Theorems · Theorem · group theory
Multiset.sum_induction
∀ {M : Type u_3} [inst : AddCommMonoid M] (p : M → Prop) (s : Multiset M),
(∀ (a b : M), p a → p b → p (a + b)) → p 0 → (∀ a ∈ s, p a) → p s.sum- Cited by
- 1 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- Multisetstatement and proof · cited by 2,627
- Multiset.sumstatement · cited by 388
- Multiset.foldr_inductionproof · cited by 2
- Multiset.sum_eq_foldrproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Finset.sum_inductionproof · cited by 13