Theorems · Theorem · convex and discrete geometry
PointedCone.IsFaceOf.lineal_congr
∀ {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.IsFaceOf C → F.lineal = C.linealThe lineality space of a face of a cone agrees with the lineality space of the cone.
- Defined in
- Mathlib.Geometry.Convex.Cone.Face.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- SetLike.coeproof · cited by 8,199
- Submodulestatement · cited by 7,192
- DivisionRingstatement and proof · cited by 1,062
- IsOrderedRingstatement and proof · cited by 777
- neg_add_cancelproof · cited by 256
- add_neg_cancelproof · cited by 213
- Submodule.extproof · cited by 204
- Submodule.toAddSubmonoidproof · cited by 162
- PointedConestatement and proof · cited by 151
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.