Theorems · Definition · convex and discrete geometry
PointedCone.toConvexCone
{R : Type u_1} →
{E : Type u_2} →
[inst : Semiring R] →
[inst_1 : PartialOrder R] →
[inst_2 : IsOrderedRing R] →
[inst_3 : AddCommMonoid E] → [inst_4 : Module R E] → PointedCone R E → ConvexCone R EEvery pointed cone is a convex cone.
- Defined in
- Mathlib.Geometry.Convex.Cone.Pointed
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- AddCommMonoidstatement and proof · cited by 12,281
- SetLike.coeproof · cited by 8,199
- PartialOrderstatement and proof · cited by 6,410
- IsOrderedRingstatement and proof · cited by 777
- PointedConestatement and proof · cited by 151
- ConvexConestatement · cited by 103
Cited by10
Results whose statement or proof uses this declaration.
- PointedCone.pointed_toConvexConestatement · cited by 2
- PointedCone.convexproof · cited by 1
- ConvexCone.coe_toPointedConestatement · cited by 0
- PointedCone.toConvexCone_injectivestatement · cited by 0
- PointedCone.toConvexCone_mapstatement · cited by 0
- PointedCone.toConvexCone_positivestatement · cited by 0
- PointedCone.salient_iff_inter_neg_eq_singletonstatement · cited by 0
- PointedCone.mem_toConvexConestatement · cited by 0
- ProperCone.pointed_toConvexConestatement · cited by 0
- PointedCone.toConvexCone_closure_pointedstatement · cited by 0