Theorems · Inductive type · convex and discrete geometry

PointedCone.IsFaceOf

{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] → PointedCone R M → PointedCone R M → Prop

A sub-cone F of a pointed cone C is a face of C if any two points of C with a strictly positive combination in F are also in F.

Defined in

Mathlib.Geometry.Convex.Cone.Face.Basic

Cited by

34 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderIsOrderedRingAddCommGroupModule