of_comp — Mathlib

English

If g is affine-homogeneous, then IsAffineHom (f ≫ g) iff IsAffineHom f.

Русский

Если g гладко-однороден, то IsAffineHom (f ≫ g) эквивалентно IsAffineHom f.

LaTeX

$$$IsAffineHom(f \circ g) \iff IsAffineHom(f)$, при условии [IsAffineHom g].$$

Lean4

theorem of_comp [IsAffineHom (f ≫ g)] [IsSeparated g] : IsAffineHom f :=
  by
  rw [← pullback.lift_snd (𝟙 _) f (Category.id_comp (f ≫ g))]
  have := MorphismProperty.pullback_snd (P := @IsAffineHom) (f ≫ g) g inferInstance
  infer_instance

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