Theorems · Theorem · convex and discrete geometry
PointedCone.IsFaceOf.isExtreme
∀ {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] {C F : PointedCone R M}, F.IsFaceOf C → IsExtreme R ↑C ↑FA face of a cone is an extreme subset of the cone.
- Defined in
- Mathlib.Geometry.Convex.Cone.Face.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
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- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- SetLike.coestatement and proof · cited by 8,199
- PartialOrderstatement and proof · cited by 6,410
- IsOrderedRingstatement and proof · cited by 777
- PointedConestatement and proof · cited by 151
- openSegmentproof · cited by 102
- PointedCone.IsFaceOfstatement and proof · cited by 34
- IsExtremestatement · cited by 22
- PointedCone.IsFaceOf.leproof · cited by 10
- PointedCone.IsFaceOf.mem_of_smul_add_smul_mem_leftproof · cited by 1
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