Theorems · Theorem · combinatorics
Multiset.filter_eq_self
∀ {α : Type u_1} {p : α → Prop} [inst : DecidablePred p] {s : Multiset α}, Multiset.filter p s = s ↔ ∀ a ∈ s, p a- Defined in
- Mathlib.Data.Multiset.Filter
- Cited by
- 6 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.
Cites4
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.cardproof · cited by 375
- Multiset.ofListproof · cited by 290
- Multiset.filterstatement and proof · cited by 102
Cited by6
Results whose statement or proof uses this declaration.
- Multiset.filter_add_notproof · cited by 4
- Sym.countPerms_coe_fill_of_notMemproof · cited by 1
- Equiv.Perm.filter_parts_partition_eq_cycleTypeproof · cited by 1
- Multiset.card_filter_le_iffproof · cited by 1
- Multiset.le_filterproof · cited by 1
- Sym.filter_ne_fillproof · cited by 1