map_inf — Mathlib

English

The image under f of the infimum of subalgebras equals the infimum of the images, provided f is injective.

Русский

Образ подгапки f от infimum подпалебр равен infimum образов при инъективности f.

LaTeX

$$$\operatorname{map} f (S \sqcap T) = \operatorname{map} f S \sqcap \operatorname{map} f T$$$

Lean4

theorem map_inf (f : A →⋆ₐ[R] B) (hf : Function.Injective f) (S T : StarSubalgebra R A) :
    map f (S ⊓ T) = map f S ⊓ map f T :=
  SetLike.coe_injective (Set.image_inter hf)

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