Theorems · Theorem · convex and discrete geometry
PointedCone.IsFaceOf.isFaceOf_iff_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] {C F₁ F₂ : PointedCone R M},
F₁.IsFaceOf C → F₂.IsFaceOf C → (F₁.IsFaceOf F₂ ↔ F₁ ≤ F₂)A face of a cone is a face of another if and only if they are contained in each other.
- Defined in
- Mathlib.Geometry.Convex.Cone.Face.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 37 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
- 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
- PointedCone.IsFaceOf.mem_of_smul_add_memproof · cited by 13
- PointedCone.IsFaceOf.leproof · cited by 10
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