Theorems · Theorem · sequences and series
HasSum.nat_add_neg
∀ {M : Type u_1} [inst : AddCommMonoid M] [inst_1 : TopologicalSpace M] {m : M} [ContinuousAdd M] {f : ℤ → M},
HasSum f m → HasSum (fun n => f ↑n + f (-↑n)) (m + f 0)- Cited by
- 10 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Finsetproof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- SetLike.coeproof · cited by 8,199
- Finset.sumproof · cited by 5,195
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- neg_negproof · cited by 960
- Finset.imageproof · cited by 910
- ContinuousAddstatement and proof · cited by 777
- HasSumstatement and proof · cited by 518
- le_totalproof · cited by 294
- neg_eq_zeroproof · cited by 171
Cited by10
Results whose statement or proof uses this declaration.
- HurwitzZeta.hasSum_nat_cosZetaproof · cited by 4
- HurwitzZeta.hasSum_nat_sinZetaproof · cited by 3
- hasSum_one_div_nat_pow_mul_fourierproof · cited by 2
- HurwitzZeta.hasSum_nat_cosKernel₀proof · cited by 1
- hasSum_nat_jacobiThetaproof · cited by 1
- HurwitzZeta.hasSum_nat_sinKernelproof · cited by 1
- tsum_nat_add_negproof · cited by 1
- HurwitzZeta.hasSum_nat_completedCosZetaproof · cited by 1
- Summable.nat_add_negproof · cited by 0
- HurwitzZeta.hasSum_nat_completedSinZetaproof · cited by 0