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Linglib.Core.Analysis.SpecialFunctions.Log.NegMulLog

Algebraic identities for negMulLog #

Mathlib's Analysis.SpecialFunctions.Log.NegMulLog has the product identity Real.negMulLog_mul but neither its inverse nor quotient companions (cf. Real.log_inv/Real.log_div beside Real.log_mul). This file completes the family; the division identity is the pointwise step of the entropy chain rule. [UPSTREAM] candidate for that file.

theorem Real.negMulLog_inv (y : ) :
y⁻¹.negMulLog = y⁻¹ * log y
theorem Real.negMulLog_div (x : ) {y : } (hy : y 0) :
y * (x / y).negMulLog = x.negMulLog + x * log y