nat_mul_neg_add_one — Mathlib

English

For f: ℕ → G, the property that f is multipliable is equivalent to the shifted sequence being multipliable; more precisely, Multipliable f is equivalent to Multipliable (fun n => f(n+k)) for all k, via tail equivalences.

Русский

Для f: ℕ → G условие мультиплируемости эквивалентно мультиплируемости сдвинутой последовательности; то есть Multipliable f эквивалентно Multipliable (fun n => f(n+k)).

LaTeX

$$$(Multipliable f) \;\Leftrightarrow\; (Multipliable (fun n \mapsto f(n+k)))$$$

Lean4

@[to_additive Summable.nat_add_neg_add_one]
theorem nat_mul_neg_add_one {f : ℤ → M} (hf : Multipliable f) : Multipliable (fun n : ℕ ↦ f n * f (-(n + 1))) :=
  hf.hasProd.nat_mul_neg_add_one.multipliable

Похожие утверждения