Theorems · Theorem · group theory
Finset.sum_fn
∀ {α : Type u_7} {M : α → Type u_8} {ι : Type u_9} [inst : (a : α) → AddCommMonoid (M a)] (s : Finset ι)
(g : ι → (a : α) → M a), ∑ c ∈ s, g c = fun a => ∑ c ∈ s, g c aAn 'unapplied' analogue of Finset.sum_apply.
- Defined in
- Mathlib.Algebra.BigOperators.Pi
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Finset.sum_applyproof · cited by 234
Cited by21
Results whose statement or proof uses this declaration.
- hasSumUniformlyOn_iff_tendstoUniformlyOnproof · cited by 12
- Matrix.mulVec_eq_sumproof · cited by 12
- Matrix.vecMul_eq_sumproof · cited by 5
- hasSumUniformly_iff_tendstoUniformlyproof · cited by 4
- Asymptotics.IsBigO.fun_sumproof · cited by 3
- iteratedDerivWithin_sumproof · cited by 2
- Asymptotics.IsLittleO.fun_sumproof · cited by 2
- AkraBazziRecurrence.strictAnti_sumCoeffsExpproof · cited by 1
- Meromorphic.fun_sumproof · cited by 1
- CircleIntegrable.fun_sumproof · cited by 1
- Finset.analyticAt_fun_sumproof · cited by 1
- iteratedDeriv_fun_sumproof · cited by 1