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_div
(x : ℝ)
{y : ℝ}
(hy : y ≠ 0)
:
y * (x / y).negMulLog = x.negMulLog + x * log y