Theorems · Theorem · sequences and series
HasSum.of_nat_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) m → HasSum (fun n => f (-(↑n + 1))) m' → HasSum f (m + m')- Cited by
- 5 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Set.rangeproof · cited by 4,705
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- ContinuousAddstatement and proof · cited by 777
- HasSumstatement and proof · cited by 518
- Set.mem_univproof · cited by 416
- IsComplproof · cited by 351
- Set.mem_rangeproof · cited by 102
- Nat.cast_injproof · cited by 70
- disjoint_iff_inf_leproof · cited by 64
- Set.mem_unionproof · cited by 47
Cited by5
Results whose statement or proof uses this declaration.
- HasSum.int_recproof · cited by 3
- Summable.of_nat_of_neg_add_oneproof · cited by 2
- HasSum.of_add_one_of_neg_add_oneproof · cited by 2
- HasSum.of_nat_of_negproof · cited by 2
- tsum_of_nat_of_neg_add_oneproof · cited by 0