Theorems · Theorem · complex analysis

MeromorphicOn.min_divisor_le_divisor_add

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {f₁ f₂ : 𝕜 → E} {z : 𝕜} {U : Set 𝕜},
  MeromorphicOn f₁ U →
    MeromorphicOn f₂ U →
      z ∈ U →
        meromorphicOrderAt (f₁ + f₂) z ≠ ⊤ →
          min ((MeromorphicOn.divisor f₁ U) z) ((MeromorphicOn.divisor f₂ U) z) ≤ (MeromorphicOn.divisor (f₁ + f₂) U) z

The divisor of f₁ + f₂ is larger than or equal to the minimum of the divisors of f₁ and f₂, respectively.

Defined in

Mathlib.Analysis.Meromorphic.Divisor

Cited by

1 results in Mathlib

Foundations

Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace