Theorems · Theorem · sequences and series
hasProd_zero_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}, (∃ b, f b = 0) → ∀ [L.LeAtTop], HasProd f 0 L- Cited by
- 3 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.
Cites18
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
- Finset.prodproof · cited by 2,356
- Filter.EventuallyEqproof · cited by 1,912
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- CommMonoidWithZerostatement and proof · cited by 913
- SummationFilterstatement and proof · cited by 607
- tendsto_const_nhdsproof · cited by 330
- HasProdstatement · cited by 157
- Filter.Tendsto.congr'proof · cited by 154
- Filter.eventually_ge_atTopproof · cited by 111
Cited by3
Results whose statement or proof uses this declaration.
- hasProd_zero_zeroproof · cited by 2
- multipliable_of_exists_eq_zeroproof · cited by 2
- tprod_of_exists_eq_zeroproof · cited by 0