toConvexCone_injective — Mathlib

English

The map sending a pointed cone to its associated convex cone is injective; different pointed cones cannot have the same convex cone.

Русский

Образуемое из pointed cone выпуклый конус uniquely определяет исходный pointed cone; отображение инъективно.

LaTeX

$$Injective ((\\uparrow) : PointedCone R E → ConvexCone R E)$$

Lean4

theorem toConvexCone_injective : Injective ((↑) : PointedCone R E → ConvexCone R E) := fun _ _ => by simp [toConvexCone]

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