Theorems · Theorem · sequences and series
tprod_of_exists_eq_zero
∀ {α : Type u_1} {β : Type u_2} [inst : CommMonoidWithZero α] [inst_1 : TopologicalSpace α] {f : β → α}
{L : SummationFilter β} [T2Space α] [L.NeBot] [L.LeAtTop], (∃ b, f b = 0) → ∏'[L] (b : β), f b = 0- Cited by
- 0 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- T2Spacestatement and proof · cited by 1,351
- CommMonoidWithZerostatement and proof · cited by 913
- SummationFilterstatement and proof · cited by 607
- tprodstatement · cited by 230
- SummationFilter.NeBotstatement and proof · cited by 130
- SummationFilter.LeAtTopstatement and proof · cited by 80
- HasProd.tprod_eqproof · cited by 49
- hasProd_zero_of_exists_eq_zeroproof · cited by 3
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