Theorems · Theorem · complex analysis
meromorphicOrderAt_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} {x : 𝕜},
MeromorphicAt f₁ x →
MeromorphicAt f₂ x → min (meromorphicOrderAt f₁ x) (meromorphicOrderAt f₂ x) ≤ meromorphicOrderAt (f₁ + f₂) xThe order of a sum is at least the minimum of the orders of the summands.
- Defined in
- Mathlib.Analysis.Meromorphic.Order
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites42
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Top.topproof · cited by 9,680
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- mul_oneproof · cited by 3,885
- WithTopstatement and proof · cited by 3,754
- Filter.Eventuallyproof · cited by 3,134
- Compl.complproof · cited by 2,925
- le_reflproof · cited by 2,061
- nhdsWithinproof · cited by 1,912
- Filter.EventuallyEqproof · cited by 1,912
- Filter.univ_mem'proof · cited by 1,672
Cited by2
Results whose statement or proof uses this declaration.
- MeromorphicOn.negPart_divisor_add_of_analyticNhdOn_rightproof · cited by 2
- MeromorphicOn.min_divisor_le_divisor_addproof · cited by 1