linearEquivIncludeRange_symm_tmul

English

There is an algebra isomorphism from S ⊗ T to the tensor product of the ranges of includeLeft and includeRight.

Русский

Существует алгебраизоморфизм от S ⊗ T к тензорному произведению диапазонов includeLeft и includeRight.

LaTeX

$$$A \\otimes_R B \\cong_A[R] (\\mathrm{includeLeft}.range) \\otimes_R (\\mathrm{includeRight}.range)$$$

Lean4

@[simp]
theorem linearEquivIncludeRange_symm_tmul (x y) : (linearEquivIncludeRange R S T).symm (x ⊗ₜ[R] y) = x.1 * y.1 :=
  rfl

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