coverEntropyInfEntourage_empty — Mathlib

English

For any nonempty F and any U, the entropy coverEntropyInfEntourage is nonnegative: 0 ≤ coverEntropyInfEntourage T F U.

Русский

Для любого непустого F и любой U ентропия неотрицательна: 0 ≤ coverEntropyInfEntourage T F U.

LaTeX

$$0 \leq coverEntropyInfEntourage(T,F,U)$$

Lean4

@[simp]
theorem coverEntropyInfEntourage_empty {T : X → X} {U : Set (X × X)} : coverEntropyInfEntourage T ∅ U = ⊥ :=
  eq_bot_mono (coverEntropyInfEntourage_le_coverEntropyEntourage T ∅ U) coverEntropyEntourage_empty

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