Theorems · Theorem · group theory
Multiset.sum_hom_ne_zero
∀ {M : Type u_5} {N : Type u_6} [inst : AddCommMonoid M] [inst_1 : AddCommMonoid N] {s : Multiset M},
s ≠ 0 → ∀ {F : Type u_8} [inst_2 : FunLike F M N] [AddHomClass F M N] (f : F), (Multiset.map (⇑f) s).sum = f s.sum- Cited by
- 2 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- AddCommMonoidstatement and proof · cited by 12,281
- Multisetstatement and proof · cited by 2,627
- FunLikestatement and proof · cited by 2,560
- Multiset.mapstatement · cited by 876
- Multiset.sumstatement · cited by 388
- AddHomClassstatement and proof · cited by 65
- Multiset.coe_eq_zeroproof · cited by 6
- List.sum_hom_nonemptyproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- map_multiset_ne_zero_sumproof · cited by 1
- AddHom.map_multiset_ne_zero_sumproof · cited by 0