map_sub — Mathlib

English

The minimum of orderTop for x and y is not greater than the orderTop of x−y: min(x.orderTop, y.orderTop) ≤ (x−y).orderTop.

Русский

Минимум orderTop для x и y не больше orderTop x−y: min(x.orderTop, y.orderTop) ≤ (x−y).orderTop.

LaTeX

$$$$ \min\left( x.orderTop, y.orderTop \right) \le (x - y).orderTop. $$$$

Lean4

@[simp]
protected theorem map_sub [AddGroup S] (f : R →+ S) {x y : HahnSeries Γ R} :
    ((x - y).map f : HahnSeries Γ S) = x.map f - y.map f := by ext; simp

Похожие утверждения