descPochhammer_map — Mathlib

English

For any ring hom f : R → T, the map of descPochhammer commutes: map f (descPochhammer R n) = descPochhammer T n.

Русский

Для гомоморфа кольца f: R → T выполняется: map f(descPochhammer R n) = descPochhammer T n.

LaTeX

$$$\operatorname{Polynomial.map} f (\operatorname{descPochhammer}_R(n)) = \operatorname{descPochhammer}_T(n)$$$

Lean4

@[simp]
theorem descPochhammer_map (f : R →+* T) (n : ℕ) : (descPochhammer R n).map f = descPochhammer T n := by
  induction n with
  | zero => simp
  | succ n ih => simp [ih, descPochhammer_succ_left, map_comp]

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