Theorems · Theorem · complex analysis
Complex.angle_mul_left
∀ {a : ℂ}, a ≠ 0 → ∀ (x y : ℂ), InnerProductGeometry.angle (a * x) (a * y) = InnerProductGeometry.angle x y- Defined in
- Mathlib.Analysis.Complex.Angle
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- MulZeroClass.mul_zeroproof · cited by 2,091
- absproof · cited by 1,814
- Real.piproof · cited by 1,774
- eq_or_neproof · cited by 1,117
- Complex.argproof · cited by 220
- InnerProductGeometry.anglestatement and proof · cited by 170
- mul_div_mul_leftproof · cited by 25
- InnerProductGeometry.angle_zero_leftproof · cited by 14
- InnerProductGeometry.angle_zero_rightproof · cited by 10
- Complex.angle_eq_abs_argproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Complex.angle_mul_rightproof · cited by 1