Algebra · hard

Statement, exactly as the model and Lean see it

theorem lg_target {α : Type u_5} [NonUnitalNonAssocCommSemiring α] (a : α) : a ∈ NonUnitalSubsemiring.center α ↔ ∀ (b : α), Commute (AddMonoid.End.mulLeft b) (AddMonoid.End.mulLeft a) := by

Mathlib declaration: NonUnitalNonAssocCommSemiring.mem_center_iff
Held-out module: Mathlib.Algebra.Ring.CentroidHom
Banned modules (itself + downstream): 2
Reference proof premises (reachable / held-out): 4 / 2

Traces

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

Not verified1 model calls · 1 Lean checks · $0.00006

Attempts

sample 0 · round 0Wrong tactic2.1 s model time

Proof

intro h
split
· intro h'
  rw [NonUnitalSubsemiring.center]
  exact h'
· intro h'
  rw [NonUnitalSubsemiring.center]
  exact h'

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

α : Type u_5
inst✝ : NonUnitalNonAssocCommSemiring α
a : α
⊢ a ∈ NonUnitalSubsemiring.center α ↔ ∀ (b : α), Commute (AddMonoid.End.mulLeft b) (AddMonoid.End.mulLeft a)

Reference proof

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

lemma _root_.NonUnitalNonAssocCommSemiring.mem_center_iff (a : α) :
    a ∈ NonUnitalSubsemiring.center α ↔ ∀ b : α, Commute (L b) (L a) := by
  rw [NonUnitalNonAssocSemiring.mem_center_iff, CentroidHom.centroid_eq_centralizer_mulLeftRight,
    Subsemiring.mem_centralizer_iff, AddMonoid.End.mulRight_eq_mulLeft, Set.union_self]
  aesop