Probability · medium

Statement, exactly as the model and Lean see it

theorem lg_target {Ω : Type u_1} {m : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {X : Ω → ℝ} (t : ℝ) (hX : AEMeasurable X μ) : MeasureTheory.AEStronglyMeasurable (fun ω => Real.exp (t * X ω)) μ := by

Mathlib declaration: ProbabilityTheory.aemeasurable_exp_mul
Held-out module: Mathlib.Probability.Moments.Basic
Banned modules (itself + downstream): 21
Reference proof premises (reachable / held-out): 13 / 0

Traces

Each configuration's full record: what was retrieved, what the model wrote, what Lean said back.

Not verified1 model calls · 1 Lean checks · $0.00005

Attempts

sample 0 · round 0Wrong tactic1.7 s model time

Proof

intro t
apply MeasureTheory.ae_strongly_measurable_exp
exact hX

What Lean printed (this is all the model sees on repair)

4:8: error: Tactic `introN` failed: There are no additional binders or `let` bindings in the goal to introduce

Ω : Type u_1
m : MeasurableSpace Ω
μ : MeasureTheory.Measure Ω
X : Ω → ℝ
t : ℝ
hX : AEMeasurable X μ
⊢ MeasureTheory.AEStronglyMeasurable (fun ω => Real.exp (t * X ω)) μ

Reference proof

Mathlib's own source for this declaration, shown for comparison. It may use lemmas the prover is not allowed to use.

lemma aemeasurable_exp_mul {X : Ω → ℝ} (t : ℝ) (hX : AEMeasurable X μ) :
    AEStronglyMeasurable (fun ω ↦ rexp (t * X ω)) μ :=
  (measurable_exp.comp_aemeasurable (hX.const_mul t)).aestronglyMeasurable