decomposeLinearEquiv_apply — Mathlib

English

On applying the linear decomposition isomorphism to a vector m ∈ M, one obtains the component-wise representation: decomposeLinearEquiv(ℳ) m = decompose ℳ m.

Русский

При применении изоморфизма разложения к элементу m ∈ M получаем его компонентное представление: decomposeLinearEquiv(ℳ) m = decompose ℳ m.

LaTeX

$$$\operatorname{decompose}_{\mathcal{M}}(m) = (\text{appropriate component form of } m)$$$

Lean4

@[simp]
theorem decomposeLinearEquiv_apply (m : M) : decomposeLinearEquiv ℳ m = decompose ℳ m :=
  rfl

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