Theorems · Theorem · complex analysis
meromorphicOrderAt_add_eq_right_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 f₁ x →
meromorphicOrderAt f₂ x < meromorphicOrderAt f₁ x → meromorphicOrderAt (f₁ + f₂) x = meromorphicOrderAt f₂ xHelper lemma for meromorphicOrderAt_add_of_ne.
- Defined in
- Mathlib.Analysis.Meromorphic.Order
- Cited by
- 1 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.
Cites8
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
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- WithTopstatement · cited by 3,754
- add_commproof · cited by 1,535
- meromorphicOrderAtstatement and proof · cited by 180
- MeromorphicAtstatement and proof · cited by 160
- meromorphicOrderAt_add_eq_left_of_ltproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- meromorphicOrderAt_add_of_neproof · cited by 0