Theorems · Theorem · order theory
Multiset.mem_inter
∀ {α : Type u_1} [inst : DecidableEq α] {s t : Multiset α} {a : α}, a ∈ s ∩ t ↔ a ∈ s ∧ a ∈ t- Defined in
- Mathlib.Data.Multiset.UnionInter
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 59 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.
Cites8
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.eraseproof · cited by 93
- Multiset.mem_cons_selfproof · cited by 44
- Multiset.cons_eraseproof · cited by 25
- Multiset.mem_of_leproof · cited by 17
- Multiset.inter_le_leftproof · cited by 6
- Multiset.inter_le_rightproof · cited by 6
- Multiset.cons_inter_of_posproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.normalizedFactors_prod_inter_eq_interproof · cited by 2
- UniqueFactorizationMonoid.prod_inter_normalizedFactors_ne_zeroproof · cited by 2
- Associates.exists_prime_dvd_of_not_inf_oneproof · cited by 1