Theorems · Theorem · complex analysis
meromorphicOrderAt_add_eq_left_of_lt
∀ {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 f₂ x →
meromorphicOrderAt f₁ x < meromorphicOrderAt f₂ x → meromorphicOrderAt (f₁ + f₂) x = meromorphicOrderAt f₁ xHelper lemma for meromorphicOrderAt_add_of_ne.
- Defined in
- Mathlib.Analysis.Meromorphic.Order
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites41
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
- WithTopstatement and proof · cited by 3,754
- Filter.Eventuallyproof · cited by 3,134
- Compl.complproof · cited by 2,925
- add_zeroproof · cited by 2,707
- nhdsWithinproof · cited by 1,912
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- LT.lt.ne'proof · cited by 1,417
Cited by3
Results whose statement or proof uses this declaration.
- MeromorphicOn.negPart_divisor_add_of_analyticNhdOn_rightproof · cited by 2
- meromorphicOrderAt_add_eq_right_of_ltproof · cited by 1
- meromorphicOrderAt_add_of_neproof · cited by 0