toNormOneClass — Mathlib

English

If S is a subring of a normed ring R and R has a norm, then the induced norm on S makes S have the unit norm, i.e., ‖1_S‖ = 1.

Русский

Если S — подполье R, нормируемого кольца, и на R задана норма, то норма единицы подполья S равна единице: \\|1_S\\| = 1.

LaTeX

$$$\\|1_S\\| = 1$ for the subring $S$ with the norm induced from $R$.$$

Lean4

instance toNormOneClass [SeminormedRing R] [NormOneClass R] [SubringClass S R] (s : S) : NormOneClass s :=
  .induced s R <| SubringClass.subtype _

Похожие утверждения