Theorems · Definition · convex and discrete geometry
PointedCone.ofSubmodule
{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] → Submodule R E → PointedCone R EA submodule is a pointed cone.
- Defined in
- Mathlib.Geometry.Convex.Cone.Pointed
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 35 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
- Submodulestatement and proof · cited by 7,192
- PartialOrderstatement and proof · cited by 6,410
- IsOrderedRingstatement and proof · cited by 777
- Submodule.restrictScalarsproof · cited by 180
- PointedConestatement · cited by 151
Cited by21
Results whose statement or proof uses this declaration.
- PointedCone.gc_ofSubmodule_linealstatement and proof · cited by 2
- PointedCone.ofSubmodule_sInfstatement · cited by 1
- PointedCone.ofSubmodule_sSupstatement · cited by 1
- PointedCone.lineal_lestatement · cited by 1
- PointedCone.neg_ofSubmodulestatement · cited by 0
- PointedCone.IsFaceOf.linealstatement and proof · cited by 0
- PointedCone.IsFaceOf.lineal_lestatement and proof · cited by 0
- PointedCone.ofSubmodule_iInfstatement and proof · cited by 0
- PointedCone.ofSubmodule_iSupstatement and proof · cited by 0
- PointedCone.ofSubmodule_infstatement · cited by 0
- PointedCone.ofSubmodule_injstatement · cited by 0
- PointedCone.ofSubmodule_le_ofSubmodulestatement · cited by 0