Theorems · Theorem · group theory
Multiset.prod_map_mul
∀ {ι : Type u_2} {M : Type u_5} [inst : CommMonoid M] {m : Multiset ι} {f g : ι → M},
(Multiset.map (fun i => f i * g i) m).prod = (Multiset.map f m).prod * (Multiset.map g m).prod- Cited by
- 16 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- Multisetstatement and proof · cited by 2,627
- CommMonoidstatement and proof · cited by 2,264
- Multiset.mapstatement · cited by 876
- Multiset.prodstatement · cited by 528
- mul_mul_mul_commproof · cited by 65
- Multiset.prod_hom₂proof · cited by 2
Cited by16
Results whose statement or proof uses this declaration.
- Height.mulHeight_smul_eq_mulHeightproof · cited by 6
- Polynomial.resultant_eq_prod_evalproof · cited by 3
- Polynomial.resultant_mul_rightproof · cited by 3
- Height.mulHeight_eval_leproof · cited by 3
- Height.mulHeight_fun_mul_eqproof · cited by 3
- Multiset.esymm_negproof · cited by 2
- Height.mulHeight₁_sum_leproof · cited by 2
- Multiset.prod_map_prodproof · cited by 2
- Height.mulHeight_linearMap_apply_leproof · cited by 2
- Polynomial.resultant_eq_prod_roots_subproof · cited by 1
- Polynomial.map_sub_roots_sprod_eq_prod_map_evalproof · cited by 1
- Complex.regularizedHGFunCoeff_add_oneproof · cited by 1