Theorems · Definition · convex and discrete geometry

ConvexCone.strictlyPositive

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

The cone of strictly positive elements. Note that this naming diverges from the mathlib convention of pos and nonneg due to "positive cone" (ConvexCone.positive) being established terminology for the non-negative elements.

Defined in

Mathlib.Geometry.Convex.Cone.Basic

Cited by

5 results in Mathlib

Foundations

Depth 15 from the axioms · uses propext

Assumes

SemiringPartialOrderAddCommGroupPartialOrderIsOrderedAddMonoidModulePosSMulStrictMono