Theorems · Theorem · sequences and series
hasSum_zero
∀ {α : Type u_1} {β : Type u_2} [inst : AddCommMonoid α] [inst_1 : TopologicalSpace α] {L : SummationFilter β},
HasSum (fun x => 0) 0 LConstant zero function has sum 0
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- nhdsproof · cited by 5,554
- Filter.Tendstoproof · cited by 3,814
- Finset.sum_congrproof · cited by 2,323
- SummationFilterstatement and proof · cited by 607
- HasSumstatement · cited by 518
- tendsto_const_nhdsproof · cited by 330
- Finset.sum_const_zeroproof · cited by 219
- SummationFilter.filterproof · cited by 110
Cited by13
Results whose statement or proof uses this declaration.
- tsum_zeroproof · cited by 63
- summable_zeroproof · cited by 5
- HasSum.nonnegproof · cited by 4
- hasSum_sumproof · cited by 4
- NNReal.exists_pos_sum_of_countableproof · cited by 4
- hasSum_zero_iff_of_nonnegproof · cited by 2
- HasFiniteFPowerSeriesOnBall.bound_zero_of_eq_zeroproof · cited by 1
- AnalyticOnNhd.eqOn_zero_of_preconnected_of_eventuallyEq_zero_auxproof · cited by 1
- HasFPowerSeriesOnBall.eventually_eq_zeroproof · cited by 1
- HasSum.nonposproof · cited by 1
- HasSum.nsmulproof · cited by 1
- hasSum_emptyproof · cited by 1