selfAdjointPart_comp_subtype_skewAdjoint

English

The self-adjoint part composed with the skew-adjoint inclusion is the identity on A.

Русский

Самосопряжённая часть, применённая к элементам космодружённого, возвращает исходное значение.

LaTeX

$$$(\text{selfAdjointPart})(\text{skewAdjoint.submodule } R A).subtype = \mathrm{id}$$$

Lean4

@[simp]
theorem selfAdjointPart_comp_subtype_skewAdjoint : (selfAdjointPart R).comp (skewAdjoint.submodule R A).subtype = 0 :=
  LinearMap.ext fun ⟨x, (hx : _ = _)⟩ ↦ Subtype.eq <| by simp [hx]

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