Theorems · Theorem · group theory
Multiset.sum_map_sub
∀ {ι : Type u_2} {G : Type u_4} [inst : SubtractionCommMonoid G] {m : Multiset ι} {f g : ι → G},
(Multiset.map (fun i => f i - g i) m).sum = (Multiset.map f m).sum - (Multiset.map g m).sum- Cited by
- 3 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
- Assumes
- SubtractionCommMonoid
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.
- Multisetstatement and proof · cited by 2,627
- sub_zeroproof · cited by 938
- Multiset.mapstatement · cited by 876
- Multiset.sumstatement · cited by 388
- SubtractionCommMonoidstatement and proof · cited by 79
- add_sub_add_commproof · cited by 28
- Multiset.sum_hom₂proof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Finset.sum_sub_distribproof · cited by 84
- exists_derivative_mul_eq_and_isIntegral_coeffproof · cited by 1
- IsAddFreimanHom.subproof · cited by 0