English
The truncation Fun' of the constant 1 is the zero function, and the coefficient at m equals 0 for m ≠ 0, and equals 1 at m = 0.
Русский
Усечение функции' константы 1 даёт нулевую коэффициентную функцию за исключением нулевого м, где коэффициент равен 1.
LaTeX
$$$$ (\\operatorname{truncFun}' n 1)_{m} = \\begin{cases} 1, & m = 0 \\\\ 0, & m \\neq 0 \\end{cases} $$$$
Lean4
/-- Coefficients of the truncated function. -/
theorem coeff_truncFun' (m : σ →₀ ℕ) (φ : MvPowerSeries σ R) :
(truncFun' n φ).coeff m = if m ≤ n then coeff m φ else 0 := by classical simp [truncFun', MvPolynomial.coeff_sum]