Theorems · Theorem · ring theory
Multiset.sum_map_mul_left
∀ {ι : Type u_1} {R : Type u_4} [inst : NonUnitalNonAssocSemiring R] {a : R} {s : Multiset ι} {f : ι → R},
(Multiset.map (fun i => a * f i) s).sum = a * (Multiset.map f s).sum- Cited by
- 3 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
- Assumes
- NonUnitalNonAssocSemiring
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.
- Multisetstatement and proof · cited by 2,627
- MulZeroClass.mul_zeroproof · cited by 2,091
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- Multiset.mapstatement and proof · cited by 876
- mul_addproof · cited by 413
- Multiset.sumstatement and proof · cited by 388
- Multiset.induction_onproof · cited by 109
- Multiset.map_consproof · cited by 93
- Multiset.sum_consproof · cited by 45
Cited by3
Results whose statement or proof uses this declaration.
- Multiset.esymm_negproof · cited by 2
- Multiset.prod_map_addproof · cited by 1
- Multiset.prod_map_sumproof · cited by 0