Theorems · Theorem · convex and discrete geometry

PointedCone.IsFaceOf.inf_right

∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : PartialOrder R] [inst_2 : IsOrderedRing R]
  [inst_3 : AddCommGroup M] [inst_4 : Module R M] {C₁ C₂ F : PointedCone R M},
  F.IsFaceOf C₁ → F.IsFaceOf C₂ → F.IsFaceOf (C₁ ⊓ C₂)

If a cone is a face of two cones simultaneously, then it's also a face of their intersection.

Defined in

Mathlib.Geometry.Convex.Cone.Face.Basic

Cited by

0 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderIsOrderedRingAddCommGroupModule