integralNormalization_eval₂_leadingCoeff_mul

English

If h holds a commutation condition and x commutes with all ring elements, then (integralNormalization p).eval₂ f (f p.leadingCoeff · x) equals f p.leadingCoeff^{natDegree(p) - 1} times p.eval₂ f x.

Русский

При условии совместимости и взаимногоComments, (integralNormalization(p)).eval₂ f (f(p.leadingCoeff)·x) равняется f(p.leadingCoeff)^{natDegree(p) - 1}·p.eval₂ f x.

LaTeX

$$$\text{If } h, f, x, \text{ then } (\operatorname{integralNormalization}(p)).\operatorname{eval}_2 f (f(p.leadingCoeff) \cdot x) = f(p.leadingCoeff)^{(p.natDegree - 1)} \cdot p.\operatorname{eval}_2 f x$$$

Lean4

theorem integralNormalization_eval₂_leadingCoeff_mul (h : 1 ≤ p.natDegree) (f : R →+* S) (x : S) :
    (integralNormalization p).eval₂ f (f p.leadingCoeff * x) = f p.leadingCoeff ^ (p.natDegree - 1) * p.eval₂ f x :=
  integralNormalization_eval₂_leadingCoeff_mul_of_commute h _ _ (.all _ _) (.all _ _)

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