eq_inf — Mathlib

English

Equivalence between global P f and local Q on affine covers of the target.

Русский

Эквивалентность между глобальным P f и локальным Q на афинных покрытиях цели.

LaTeX

$$$P f \Leftrightarrow (\forall\text{ affine cover } U)\; Q(f|_{U})$$$

Lean4

theorem eq_inf : @IsClosedImmersion = (topologically IsClosedEmbedding) ⊓ @SurjectiveOnStalks :=
  by
  ext X Y f
  rw [isClosedImmersion_iff, and_comm]
  rfl

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