powerSeriesFamily_smul — Mathlib

English

Let [Zero Γ], f : Γ → R with f ≠ 0 and hn: ∀ m < n, f m = 0. Then n ≤ order(ofSuppBddBelow f (forallLTEqZero_supp_BddBelow f n hn)).

Русский

Пусть [Zero Γ], f : Γ → R, f ≠ 0, и hn: ∀ m < n, f m = 0. Тогда n ≤ order(ofSuppBddBelow f (forallLTEqZero_supp_BddBelow f n hn)).

LaTeX

$$n ≤ order (ofSuppBddBelow f (forallLTEqZero_supp_BddBelow f n hn))$$

Lean4

theorem powerSeriesFamily_smul {x : HahnSeries Γ V} (f : PowerSeries R) (r : R) :
    powerSeriesFamily x (r • f) = HahnSeries.single (0 : Γ) r • powerSeriesFamily x f :=
  by
  ext1 n
  simp [mul_smul]

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