Theorems · Theorem · convex and discrete geometry
ConvexCone.IsGenerating.isReproducing
Deprecated since 2026-03-30Use ConvexCone.IsReproducing.of_span_eq_top instead.
∀ {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.IsReproducingAlias of ConvexCone.IsReproducing.of_span_eq_top.
- Defined in
- Mathlib.Geometry.Convex.Cone.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement · cited by 20,661
- AddCommGroupstatement · cited by 12,871
- Top.topstatement · cited by 9,680
- LinearOrderstatement · cited by 8,572
- SetLike.coestatement · cited by 8,199
- Ringstatement · cited by 7,463
- Submodulestatement · cited by 7,192
- Nontrivialstatement · cited by 2,416
- Submodule.spanstatement · cited by 1,504
- AddLeftStrictMonostatement · cited by 203
- ConvexConestatement · cited by 103
- ConvexCone.IsReproducingstatement · cited by 8
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