Theorems · Theorem · sequences and series
tsum_setProd_singleton_left
∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : AddCommMonoid α] [inst_1 : TopologicalSpace α] (b : β)
(t : Set γ) (f : β × γ → α), ∑' (x : ↑({b} ×ˢ t)), f ↑x = ∑' (c : ↑t), f (b, ↑c)- Cited by
- 0 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- AddCommMonoidstatement and proof · cited by 12,281
- Set.Elemstatement and proof · cited by 7,166
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- SProd.sprodstatement · cited by 1,750
- tsumstatement and proof · cited by 1,148
- Function.Injective.injOnproof · cited by 280
- Set.singleton_prodproof · cited by 16
- Prod.mk_right_injectiveproof · cited by 15
- tsum_congr_set_coeproof · cited by 5
- tsum_imageproof · cited by 3
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