Theorems · Theorem · complex analysis
Complex.arg_neg_eq_arg_add_pi_of_im_neg
∀ {x : ℂ}, x.im < 0 → (-x).arg = x.arg + Real.pi- Cited by
- 3 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 and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Norm.normproof · cited by 5,413
- Real.pistatement and proof · cited by 1,774
- add_commproof · cited by 1,535
- Complex.reproof · cited by 882
- Complex.imstatement and proof · cited by 591
- Complex.argstatement and proof · cited by 220
- norm_negproof · cited by 190
- neg_divproof · cited by 161
- Real.arccosproof · cited by 90
- Left.neg_pos_iffproof · cited by 22
Cited by3
Results whose statement or proof uses this declaration.
- Complex.arg_neg_coe_angleproof · cited by 3
- Complex.arg_neg_eq_arg_sub_pi_iffproof · cited by 0
- Complex.arg_neg_eq_arg_add_pi_iffproof · cited by 0