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theorem proved term proof

mellinIntegrand_after_inversion

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formal statement (Lean)

  88theorem mellinIntegrand_after_inversion
  89    {f : ℝ → ℝ} (hf : ReciprocalSymmetric f)
  90    (s x : ℝ) (hx : 0 < x) :
  91    f x⁻¹ * mellinKernel s x⁻¹ =
  92      f x * x ^ (mellinReflect s) := by

proof body

Term-mode proof.

  93  have hfx : f x⁻¹ = f x := (hf x hx).symm
  94  rw [hfx]
  95  unfold mellinKernel mellinReflect
  96  exact congrArg (fun y => f x * y) (mellin_reflection_via_substitution s x hx)
  97
  98/-! ## 3. Reflection theorem -/
  99
 100/-- If a Mellin transform package is admissible for a reciprocally symmetric
 101kernel, then the transform is invariant under `s ↔ 1-s`. -/

depends on (12)

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