`BookProof.RadialMollifier.polarSymm_eq` (r θ : ℝ) : Complex.polarCoord.symm (r, θ) = (r : ℂ) * Complex.exp ((θ : ℂ) * Complex.I)

Proved

BookProof.RadialMollifier.polarSymm_eq

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterRadialMollifier.

BookProof.RadialMollifier.polarSymm_eq (r θ : ℝ) : Complex.polarCoord.symm (r, θ) = (r : ℂ) * Complex.exp ((θ : ℂ) * Complex.I)

Formalization note: Lean 4 identifier BookProof.RadialMollifier.polarSymm_eq.

Preamble

-- Generated from ChapterRadialMollifier.lean — theorem BookProof.RadialMollifier.polarSymm_eq
import Mathlib
import Definitions.Def_ChapterRadialMollifier
open BookProof.RadialMollifier



open MeasureTheory Metric Set Complex intervalIntegral Real
open scoped Convolution Topology ContDiff Real

noncomputable section

Formal statement

theorem BookProof.RadialMollifier.polarSymm_eq (r θ : ℝ) :
    Complex.polarCoord.symm (r, θ) = (r : ℂ) * Complex.exp ((θ : ℂ) * Complex.I) := by sorry

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