Theorems · Theorem · combinatorics
Multiset.eq_zero_of_forall_notMem
∀ {α : Type u_1} {s : Multiset α}, (∀ (x : α), x ∉ s) → s = 0- Defined in
- Mathlib.Data.Multiset.ZeroCons
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Multiset.eq_zero_iff_forall_notMemproof · cited by 7
- Finset.eq_empty_of_forall_notMemproof · cited by 6
- Nat.Partition.partition_zero_partsproof · cited by 6
- Multiset.eq_zero_of_subset_zeroproof · cited by 3
- prime_factors_uniqueproof · cited by 3
- UniqueFactorizationMonoid.normalizedFactors_prod_of_primeproof · cited by 2
- Polynomial.roots_eq_zero_iff_isRoot_eq_botproof · cited by 1
- isAddFreimanHom_emptyproof · cited by 0
- isMulFreimanHom_emptyproof · cited by 0
- isAddFreimanIso_emptyproof · cited by 0
- isMulFreimanIso_emptyproof · cited by 0
- UniqueFactorizationMonoid.normalizedFactors_multiset_prodproof · cited by 0