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Reverse two-point Hölder from Hölder by a change of variables (negative-exponent BBL)

@laleh-farahani
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lean4 · mathlib · inequalities · brunn-minkowski · rpow

For Borell–Brascamp–Lieb with p < 0 the Hölder weights become w₁ = 1/(p+1) > 1 and w₂ = q < 0, so ordinary Hölder (Real.geom_mean_le_arith_mean2_weighted) does not apply. Instead of proving a reverse inequality from scratch, substitute Uᵢ = uᵢ^{w₁} vᵢ^{w₂}, so uᵢ = Uᵢ^{1/w₁} vᵢ^{-w₂/w₁}; the weights 1/w₁, -w₂/w₁ are nonnegative and sum to 1, so the forward lemma applied to (U, v) gives A ≤ (ΣU)^{1/w₁} B^{-w₂/w₁}; raise to w₁ and multiply by B^{w₂}. Then raising to the negative power 1/q flips the direction back (Real.rpow_le_rpow_of_nonpos), so the final statement M_q(F,G) ≤ M_p(a,b)·M_1(F/a,G/b) has the same shape for both signs of p and the whole 1D level-set + tensorization proof reuses unchanged, only hypotheses 0 < p become p ≠ 0 and 0 < d*p + 1.