Theorems · Theorem · complex analysis
MeromorphicOn.divisor_ofNat
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {U : Set 𝕜} (n : ℕ), MeromorphicOn.divisor (OfNat.ofNat n) U = 0The divisor of a constant function is 0.
- Defined in
- Mathlib.Analysis.Meromorphic.Divisor
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NontriviallyNormedField
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.
- Setstatement and proof · cited by 53,352
- NormedAddCommGroupproof · cited by 15,752
- NormedSpaceproof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Function.locallyFinsuppWithinstatement and proof · cited by 127
- MeromorphicOn.divisorstatement and proof · cited by 90
- MeromorphicOn.divisor_constproof · cited by 4
- Semiring.toGrindSemiring_ofNatproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- MeromorphicOn.divisor_powproof · cited by 2
- MeromorphicOn.divisor_zpowproof · cited by 1
- MeromorphicOn.divisor_prodproof · cited by 1