locallyOfFiniteType_of_isOpenImmersion

English

If f is an open immersion, then LocallyOfFinitePresentation holds for f.

Русский

Если f — открытое вмещение, то f локально презентационен.

LaTeX

$$$[\text{IsOpenImmersion}(f)] \Rightarrow \text{LocallyOfFinitePresentation}(f).$$$

Lean4

instance (priority := 900) locallyOfFiniteType_of_isOpenImmersion [IsOpenImmersion f] : LocallyOfFiniteType f :=
  HasRingHomProperty.of_isOpenImmersion RingHom.finiteType_holdsForLocalizationAway.containsIdentities

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