Algebra · hard

Statement, exactly as the model and Lean see it

theorem lg_target {R : Type u_1} {σ : Type u_2} [CommSemiring R] [NoZeroDivisors R] (i : σ) (p : MvPolynomial σ R) (n : ℕ) (hp : p ≠ 0) : MvPolynomial.degreeOf i (p ^ n) = n * MvPolynomial.degreeOf i p := by

Mathlib declaration: MvPolynomial.degreeOf_pow_eq
Held-out module: Mathlib.Algebra.MvPolynomial.NoZeroDivisors
Banned modules (itself + downstream): 18
Reference proof premises (reachable / held-out): 3 / 1

Traces

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

No configuration has attempted this theorem yet.

Reference proof

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

theorem degreeOf_pow_eq (i : σ) (p : MvPolynomial σ R) (n : ℕ) (hp : p ≠ 0) :
    degreeOf i (p ^ n) = n * degreeOf i p := by
  rw [pow_eq_prod_const, degreeOf_prod_eq (range n) (fun _ ↦ p) (fun _ _ ↦ hp)]
  simp