Theorems · Theorem · complex analysis
analyticOrderAt_smul_eq_top_of_right
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {g : 𝕜 → E} {z₀ : 𝕜} {f : 𝕜 → 𝕜}, analyticOrderAt g z₀ = ⊤ → analyticOrderAt (f • g) z₀ = ⊤- Defined in
- Mathlib.Analysis.Analytic.Order
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Top.topstatement and proof · cited by 9,680
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ENatstatement · cited by 4,985
- IsOpenproof · cited by 2,400
- smul_zeroproof · cited by 665
- analyticOrderAtstatement and proof · cited by 69
- eventually_nhds_iffproof · cited by 21
- analyticOrderAt_eq_topproof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- analyticOrderAt_smulproof · cited by 1
- analyticOrderAt_mul_eq_top_of_rightproof · cited by 0