Inequalities · easy

Statement, exactly as the model and Lean see it

theorem lg_target (c : ℝ) : (fun x => Real.log (x * c)) =O[Filter.atTop] Real.log := by

Mathlib declaration: Real.isBigO_log_mul_const_log_atTop
Held-out module: Mathlib.Analysis.SpecialFunctions.Log.Base
Banned modules (itself + downstream): 19
Reference proof premises (reachable / held-out): 1 / 1

Traces

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

Not verified1 model calls · 1 Lean checks · $0.00004

Attempts

sample 0 · round 0Wrong tactic10.5 s model time

Proof

intros x hxc
apply Real.log_mul' (Real.log_pos c)
exact hxc

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

4:2: error: Tactic `introN` failed: There are no additional binders or `let` bindings in the goal to introduce

c : ℝ
⊢ (fun x => Real.log (x * c)) =O[Filter.atTop] Real.log

Reference proof

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

theorem isBigO_log_mul_const_log_atTop (c : ℝ) : (fun x ↦ log (x * c)) =O[atTop] log := by
  simpa [mul_comm] using isBigO_log_const_mul_log_atTop c