instIsClosedImmersionLiftIdOfIsSeparated

English

The range of the diagonal of a morphism is contained in the diagonal cover diagonal range.

Русский

Область образа диагонали морфизма лежит внутри диагонального диапазона покрытия.

LaTeX

$$Set.range (pullback.diagonal f).base \subseteq diagonalCoverDiagonalRange f 𝒰 𝒱$$

Lean4

instance [X.IsSeparated] : IsClosedImmersion (prod.lift (𝟙 X) (𝟙 X)) := by
  rwa [← isSeparated_iff_isClosedImmersion_prod_lift]

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