Theorems · Theorem · combinatorics
Multiset.exists_mem_of_rel_of_mem
∀ {α : Type u_1} {β : Type v} {r : α → β → Prop} {s : Multiset α} {t : Multiset β},
Multiset.Rel r s t → ∀ {a : α}, a ∈ s → ∃ b ∈ t, r a b- Defined in
- Mathlib.Data.Multiset.ZeroCons
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.Relstatement and proof · cited by 47
- Multiset.mem_cons_selfproof · cited by 44
- Multiset.mem_consproof · cited by 29
Cited by4
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.exists_mem_normalizedFactors_of_dvdproof · cited by 8
- UniqueFactorizationMonoid.exists_mem_factors_of_dvdproof · cited by 4
- irreducible_iff_prime_of_existsUnique_irreducible_factorsproof · cited by 1
- Multiset.rel_replicate_leftproof · cited by 1