Theorems · Theorem · group theory
Finset.sum_coe_sort
∀ {ι : Type u_1} {M : Type u_4} (s : Finset ι) [inst : AddCommMonoid M] (f : ι → M), ∑ i, f ↑i = ∑ i ∈ s, f i- Cited by
- 24 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.univstatement · cited by 3,473
- Finset.sum_attachproof · cited by 54
Cited by24
Results whose statement or proof uses this declaration.
- Finset.sum_subtypeproof · cited by 11
- ProbabilityTheory.Kernel.iIndepFun.indepFun_finsetSum_of_notMemproof · cited by 5
- Finset.sum_finset_coeproof · cited by 4
- Polynomial.coeff_mul_invOneSubPow_eq_hilbertPoly_evalproof · cited by 3
- LinearMap.trace_eq_sum_trace_restrict'proof · cited by 2
- ProbabilityTheory.HasSubgaussianMGF.sum_of_iIndepFunproof · cited by 2
- Module.IsLocalRing.linearIndependent_of_flatproof · cited by 2
- linearIndependent_iff_finset_linearIndependentproof · cited by 2
- LinearIndependent.of_isLocalizedModuleproof · cited by 2
- TensorProduct.rTensor_injective_of_forall_vanishesTriviallyproof · cited by 2
- LinearMap.trace_eq_sum_trace_restrict_of_eq_biSupproof · cited by 1
- Submodule.mem_span_image_finset_iff_exists_fun'proof · cited by 1