Theorems · Theorem · combinatorics
Multiset.exists_mem_of_ne_zero
∀ {α : Type u_1} {s : Multiset α}, s ≠ 0 → ∃ a, a ∈ s- Defined in
- Mathlib.Data.Multiset.ZeroCons
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
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.
- Multisetstatement and proof · cited by 2,627
Cited by13
Results whose statement or proof uses this declaration.
- Finset.nonempty_of_ne_emptyproof · cited by 9
- Multiset.empty_or_exists_memproof · cited by 5
- card_support_eq_three_iffproof · cited by 3
- UniqueFactorizationMonoid.card_factors_of_irreducibleproof · cited by 2
- WfDvdMonoid.not_isUnit_iff_exists_factors_eqproof · cited by 2
- prime_factors_irreducibleproof · cited by 2
- UniqueFactorizationMonoid.normalizedFactors_posproof · cited by 1
- Associates.exists_prime_dvd_of_not_inf_oneproof · cited by 1
- Multiset.sum_lt_sum_of_nonemptyproof · cited by 1
- FractionalOperation.IsValid.containsproof · cited by 1
- Multiset.prod_lt_prod_of_nonempty'proof · cited by 1
- Polynomial.roots_eq_zero_of_irreducible_of_natDegree_ne_oneproof · cited by 0