Theorems · Theorem · combinatorics
Multiset.mem_cons
∀ {α : Type u_1} {a b : α} {s : Multiset α}, a ∈ b ::ₘ s ↔ a = b ∨ a ∈ s- Defined in
- Mathlib.Data.Multiset.ZeroCons
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, 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.
- Multisetstatement and proof · cited by 2,627
- Multiset.consstatement · cited by 313
Cited by29
Results whose statement or proof uses this declaration.
- Multiset.mem_cons_selfproof · cited by 44
- Multiset.mem_cons_of_memproof · cited by 35
- Finset.mem_consproof · cited by 35
- UniqueFactorizationMonoid.exists_mem_normalizedFactors_of_dvdproof · cited by 8
- Directed.finset_leproof · cited by 6
- WfDvdMonoid.exists_factorsproof · cited by 5
- Multiset.Pi.cons_nestatement · cited by 5
- Multiset.exists_mem_of_rel_of_memproof · cited by 4
- Multiset.dvd_sumproof · cited by 4
- UniqueFactorizationMonoid.exists_mem_factors_of_dvdproof · cited by 4
- IsAddFreimanHom.add_eq_addproof · cited by 3
- Multiset.le_infproof · cited by 3