Theorems · Theorem · convex and discrete geometry
ConvexCone.strictlyPositive_le_positive
∀ {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 ≤ ConvexCone.positive R M- Defined in
- Mathlib.Geometry.Convex.Cone.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- le_of_ltproof · cited by 1,175
- PosSMulStrictMonostatement and proof · cited by 128
- ConvexConestatement · cited by 103
- ConvexCone.positivestatement · cited by 6
- ConvexCone.strictlyPositivestatement · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- ConvexCone.salient_strictlyPositiveproof · cited by 0