feat(Entropy): prove sandwiched Rényi DPI; remove axiom#1073
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dennj wants to merge 1 commit intoleanprover-community:masterfrom
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feat(Entropy): prove sandwiched Rényi DPI; remove axiom#1073dennj wants to merge 1 commit intoleanprover-community:masterfrom
dennj wants to merge 1 commit intoleanprover-community:masterfrom
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Replace `sandwichedRenyiEntropy_DPI_ax` with a real proof via complex interpolation. Also prove `faithful` for any axiomatic relative entropy (Tomamichel construction), so `RelEntropy qRelativeEnt` instantiates without `sorry`. The downstream `SteinsLemma.limit_hypotesting_eq_limit_rel_entropy` loses one axiom. Side effects: extract classical Hellinger overlap to a new `ClassicalInfo/Hellinger.lean`, split unbundled matrix-map properties into `CPTPMap/Unbundled.lean`, add a few upstream-worthy lemmas to `ForMathlib/`, and inline a number of single-use private helpers across `Dual.lean`, `Relative.lean`, and `DPI.lean`.
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Replace
sandwichedRenyiEntropy_DPI_axwith a real proof via complex interpolation. Also provefaithfulfor any axiomatic relative entropy (Tomamichel construction), soRelEntropy qRelativeEntinstantiates withoutsorry. The downstreamSteinsLemma.limit_hypotesting_eq_limit_rel_entropyloses one axiom.Side effects: extract classical Hellinger overlap to a new
ClassicalInfo/Hellinger.lean, split unbundled matrix-map properties intoCPTPMap/Unbundled.lean, add a few upstream-worthy lemmas toForMathlib/, and inline a number of single-use private helpers acrossDual.lean,Relative.lean, andDPI.lean.This PR is quite big and I need some help to simplify and golfing