Theorems · Theorem · convex and discrete geometry

PointedCone.IsFaceOf.map

∀ {R : Type u_1} {M : Type u_2} {N : Type u_3} [inst : Semiring R] [inst_1 : PartialOrder R] [inst_2 : IsOrderedRing R]
  [inst_3 : AddCommGroup M] [inst_4 : Module R M] {C F : PointedCone R M} [inst_5 : AddCommGroup N]
  [inst_6 : Module R N] (f : M →ₗ[R] N),
  Function.Injective ⇑f → F.IsFaceOf C → (PointedCone.map f F).IsFaceOf (PointedCone.map f C)

The image of a face of a cone under an injective linear map is a face of the image of the cone.

Defined in

Mathlib.Geometry.Convex.Cone.Face.Basic

Cited by

3 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderIsOrderedRingAddCommGroupModuleAddCommGroupModule