netEntropyInfEntourage_univ — Mathlib

English

If F is nonempty, netEntropyInfEntourage T F univ = 0.

Русский

Если F непусто, то netEntropyInfEntourage T F univ = 0.

LaTeX

$$$F\neq\emptyset\Rightarrow \operatorname{netEntropyInfEntourage}(T,F,\mathrm{univ})=0$$$

Lean4

theorem netEntropyInfEntourage_univ (T : X → X) {F : Set X} (h : F.Nonempty) : netEntropyInfEntourage T F univ = 0 :=
  by
  rw [← expGrowthInf_const one_ne_zero one_ne_top, netEntropyInfEntourage]
  simp only [netMaxcard_univ T h, ENat.toENNReal_one]

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