Theorems · Theorem · convex and discrete geometry
PointedCone.IsFaceOf.inf
∀ {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] {C₁ C₂ F₁ F₂ : PointedCone R M},
F₁.IsFaceOf C₁ → F₂.IsFaceOf C₂ → (F₁ ⊓ F₂).IsFaceOf (C₁ ⊓ C₂)The intersection of two faces of two cones is a face of the intersection of the cones.
- Defined in
- Mathlib.Geometry.Convex.Cone.Face.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- LE.le.transproof · cited by 3,151
- IsOrderedRingstatement and proof · cited by 777
- Set.inter_subset_leftproof · cited by 360
- Set.inter_subset_rightproof · cited by 329
- PointedConestatement and proof · cited by 151
- le_inf_iffproof · cited by 48
- PointedCone.IsFaceOfstatement and proof · cited by 34
- PointedCone.IsFaceOf.mem_of_smul_add_memproof · cited by 13
Cited by2
Results whose statement or proof uses this declaration.
- PointedCone.IsFaceOf.inf_leftproof · cited by 0
- PointedCone.IsFaceOf.inf_rightproof · cited by 0