Theorems · Theorem · convex and discrete geometry

PointedCone.DualFG.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 = C

A dually finitely generated cone is the dual of a finitely generated cone.

Defined in

Mathlib.Geometry.Convex.Cone.DualFinite

Cited by

2 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingPartialOrderIsOrderedRingAddCommGroupModuleAddCommGroupModule