproof · cited by 8
- Multiset.cons_le_consproof · cited by 6
- Multiset.mem_singleton_selfproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Multiset.disjoint_leftproof · cited by 9
- IsLocalization.OverPrime.mem_normalizedFactors_of_isPrimeproof · cited by 1
- UniqueFactorizationMonoid.factors_eq_singleton_of_irreducibleproof · cited by 0