Number theory · easy

Statement, exactly as the model and Lean see it

theorem lg_target (q : ℚ) : IsAlgebraic ℤ (Real.tan (↑q * Real.pi)) := by

Mathlib declaration: Real.isAlgebraic_tan_rat_mul_pi
Held-out module: Mathlib.NumberTheory.Niven
Banned modules (itself + downstream): 2
Reference proof premises (reachable / held-out): 5 / 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.

/-- `tan(q * π)` for `q : ℚ` is algebraic over `ℤ`, using the real `tan` function. -/
theorem isAlgebraic_tan_rat_mul_pi (q : ℚ) : IsAlgebraic ℤ <| tan <| q * π :=
  isAlgebraic_algebraMap_iff (A := ℂ) RCLike.ofReal_injective |>.mp <| by
    simp [Complex.isAlgebraic_tan_rat_mul_pi]