Theorems · Theorem · combinatorics
Multiset.filter_congr
∀ {α : Type u_1} {p q : α → Prop} [inst : DecidablePred p] [inst_1 : DecidablePred q] {s : Multiset α},
(∀ x ∈ s, p x ↔ q x) → Multiset.filter p s = Multiset.filter q s- Defined in
- Mathlib.Data.Multiset.Filter
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
- Assumes
- DecidablePredDecidablePred
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.ofListproof · cited by 290
- Multiset.filterstatement · cited by 102
Cited by11
Results whose statement or proof uses this declaration.
- Finset.filter_congrproof · cited by 167
- Multiset.map_toEnumFinset_fstproof · cited by 7
- Multiset.filter_eqproof · cited by 5
- Nat.Partition.indiscrete_partsproof · cited by 3
- Multiset.coe_ndinterproof · cited by 1
- Multiset.count_map_eq_countproof · cited by 1
- Multiset.filter_attach'proof · cited by 1
- Multiset.map_count_True_eq_filter_cardproof · cited by 1
- Multiset.map_filter'proof · cited by 1
- Multiset.filter_commproof · cited by 0
- Equiv.Perm.CycleType.count_defproof · cited by 0