Theorems · Theorem · combinatorics
Multiset.nodup_cons
∀ {α : Type u_1} {a : α} {s : Multiset α}, (a ::ₘ s).Nodup ↔ a ∉ s ∧ s.Nodup- Defined in
- Mathlib.Data.Multiset.ZeroCons
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
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.consstatement · cited by 313
- Multiset.Nodupstatement · cited by 148
- Quot.induction_onproof · cited by 36
Cited by10
Results whose statement or proof uses this declaration.
- Finset.cons_inductionproof · cited by 85
- Equiv.Perm.card_support_swapproof · cited by 2
- Finset.mk_consstatement · cited by 1
- Set.card_fintypeInsertOfNotMemproof · cited by 1
- Cubic.discr_ne_zero_iff_roots_nodupproof · cited by 1
- RootPairing.Base.cartanMatrix_mem_of_neproof · cited by 0
- Multiset.Nodup.notMemproof · cited by 0
- Finset.nonempty_mkproof · cited by 0
- Multiset.Nodup.of_consproof · cited by 0
- Multiset.Nodup.consproof · cited by 0