norm_algebraMap_nnreal — Mathlib

English

Additional details about the induced NormedAlgebra structure on a domain via a non-unital AlgHom, including the two auxiliary equalities with norm bounds.

Русский

Дополнительные детали структуры NormedAlgebra, индуцированной через некорректное гомоморфизм АЛГ, включая нормовые неравенства.

LaTeX

$$$\\text{InducedNorm}(f) \\Rightarrow \\|f(a)\\| \\le \\|a\\| \\cdot \\|f(1)\\|$$$

Lean4

@[simp]
theorem norm_algebraMap_nnreal (x : ℝ≥0) : ‖algebraMap ℝ≥0 𝕜' x‖ = x :=
  (norm_algebraMap' 𝕜' (x : ℝ)).symm ▸ Real.norm_of_nonneg x.prop

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