Theorems · Theorem · convex and discrete geometry

ProperCone.coe_positive

∀ (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] [inst_6 : PartialOrder E]
  [inst_7 : IsOrderedAddMonoid E] [inst_8 : PosSMulMono R E] [inst_9 : OrderClosedTopology E],
  ↑(ProperCone.positive R E) = Set.Ici 0

Defined in: Mathlib.Analysis.Convex.Cone.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Semiring PartialOrder IsOrderedRing AddCommMonoid TopologicalSpace Module PartialOrder IsOrderedAddMonoid PosSMulMono OrderClosedTopology

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Setstatement · cited by 53,352
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 and proof · cited by 8,199
PartialOrderstatement and proof · cited by 6,410
IsOrderedAddMonoidstatement and proof · cited by 1,659
Set.Icistatement · cited by 1,070
IsOrderedRingstatement and proof · cited by 777
OrderClosedTopologystatement and proof · cited by 445
PosSMulMonostatement and proof · cited by 188

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