Theorems · Theorem · convex and discrete geometry
ProperCone.nonempty
∀ {R : Type u_2} {E : Type u_3} [inst : Semiring R] [inst_1 : PartialOrder R] [inst_2 : IsOrderedRing R]
[inst_3 : AddCommMonoid E] [inst_4 : TopologicalSpace E] [inst_5 : Module R E] (C : ProperCone R E), (↑C).Nonempty- Defined in
- Mathlib.Analysis.Convex.Cone.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- SetLike.coestatement · cited by 8,199
- PartialOrderstatement and proof · cited by 6,410
- Set.Nonemptystatement · cited by 2,627
- IsOrderedRingstatement and proof · cited by 777
- ProperConestatement and proof · cited by 57
- ClosedSubmodule.toSubmoduleproof · cited by 51
- Submodule.nonemptyproof · cited by 3
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