Theorems · Theorem · convex and discrete geometry

ProperCone.mem_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] {x : E},
  x ∈ ProperCone.positive R E ↔ 0 ≤ x

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

SemiringPartialOrderIsOrderedRingAddCommMonoidTopologicalSpaceModulePartialOrderIsOrderedAddMonoidPosSMulMonoOrderClosedTopology