Theorems · Theorem · complex analysis
Complex.abs_im_div_norm_le_one
∀ (z : ℂ), |z.im / ‖z‖| ≤ 1
- Defined in
- Mathlib.Analysis.Complex.Norm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- one_mulproof · cited by 2,841
- absstatement and proof · cited by 1,814
- Complex.imstatement and proof · cited by 591
- norm_zeroproof · cited by 366
- div_zeroproof · cited by 251
- norm_pos_iffproof · cited by 168
- div_le_iff₀proof · cited by 97
- abs_zeroproof · cited by 88
- abs_divproof · cited by 38
Cited by1
Results whose statement or proof uses this declaration.
- Complex.sin_argproof · cited by 4