Theorems · Theorem · complex analysis
Complex.sameRay_iff
∀ {x y : ℂ}, SameRay ℝ x y ↔ x = 0 ∨ y = 0 ∨ x.arg = y.arg- Defined in
- Mathlib.Analysis.Complex.Arg
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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.normproof · cited by 5,413
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- mul_commproof · cited by 2,262
- Complex.ofRealproof · cited by 1,654
- eq_or_neproof · cited by 1,117
- one_ne_zeroproof · cited by 885
- div_oneproof · cited by 629
- Complex.argstatement and proof · cited by 220
- SameRaystatement · cited by 149
Cited by6
Results whose statement or proof uses this declaration.
- Polynomial.sub_one_pow_totient_lt_cyclotomic_evalproof · cited by 2
- Complex.sameRay_of_arg_eqproof · cited by 2
- Polynomial.cyclotomic_eval_lt_add_one_pow_totientproof · cited by 1
- Complex.norm_sub_eq_iffproof · cited by 0
- Complex.norm_add_eq_iffproof · cited by 0
- Complex.sameRay_iff_arg_div_eq_zeroproof · cited by 0