Theorems · Theorem · convex and discrete geometry
PointedCone.IsFaceOf.lineal_le
∀ {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 → ↑C.lineal ≤ FThe lineality space of a cone lies in every face.
- Defined in
- Mathlib.Geometry.Convex.Cone.Face.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- DivisionRingstatement and proof · cited by 1,062
- IsOrderedRingstatement and proof · cited by 777
- add_neg_cancelproof · cited by 213
- PointedConestatement and proof · cited by 151
- PointedCone.IsFaceOfstatement and proof · cited by 34
- PointedCone.ofSubmodulestatement and proof · cited by 21
- PointedCone.linealstatement and proof · cited by 10
- PointedCone.IsFaceOf.mem_of_add_mem_leftproof · cited by 5
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