Theorems · Theorem · group theory
FunLike.coe_sum
∀ {F : Type u_8} {α : Type u_9} {β : Type u_10} {ι : Type u_11} [inst : FunLike F α β] [inst_1 : AddCommMonoid β]
[inst_2 : AddCommMonoid F] [IsZeroApply F α β] [IsAddApply F α β] (s : Finset ι) (f : ι → F),
⇑(∑ i ∈ s, f i) = ∑ i ∈ s, ⇑(f i)- Defined in
- Mathlib.Algebra.BigOperators.Pi
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- DFunLike.coestatement and proof · cited by 62,936
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement and proof · cited by 5,195
- FunLikestatement and proof · cited by 2,560
- Finset.sum_applyproof · cited by 234
- sum_applyproof · cited by 83
- IsAddApplystatement and proof · cited by 75
- IsZeroApplystatement and proof · cited by 72
Cited by6
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.coe_finsetSumproof · cited by 0
- MultilinearMap.coe_sumproof · cited by 0
- ProbabilityTheory.Kernel.coe_finset_sumproof · cited by 0
- QuadraticMap.coeFn_sumproof · cited by 0
- MeasureTheory.VectorMeasure.coe_finsetSumproof · cited by 0
- ContinuousLinearMap.coe_sum'proof · cited by 0