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theories/probability.v

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@@ -2889,7 +2889,10 @@ congr (_ + _).
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by apply/measurableT_comp => //; exact: measurable_XMonemX.
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by have /integrableP[_] := @beta_prob_integrable R a b c d.
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rewrite /beta_pdf.
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under eq_integral do rewrite EFinM -muleA muleC -muleA.
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under eq_integral.
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move=> x _.
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rewrite EFinM -(muleA (x ^+ c)%:E) muleC -(muleA (`1-x ^+ d)%:E).
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over.
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rewrite /=.
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transitivity ((beta_fun a b)^-1%:E * \int[mu]_(x in `[0%R, 1%R])
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(@XMonemX R (a + c).-1 (b + d).-1 \_`[0,1] x)%:E)%E.

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