Theorems · Theorem · convex and discrete geometry
ConvexCone.IsGenerating.of_top_le_span
Deprecated since 2026-03-30Mathlib marks this declaration as deprecated.
∀ {R : Type u_2} {M : Type u_4} [inst : Semiring R] [inst_1 : PartialOrder R] [inst_2 : AddCommMonoid M]
[inst_3 : Module R M] {C : ConvexCone R M}, ⊤ ≤ Submodule.span R ↑C → C.IsGeneratingA sufficient criteria for a convex cone C to be generating is that top is less than or equal
to the linear span of C.
- Defined in
- Mathlib.Geometry.Convex.Cone.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
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Cites11
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
- AddCommMonoidstatement and proof · cited by 12,281
- Top.topstatement and proof · cited by 9,680
- SetLike.coestatement and proof · cited by 8,199
- Submodulestatement · cited by 7,192
- PartialOrderstatement and proof · cited by 6,410
- Submodule.spanstatement and proof · cited by 1,504
- eq_top_iffproof · cited by 236
- ConvexConestatement and proof · cited by 103
- ConvexCone.IsGeneratingstatement · cited by 7
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