Theorems · Theorem · complex analysis
Complex.arg_nonneg_iff
∀ {z : ℂ}, 0 ≤ z.arg ↔ 0 ≤ z.im- Cited by
- 4 results in Mathlib
- Foundations
- Depth 197 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 and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Norm.normproof · cited by 5,413
- MulZeroClass.zero_mulproof · cited by 1,625
- eq_or_neproof · cited by 1,117
- Complex.imstatement and proof · cited by 591
- Complex.argstatement and proof · cited by 220
- norm_pos_iffproof · cited by 168
- le_div_iff₀proof · cited by 75
- Complex.arg_zeroproof · cited by 22
- Complex.arg_le_piproof · cited by 8
- Complex.neg_pi_lt_argproof · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- PhragmenLindelof.quadrant_Iproof · cited by 4
- Complex.cpow_inv_two_im_eq_sqrtproof · cited by 4
- Complex.arg_neg_iffproof · cited by 2
- Complex.arg_of_im_nonneg_of_ne_zeroproof · cited by 1