Theorems · Theorem · convex and discrete geometry
PointedCone.DualFG.iff_exists_fg_dual
∀ {R : Type u_1} {M : Type u_2} {N : Type u_3} [inst : CommRing R] [inst_1 : PartialOrder R] [inst_2 : IsOrderedRing R]
[inst_3 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : AddCommGroup N] [inst_6 : Module R N]
{p : M →ₗ[R] N →ₗ[R] R} {C : PointedCone R N},
PointedCone.DualFG p C ↔ ∃ D, Submodule.FG D ∧ PointedCone.dual p ↑D = CA cone is dually finitely generated if and only if it is the dual of a finitely generated cone.
- Defined in
- Mathlib.Geometry.Convex.Cone.DualFinite
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
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- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Finsetproof · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- SetLike.coestatement and proof · cited by 8,199
- PartialOrderstatement and proof · cited by 6,410
- Submodule.spanproof · cited by 1,504
- IsOrderedRingstatement and proof · cited by 777
- Submodule.FGstatement and proof · cited by 230
- PointedConestatement and proof · cited by 151
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