Theorems · Theorem · ring theory
Multiset.sum_map_mul_right
∀ {ι : Type u_1} {R : Type u_4} [inst : NonUnitalNonAssocSemiring R] {a : R} {s : Multiset ι} {f : ι → R},
(Multiset.map (fun i => f i * a) s).sum = (Multiset.map f s).sum * a- Cited by
- 5 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.zero_mulproof · cited by 1,625
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- Multiset.mapstatement and proof · cited by 876
- Multiset.sumstatement and proof · cited by 388
- add_mulproof · cited by 363
- Multiset.induction_onproof · cited by 109
- Multiset.map_consproof · cited by 93
- Multiset.sum_consproof · cited by 45
Cited by5
Results whose statement or proof uses this declaration.
- Multiset.prod_X_add_C_eq_sum_esymmproof · cited by 3
- exists_derivative_mul_eq_and_isIntegral_coeffproof · cited by 1
- Multiset.prod_map_sumproof · cited by 0
- FiniteField.sum_subgroup_pow_eq_zeroproof · cited by 0
- Multiset.sum_map_divproof · cited by 0