Theorems · Theorem · order theory
Multiset.add_eq_union_left_of_le
∀ {α : Type u_1} [inst : DecidableEq α] {s t u : Multiset α}, t ≤ s → (u + s = u ∪ t ↔ Disjoint u s ∧ s = t)- Defined in
- Mathlib.Data.Multiset.UnionInter
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 64 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.
Cites7
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
- LE.le.antisymmproof · cited by 507
- Eq.trans_leproof · cited by 155
- Multiset.add_eq_union_iff_disjointproof · cited by 6
- Multiset.union_le_addproof · cited by 1
- Multiset.le_of_add_le_add_leftproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Multiset.finsetSum_eq_sup_iff_disjointproof · cited by 2
- Multiset.add_eq_union_right_of_leproof · cited by 0