range_polarizationIn — Mathlib

English

The image of Polarization restricted to the root span equals the range of PolarizationIn.

Русский

Образ Polarization, ограниченный на корневой охват, равен диапазону PolarizationIn.

LaTeX

$$$\\operatorname{range}(P.Polarization)\\circ (P.rootSpan R) = \\operatorname{range}(P.PolarizationIn R)$$$

Lean4

theorem range_polarizationIn : Submodule.map P.Polarization (P.rootSpan R) = LinearMap.range (P.PolarizationIn R) :=
  by
  ext x
  simp [PolarizationIn_eq]

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