f_int_ofNat — Mathlib

English

For k ∈ ℕ, a ≤ 1, and n ∈ ℕ, f_int(k, a, t, -Succ(n)) equals f_nat(k, 1 − a, t, n).

Русский

Если k ∈ ℕ, a ≤ 1 и n ∈ ℕ, то f_int(k,a,t, −Succ(n)) = f_nat(k, 1−a, t, n).

LaTeX

$$$f_{int}(k,a,t,-\mathrm{Succ}(n)) = f_{nat}(k,1-a,t,n).$$$

Lean4

theorem f_int_ofNat (k : ℕ) {a : ℝ} (ha : 0 ≤ a) (t : ℝ) (n : ℕ) : f_int k a t (Int.ofNat n) = f_nat k a t n := by
  rw [f_int, f_nat, Int.ofNat_eq_coe, Int.cast_natCast, abs_of_nonneg (by positivity)]

Похожие утверждения