Theorems · Theorem · convex and discrete geometry
PointedCone.IsFaceOf.le
∀ {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] {F C : PointedCone R M}, F.IsFaceOf C → F ≤ C- Defined in
- Mathlib.Geometry.Convex.Cone.Face.Basic
- 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.
Cites7
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
- IsOrderedRingstatement and proof · cited by 777
- PointedConestatement and proof · cited by 151
- PointedCone.IsFaceOfstatement and proof · cited by 34
Cited by10
Results whose statement or proof uses this declaration.
- PointedCone.IsFaceOf.mapproof · cited by 3
- PointedCone.IsFaceOf.infproof · cited by 2
- PointedCone.IsFaceOf.of_comap_surjectiveproof · cited by 1
- PointedCone.IsFaceOf.comapproof · cited by 1
- PointedCone.IsFaceOf.fstproof · cited by 1
- PointedCone.IsFaceOf.isExtremeproof · cited by 0
- PointedCone.IsFaceOf.isFaceOf_iff_leproof · cited by 0
- PointedCone.IsFaceOf.lineal_congrproof · cited by 0
- PointedCone.IsFaceOf.transproof · cited by 0
- PointedCone.IsFaceOf.prodproof · cited by 0