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Theorems · Theorem · convex and discrete geometry

ConvexCone.pointed_positive

∀ {R : Type u_2} {M : Type u_4} [inst : Semiring R] [inst_1 : PartialOrder R] [inst_2 : AddCommMonoid M]
  [inst_3 : PartialOrder M] [inst_4 : IsOrderedAddMonoid M] [inst_5 : Module R M] [inst_6 : PosSMulMono R M],
  (ConvexCone.positive R M).Pointed

The positive cone of an ordered module is always pointed.

Defined in
Mathlib.Geometry.Convex.Cone.Basic
Cited by
0 results in Mathlib
Foundations
Depth 18 from the axioms · uses no axioms
Assumes
SemiringPartialOrderAddCommMonoidPartialOrderIsOrderedAddMonoidModulePosSMulMono
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Module · cited by 20661ModuleSemiring · cited by 13802SemiringAddCommMonoid · cited by 12281AddCommMonoidPartialOrder · cited by 6410PartialOrderle_refl · cited by 2061le_reflIsOrderedAddMonoid · cited by 1659IsOrderedAddMonoidPosSMulMono · cited by 188PosSMulMonoConvexCone.Pointed · cited by 14ConvexCone.PointedConvexCone.positive · cited by 6ConvexCone.positiveConvexCone.pointed_positiveCITED BYCITES

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