LeanMachineLearning

Learning.IT.filtrationAction_le_filtration_selfπŸ”—

Lemma

No docstring.

πŸ”—theorem
Learning.IT.filtrationAction_le_filtration_self.{u_1, u_2}
  {𝓐 : Type u_1} {𝓨 : Type u_2} {m𝓐 : MeasurableSpace 𝓐}
  {m𝓨 : MeasurableSpace 𝓨} (n : β„•) :
  ↑(filtrationAction 𝓐 𝓨) n ≀ ↑(IT.filtration 𝓐 𝓨) n
Learning.IT.filtrationAction_le_filtration_self.{u_1,
    u_2}
  {𝓐 : Type u_1} {𝓨 : Type u_2}
  {m𝓐 : MeasurableSpace 𝓐}
  {m𝓨 : MeasurableSpace 𝓨} (n : β„•) :
  ↑(filtrationAction 𝓐 𝓨) n ≀
    ↑(IT.filtration 𝓐 𝓨) n

Code

lemma filtrationAction_le_filtration_self (n : β„•) :
    filtrationAction 𝓐 𝓨 n ≀ IT.filtration 𝓐 𝓨 n
Proof
by
  by_cases hn : n = 0
  Β· simp only [hn, filtrationAction_zero_eq_comap]
    rw [← measurable_iff_comap_le]
    exact adapted_action 0
  simp only [filtrationAction, hn, ↓reduceIte, sup_le_iff]
  constructor
  Β· exact (IT.filtration 𝓐 𝓨).mono (by grind)
  Β· rw [← measurable_iff_comap_le]
    exact adapted_action _

Actions: Source Β· Open Issue

Meaning unchanged since v4.33.0-rc1-29-gce231eb, the oldest revision on record (2026-07-30).

Self-contained, with its dependencies inlined and proofs replaced by sorry: download the raw file Β· open it in the Lean web editor.

Dependency graph

Audit surface: 3 project declarations, 29 external constants

βœ“ Proved: no sorry anywhere in its closure

This is the tool's own reading of one build's recorded axioms, and it is not robust against an author who wants it to pass. Checking meant to be relied on should go through Comparator, which replays the proof through the kernel from an export against an explicit list of permitted axioms.