Theorems · Theorem · convex and discrete geometry
ConvexCone.IsReproducing.of_span_eq_top
∀ {R : Type u_7} {M : Type u_8} [inst : Ring R] [inst_1 : LinearOrder R] [AddLeftStrictMono R] [inst_3 : AddCommGroup M]
[Nontrivial M] [inst_5 : Module R M] {C : ConvexCone R M}, Submodule.span R ↑C = ⊤ → C.IsReproducing- Defined in
- Mathlib.Geometry.Convex.Cone.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
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
- AddCommGroupstatement and proof · cited by 12,871
- Top.topstatement and proof · cited by 9,680
- LinearOrderstatement and proof · cited by 8,572
- SetLike.coestatement and proof · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- Set.Nonemptyproof · cited by 2,627
- Nontrivialstatement and proof · cited by 2,416
- Submodule.spanstatement and proof · cited by 1,504
- sub_selfproof · cited by 996
- zero_smulproof · cited by 716
Cited by2
Results whose statement or proof uses this declaration.
- ConvexCone.IsGenerating.isReproducingproof · cited by 0
- ConvexCone.span_eq_top_iff_isReproducingproof · cited by 0