Theorems · Theorem · ring theory
star_sum
∀ {R : Type u_1} [inst : AddCommMonoid R] [inst_1 : StarAddMonoid R] {α : Type u_2} (s : Finset α) (f : α → R),
star (∑ x ∈ s, f x) = ∑ x ∈ s, star (f x)- Defined in
- Mathlib.Algebra.Star.BigOperators
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Quot.sound
- Assumes
- AddCommMonoidStarAddMonoid
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.
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement · cited by 5,195
- Star.starstatement · cited by 1,082
- map_sumproof · cited by 455
- StarAddMonoidstatement and proof · cited by 296
- starAddEquivproof · cited by 25
Cited by9
Results whose statement or proof uses this declaration.
- Matrix.conjTranspose_mulproof · cited by 9
- Matrix.star_dotProduct_starproof · cited by 3
- star_finsuppSumproof · cited by 2
- isSelfAdjoint_sumproof · cited by 2
- CStarMatrix.inner_toCLM_conjTranspose_leftproof · cited by 1
- Matrix.dotProduct_starproof · cited by 1
- Matrix.star_dotProductproof · cited by 1
- star_gaussSum_eqproof · cited by 0
- Matrix.trace_conjTransposeproof · cited by 0