restrictScalars — Mathlib

English

Reinterpret a seminorm from 𝕜' to a subfield 𝕜; the rutin p.restrictScalars gives a seminorm on E over 𝕜.

Русский

Переопределение семинормы из 𝕜' в 𝕜; p.restrictScalars задаёт семинорму на E над 𝕜.

LaTeX

$$$p.restrictScalars :\ Seminorm 𝕜 E$$$

Lean4

/-- Reinterpret a seminorm over a field `𝕜'` as a seminorm over a smaller field `𝕜`. This will
typically be used with `RCLike 𝕜'` and `𝕜 = ℝ`. -/
protected def restrictScalars (p : Seminorm 𝕜' E) : Seminorm 𝕜 E :=
  { p with smul' := fun a x => by rw [← smul_one_smul 𝕜' a x, p.smul', norm_smul, norm_one, mul_one] }

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