Theorems · Theorem · complex analysis
Complex.abs_im_lt_norm
∀ {z : ℂ}, |z.im| < ‖z‖ ↔ z.re ≠ 0- Defined in
- Mathlib.Analysis.Complex.Norm
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Norm.normstatement and proof · cited by 5,413
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- MulZeroClass.mul_zeroproof · cited by 2,091
- absstatement and proof · cited by 1,814
- Complex.restatement and proof · cited by 882
- Complex.Iproof · cited by 866
- Complex.imstatement and proof · cited by 591
- zero_subproof · cited by 335
- Complex.mul_reproof · cited by 115
Cited by3
Results whose statement or proof uses this declaration.
- Complex.arg_le_pi_div_two_iffproof · cited by 4
- Complex.neg_pi_div_two_le_arg_iffproof · cited by 2
- Complex.abs_im_eq_normproof · cited by 0