Theorems · Theorem · combinatorics
Multiset.mem_filter
∀ {α : Type u_1} {p : α → Prop} [inst : DecidablePred p] {a : α} {s : Multiset α}, a ∈ Multiset.filter p s ↔ a ∈ s ∧ p a- Defined in
- Mathlib.Data.Multiset.Filter
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
- Assumes
- DecidablePred
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.filterstatement · cited by 102
Cited by10
Results whose statement or proof uses this declaration.
- Finset.mem_filterproof · cited by 185
- Multiset.mem_of_mem_filterproof · cited by 4
- Multiset.of_mem_filterproof · cited by 3
- Multiset.Nodup.mem_erase_iffproof · cited by 3
- Multiset.mem_filter_of_memproof · cited by 1
- Multiset.count_map_eq_countproof · cited by 1
- Submonoid.LocalizationMap.uniqueFactorizationMonoidproof · cited by 1
- Finset.sym_filterNe_memproof · cited by 1
- Multiset.card_filter_le_iffproof · cited by 1
- Sym.filter_ne_fillproof · cited by 1