nonarchimedean' — Mathlib

English

The p-adic norm on Q_p is defined as a lift of the PadicSeq norm, giving a non-Archimedean absolute value.

Русский

p-адическая норма на Q_p определяется как перенос нормы PadicSeq, образуя неархимедову абсолютную величину.

LaTeX

$$Theorem: padicNormE is the lifted absolute value on Q_p from PadicSeq.norm.$$

Lean4

/-- Theorems about `padicNormE` are named with a `'` so the names do not conflict with the
equivalent theorems about `norm` (`‖ ‖`). -/
theorem nonarchimedean' (q r : ℚ_[p]) : padicNormE (q + r : ℚ_[p]) ≤ max (padicNormE q) (padicNormE r) :=
  Quotient.inductionOn₂ q r <| norm_nonarchimedean

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