instQuasiCompactOfIsAffineHom — Mathlib

English

As in localizationToStalk_mk, the proof identifies the local behavior of mk f s with a germ.

Русский

Как и в localizationToStalk_mk, доказательство соединяет локальное поведение mk f s с Germ.

LaTeX

$$$(localizationToStalk M x).hom (LocalizedModule.mk f s) = (\\tilde{M}).germ (\\mathrm{basicOpen}(s)) x s.2 (\\mathrm{const} M f s (\\mathrm{basicOpen} s) _)$$$

Lean4

instance (priority := 900) [IsAffineHom f] : QuasiCompact f :=
  (quasiCompact_iff_forall_affine f).mpr (fun U hU ↦ (IsAffineHom.isAffine_preimage U hU).isCompact)

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