Theorems · Theorem · convex and discrete geometry
ConvexCone.salient_strictlyPositive
∀ {R : Type u_2} {M : Type u_4} [inst : Semiring R] [inst_1 : PartialOrder R] [inst_2 : AddCommGroup M]
[inst_3 : PartialOrder M] [inst_4 : IsOrderedAddMonoid M] [inst_5 : Module R M] [inst_6 : PosSMulStrictMono R M],
(ConvexCone.strictlyPositive R M).SalientThe strictly positive cone of an ordered module is always salient.
- Defined in
- Mathlib.Geometry.Convex.Cone.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- PartialOrderstatement and proof · cited by 6,410
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- PosSMulStrictMonostatement and proof · cited by 128
- ConvexCone.Salientstatement · cited by 7
- ConvexCone.strictlyPositivestatement · cited by 5
- ConvexCone.salient_positiveproof · cited by 1
- ConvexCone.Salient.antiproof · cited by 1
- ConvexCone.strictlyPositive_le_positiveproof · cited by 1
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