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theorem proved term proof

polyCost_pow

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formal statement (Lean)

 157theorem polyCost_pow {P : Polynomial F} (hP : P ≠ 0) (k : ℕ) :
 158    polyCost (P ^ k) = (k : ℝ) * polyCost P := by

proof body

Term-mode proof.

 159  induction k with
 160  | zero => simp [polyCost_one]
 161  | succ k ih =>
 162    have hPk : P ^ k ≠ 0 := pow_ne_zero k hP
 163    rw [pow_succ, polyCost_mul hPk hP, ih]
 164    push_cast
 165    ring
 166
 167/-- Cost is monotonic under multiplication by nonzero polynomials. -/

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