Theorems · Theorem · several complex variables
UpperHalfPlane.prod_eq_zero_iff
∀ {ι : Type u_1} {f : ι → UpperHalfPlane → ℂ} {s : Finset ι},
(∀ i ∈ s, MDiff (f i)) → (∏ i ∈ s, f i = 0 ↔ ∃ i ∈ s, f i = 0)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 288 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Complexstatement and proof · cited by 5,565
- Compl.complproof · cited by 2,925
- Finset.prodstatement and proof · cited by 2,356
- nhdsWithinproof · cited by 1,912
- modelWithCornersSelfstatement and proof · cited by 920
- UpperHalfPlanestatement and proof · cited by 626
- Filter.Frequentlyproof · cited by 414
- MDifferentiablestatement and proof · cited by 134
- Finset.prod_applyproof · cited by 70
- Finset.prod_eq_zeroproof · cited by 44
- Filter.Frequently.of_forallproof · cited by 25
Cited by1
Results whose statement or proof uses this declaration.
- ModularForm.norm_ne_zeroproof · cited by 1