Theorems · Theorem · sequences and series
HasSum.of_add_one_of_neg_add_one
∀ {M : Type u_1} [inst : AddCommMonoid M] [inst_1 : TopologicalSpace M] {m m' : M} [ContinuousAdd M] {f : ℤ → M},
HasSum (fun n => f (↑n + 1)) m → HasSum (fun n => f (-(↑n + 1))) m' → HasSum f (m + f 0 + m')- Cited by
- 2 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- AddCommMonoidstatement and proof · cited by 12,281
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- add_commproof · cited by 1,535
- ContinuousAddstatement and proof · cited by 777
- HasSumstatement and proof · cited by 518
- HasSum.of_nat_of_neg_add_oneproof · cited by 5
- HasSum.zero_addproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- tsum_of_add_one_of_neg_add_oneproof · cited by 0
- Summable.of_add_one_of_neg_add_oneproof · cited by 0