Theorems · Theorem · order theory
Multiset.add_eq_union_iff_disjoint
∀ {α : Type u_1} [inst : DecidableEq α] {s t : Multiset α}, s + t = s ∪ t ↔ Disjoint s t- Defined in
- Mathlib.Data.Multiset.UnionInter
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 63 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.
Cites6
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
- Disjointstatement · cited by 2,201
- Multiset.countproof · cited by 302
- Multiset.count_addproof · cited by 23
- Multiset.count_interproof · cited by 9
- Multiset.count_unionproof · cited by 6
Cited by6
Results whose statement or proof uses this declaration.
- Equiv.Perm.Disjoint.cycleType_mulproof · cited by 14
- Multiset.add_eq_union_left_of_leproof · cited by 2
- Multiset.range_add_eq_unionproof · cited by 1
- Finset.noncommProd_union_of_disjointproof · cited by 1
- Finset.noncommSum_union_of_disjointproof · cited by 0
- Multiset.Ico_add_Ico_eq_Icoproof · cited by 0