Theorems · Theorem · convex and discrete geometry
ConvexCone.salient_positive
∀ {R : Type u_2} [inst : Semiring R] [inst_1 : PartialOrder R] {G : Type u_7} [inst_2 : AddCommGroup G]
[inst_3 : PartialOrder G] [inst_4 : IsOrderedAddMonoid G] [inst_5 : Module R G] [inst_6 : PosSMulMono R G],
(ConvexCone.positive R G).SalientThe positive cone of an ordered module is always salient.
- Defined in
- Mathlib.Geometry.Convex.Cone.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- neg_add_cancelproof · cited by 256
- lt_irreflproof · cited by 190
- PosSMulMonostatement and proof · cited by 188
- LE.le.lt_of_ne'proof · cited by 41
- add_pos_of_nonneg_of_posproof · cited by 11
- ConvexCone.Salientstatement · cited by 7
- ConvexCone.positivestatement and proof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- ConvexCone.salient_strictlyPositiveproof · cited by 0