Theorems · Theorem · order theory
Multiset.toFinset_eq_singleton_iff
∀ {α : Type u_1} [inst : DecidableEq α] (s : Multiset α) (a : α), s.toFinset = {a} ↔ s.card ≠ 0 ∧ s = s.card • {a}- Defined in
- Mathlib.Algebra.Order.Group.Finset
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 78 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.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- mul_oneproof · cited by 3,885
- Multisetstatement and proof · cited by 2,627
- Multiset.cardstatement and proof · cited by 375
- Multiset.countproof · cited by 302
- Multiset.toFinsetstatement and proof · cited by 230
- Finset.mem_singletonproof · cited by 103
- Multiset.mem_toFinsetproof · cited by 39
- Multiset.ext'proof · cited by 31
- Multiset.count_eq_zero_of_notMemproof · cited by 27
- Multiset.count.congr_simpproof · cited by 22
- Multiset.card_eq_zeroproof · cited by 13
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