Theorems · Theorem · convex and discrete geometry
PointedCone.IsFaceOf.mem_of_add_mem_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] {C F : PointedCone R M},
F.IsFaceOf C → ∀ {x y : M}, x ∈ C → y ∈ C → x + y ∈ F → y ∈ F- Defined in
- Mathlib.Geometry.Convex.Cone.Face.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- PartialOrderstatement and proof · cited by 6,410
- add_commproof · cited by 1,535
- IsOrderedRingstatement and proof · cited by 777
- PointedConestatement and proof · cited by 151
- PointedCone.IsFaceOfstatement and proof · cited by 34
- PointedCone.IsFaceOf.mem_of_add_mem_leftproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- PointedCone.IsFaceOf.add_mem_iff_memproof · cited by 0
- PointedCone.IsFaceOf.transproof · cited by 0