Theorems · Theorem · order theory
Multiset.filter_inter
∀ {α : Type u_1} [inst : DecidableEq α] (p : α → Prop) [inst_1 : DecidablePred p] (s t : Multiset α),
Multiset.filter p (s ∩ t) = Multiset.filter p s ∩ Multiset.filter p t- Defined in
- Mathlib.Data.Multiset.UnionInter
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqDecidablePred
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- le_antisymmproof · cited by 2,068
- Multiset.filterstatement and proof · cited by 102
- inf_le_infproof · cited by 54
- Multiset.mem_of_leproof · cited by 17
- Multiset.inter_le_leftproof · cited by 6
- Multiset.filter_leproof · cited by 6
- Multiset.inter_le_rightproof · cited by 6
- Multiset.le_interproof · cited by 4
- Multiset.filter_le_filterproof · cited by 3
- Multiset.of_mem_filterproof · cited by 3
- Multiset.le_filterproof · cited by 1
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