linearEquivIncludeRange_symm_toLinearMap

English

The symmetric inverse of linearEquivIncludeRange corresponds to the product of ranges of includeLeft and includeRight under multiplication.

Русский

Обратное симметрическое к линейному эквив IncludeRange соответствует произведению диапазонов включения слева и справа под умножением.

LaTeX

$$$(linearEquivIncludeRange R S T).symm.toLinearMap = (LinearMap.range includeLeft).mulMap (LinearMap.range includeRight)$$$

Lean4

theorem linearEquivIncludeRange_symm_toLinearMap :
    (linearEquivIncludeRange R S T).symm.toLinearMap =
      (LinearMap.range includeLeft).mulMap (LinearMap.range includeRight) :=
  rfl

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