Theorems · Theorem · convex and discrete geometry

PointedCone.IsFaceOf.mem_of_smul_add_mem

∀ {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] {F C : PointedCone R M},
  F.IsFaceOf C → ∀ {x y : M} {a : R}, x ∈ C → y ∈ C → 0 < a → a • x + y ∈ F → x ∈ F

Defined in

Mathlib.Geometry.Convex.Cone.Face.Basic

Cited by

13 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderIsOrderedRingAddCommGroupModule