Theorems · Theorem · convex and discrete geometry

PointedCone.DualFG.dual_dual_flip

∀ {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 → PointedCone.dual p ↑(PointedCone.dual p.flip ↑C) = C

The double dual of a dually finitely generated cone is the cone itself.

Defined in

Mathlib.Geometry.Convex.Cone.DualFinite

Cited by

1 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingPartialOrderIsOrderedRingAddCommGroupModuleAddCommGroupModule