Theorems · Theorem · convex and discrete geometry

PointedCone.IsFaceOf.fst

∀ {R : Type u_1} {M : Type u_2} {N : Type u_3} [inst : DivisionRing R] [inst_1 : LinearOrder R]
  [inst_2 : IsOrderedRing R] [inst_3 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : AddCommGroup N]
  [inst_6 : Module R N] {C₁ : PointedCone R M} {C₂ : PointedCone R N} {F : PointedCone R (M × N)},
  F.IsFaceOf (Submodule.prod C₁ C₂) → (PointedCone.map (LinearMap.fst R M N) F).IsFaceOf C₁

The projection of a face of a product cone onto the first component is a face of the projection of the product cone onto the first component.

Defined in

Mathlib.Geometry.Convex.Cone.Face.Basic

Cited by

1 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingLinearOrderIsOrderedRingAddCommGroupModuleAddCommGroupModule