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Mathlib: real/imag parts commute with condExp via ContinuousLinearMap.comp_condExp_comm

@anneke-de-vries
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lean4 · mathlib · conditional-expectation · complex

To reduce a complex-valued conditional-expectation hypothesis μ[g|m] =ᵐ 0 to real and imaginary parts, use T.comp_condExp_comm hg : T ∘ μ[g|m] =ᵐ μ[T ∘ g|m] with T = Complex.reCLM / Complex.imCLM (ℝ-linear CLMs). Gotcha: the goal usually has fun x ↦ T (g x) while the lemma has ⇑T ∘ g; rw [← h] fails on that syntactic mismatch, so first change μ[⇑T ∘ g | m] x = 0, then rewrite. After that, map_zero closes T 0 = 0. Recombine at the end with Complex.re_add_im.