Theorems · Definition · convex and discrete geometry

ConvexCone.positive

(R : Type u_2) →
  (M : Type u_4) →
    [inst : Semiring R] →
      [inst_1 : PartialOrder R] →
        [inst_2 : AddCommMonoid M] →
          [inst_3 : PartialOrder M] →
            [IsOrderedAddMonoid M] → [inst_5 : Module R M] → [PosSMulMono R M] → ConvexCone R M

The positive cone is the convex cone formed by the set of nonnegative elements in an ordered module.

Defined in

Mathlib.Geometry.Convex.Cone.Basic

Cited by

6 results in Mathlib

Foundations

Depth 13 from the axioms · uses no axioms

Assumes

SemiringPartialOrderAddCommMonoidPartialOrderIsOrderedAddMonoidModulePosSMulMono