f_int_negSucc — Mathlib

English

For a ≥ 0, f_int(k, a, t, Int.ofNat n) equals f_nat(k, a, t, n).

Русский

Для a ≥ 0: f_int(k,a,t,Int.ofNat n) = f_nat(k,a,t,n).

LaTeX

$$$f_{int}(k,a,t,\mathrm{Int.ofNat}(n)) = f_{nat}(k,a,t,n).$$$

Lean4

theorem f_int_negSucc (k : ℕ) {a : ℝ} (ha : a ≤ 1) (t : ℝ) (n : ℕ) :
    f_int k a t (Int.negSucc n) = f_nat k (1 - a) t n :=
  by
  have : (Int.negSucc n) + a = -(n + (1 - a)) := by { push_cast; ring
  }
  rw [f_int, f_nat, this, abs_neg, neg_sq, abs_of_nonneg (by linarith)]

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