Theorems · Theorem · convex and discrete geometry

PointedCone.IsFaceOf.prod

∀ {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 F₁ : PointedCone R M} {C₂ F₂ : PointedCone R N},
  F₁.IsFaceOf C₁ → F₂.IsFaceOf C₂ → PointedCone.IsFaceOf (Submodule.prod F₁ F₂) (Submodule.prod C₁ C₂)

The product of two faces of two cones is a face of the product of the cones.

Defined in

Mathlib.Geometry.Convex.Cone.Face.Basic

Cited by

0 results in Mathlib

Foundations

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

Assumes

DivisionRingLinearOrderIsOrderedRingAddCommGroupModuleAddCommGroupModule