Theorems · Theorem · convex and discrete geometry

PointedCone.IsFaceOf.of_mem_of_add_mem_left

∀ {R : Type u_1} {M : Type u_2} [inst : DivisionRing R] [inst_1 : LinearOrder R] [inst_2 : IsOrderedRing R]
  [inst_3 : AddCommGroup M] [inst_4 : Module R M] {C F : PointedCone R M},
  F ≤ C → (∀ {x y : M}, x ∈ C → y ∈ C → x + y ∈ F → x ∈ F) → F.IsFaceOf C

Defined in

Mathlib.Geometry.Convex.Cone.Face.Basic

Cited by

1 results in Mathlib

Foundations

Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingLinearOrderIsOrderedRingAddCommGroupModule