Theorems · Theorem · complex analysis
Complex.arg_eq_nhds_of_im_neg
∀ {z : ℂ}, z.im < 0 → Complex.arg =ᶠ[nhds z] fun x => -Real.arccos (x.re / ‖x‖)- 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Complexstatement and proof · cited by 5,565
- nhdsstatement · cited by 5,554
- Norm.normstatement · cited by 5,413
- Filter.EventuallyEqstatement · cited by 1,912
- Complex.restatement · cited by 882
- Filter.Eventually.monoproof · cited by 646
- Complex.imstatement and proof · cited by 591
- Complex.argstatement · cited by 220
- Continuous.tendstoproof · cited by 206
- Filter.Tendsto.eventuallyproof · cited by 174
- Real.arccosstatement · cited by 90
Cited by1
Results whose statement or proof uses this declaration.
- Complex.continuousAt_argproof · cited by 3