English
If IsBigOWith holds, then replacing f by its norm preserves the relation: IsBigOWith c l f' g → IsBigOWith c l ||f'|| g.
Русский
Если IsBigOWith выполняется для f и g, замена f на ||f|| сохраняет отношение: IsBigOWith c l f' g → IsBigOWith c l ||f'|| g.
LaTeX
$$IsBigOWith c l f g → IsBigOWith c l (fun x => ‖f' x‖) g$$
Lean4
/-- The Landau notation `f =o[l] g` where `f` and `g` are two functions on a type `α` and `l` is
a filter on `α`, means that eventually for `l`, `‖f‖` is bounded by an arbitrarily small constant
multiple of `‖g‖`. In other words, `‖f‖ / ‖g‖` tends to `0` along `l`, modulo division by zero
issues that are avoided by this definition. -/
def IsLittleO :=
val_proj @wrapped✝.{}
