norm_add_le — Mathlib

English

The norm satisfies the ultrametric inequality with respect to addition: ||x+y|| ≤ max(||x||, ||y||).

Русский

Норма удовлетворяет неравенству треугольника Торчинского: ||x+y|| ≤ max(||x||, ||y||).

LaTeX

$$$$ \|x+y\| \le \max(\|x\|, \|y\|). $$$$

Lean4

theorem norm_add_le (x y : L) : norm (x + y) ≤ max (norm x) (norm y) :=
  by
  simp only [norm, NNReal.coe_le_coe, le_max_iff, StrictMono.le_iff_le hv.strictMono]
  exact le_max_iff.mp (Valuation.map_add_le_max' val.v _ _)

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