Theorems · Theorem · sequences and series
tsum_pi_single
∀ {α : Type u_1} {β : Type u_2} [inst : AddCommMonoid α] [inst_1 : TopologicalSpace α] [inst_2 : DecidableEq β] (b : β)
(a : α), ∑' (b' : β), Pi.single b a b' = a- Cited by
- 3 results in Mathlib
- Foundations
- Depth 80 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 · cited by 2,068
- tsumstatement · cited by 1,148
- Pi.singlestatement · cited by 518
- Pi.single_eq_sameproof · cited by 144
- Pi.single_eq_of_neproof · cited by 116
- tsum_eq_singleproof · cited by 19
Cited by3
Results whose statement or proof uses this declaration.
- NormedSpace.exp_zeroproof · cited by 8
- ordinaryHypergeometric_zeroproof · cited by 0
- FormalMultilinearSeries.ofScalarsSum_zeroproof · cited by 0