Theorems · Theorem · combinatorics
Multiset.rel_add_left
∀ {α : Type u_1} {β : Type v} {r : α → β → Prop} {as₀ as₁ : Multiset α} {bs : Multiset β},
Multiset.Rel r (as₀ + as₁) bs ↔ ∃ bs₀ bs₁, Multiset.Rel r as₀ bs₀ ∧ Multiset.Rel r as₁ bs₁ ∧ bs = bs₀ + bs₁- Defined in
- Mathlib.Data.Multiset.AddSub
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Multiset.consproof · cited by 313
- Multiset.induction_onproof · cited by 109
- Multiset.Relstatement and proof · cited by 47
- Multiset.zero_addproof · cited by 15
- Multiset.cons_addproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- Multiset.rel_add_rightproof · cited by 0