Theorems · Theorem · convex and discrete geometry
PointedCone.DualFG.dual_of_finite
∀ {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) {s : Set M}, s.Finite → PointedCone.DualFG p (PointedCone.dual p s)The dual of a finite set is dually finitely generated.
- Defined in
- Mathlib.Geometry.Convex.Cone.DualFinite
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
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- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- PartialOrderstatement and proof · cited by 6,410
- Set.Finitestatement and proof · cited by 1,814
- IsOrderedRingstatement and proof · cited by 777
- Set.Finite.toFinsetproof · cited by 351
- Set.Finite.coe_toFinsetproof · cited by 124
- PointedCone.dualstatement and proof · cited by 47
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