Res To Imag Axis Real re mul eq
ResToImagAxis.Real.re_mul_eq
Plain-language statement
Real part of a product on the imaginary axis is the product of real parts, when both factors are real-valued there.
Exact Lean statement
theorem ResToImagAxis.Real.re_mul_eq {F G : ℍ → ℂ} (hF : ResToImagAxis.Real F)
(hG : ResToImagAxis.Real G) (t : ℝ) :
((F * G).resToImagAxis t).re = (F.resToImagAxis t).re * (G.resToImagAxis t).reFormal artifact
Lean source
theorem ResToImagAxis.Real.re_mul_eq {F G : ℍ → ℂ} (hF : ResToImagAxis.Real F) (hG : ResToImagAxis.Real G) (t : ℝ) : ((F * G).resToImagAxis t).re = (F.resToImagAxis t).re * (G.resToImagAxis t).re := by simp only [Function.resToImagAxis, ResToImagAxis] split_ifs with ht · have hFreal := hF t ht have hGreal := hG t ht simp only [Function.resToImagAxis, ResToImagAxis, ht, ↓reduceDIte] at hFreal hGreal simp [Pi.mul_apply, Complex.mul_re, hFreal, hGreal] · simp- Project
- Sphere Packing in Dimension 8
- License
- Apache-2.0
- Commit
- acfc6204e65a
- Source
- SpherePacking/ModularForms/ResToImagAxis.lean:215-224
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