Theorems · Theorem · combinatorics
Multiset.mem_sub_of_nodup
∀ {α : Type u_1} [inst : DecidableEq α] {a : α} {s t : Multiset α}, s.Nodup → (a ∈ s - t ↔ a ∈ s ∧ a ∉ t)- Defined in
- Mathlib.Data.Multiset.AddSub
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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_transproof · cited by 985
- Multiset.Nodupstatement and proof · cited by 148
- Multiset.mem_of_leproof · cited by 17
- Multiset.mem_addproof · cited by 16
- Multiset.count_posproof · cited by 12
- Multiset.count_subproof · cited by 12
- Multiset.count_eq_zeroproof · cited by 10
- Multiset.nodup_iff_count_le_oneproof · cited by 8
- Multiset.sub_le_selfproof · cited by 3
- Multiset.le_sub_addproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Finset.mem_sdiffproof · cited by 44