heval_X — Mathlib

English

The hsum of powerSeries x at 0 equals the constantCoeff scaled unit Hahn series.

Русский

Сумма по степенным рядами в нуле равна константному коэффициенту, умноженному на единичный Hahn-ряд.

LaTeX

$$powerSeriesFamily_hsum_zero (f : PowerSeries R) : (powerSeriesFamily 0 f).hsum = f.constantCoeff • (1 : HahnSeries Γ V)$$

Lean4

theorem heval_X (hx : 0 < x.orderTop) : heval x X = x :=
  by
  rw [X_eq, monomial_eq_mk, heval_apply, powerSeriesFamily, smulFamily]
  simp only [coeff_mk, powers_toFun, hx, ↓reduceIte, ite_smul, one_smul, zero_smul]
  ext g
  rw [coeff_hsum, finsum_eq_single _ 1 (fun n hn ↦ by simp [hn])]
  simp

Похожие утверждения