Theorems · Theorem · convex and discrete geometry

PointedCone.subset_dual_dual

∀ {R : Type u_1} [inst : CommSemiring R] [inst_1 : PartialOrder R] [inst_2 : IsOrderedRing R] {M : Type u_2}
  [inst_3 : AddCommMonoid M] [inst_4 : Module R M] {N : Type u_3} [inst_5 : AddCommMonoid N] [inst_6 : Module R N]
  {p : M →ₗ[R] N →ₗ[R] R} {s : Set M}, s ⊆ ↑(PointedCone.dual p.flip ↑(PointedCone.dual p s))

Any set is a subset of its double dual cone.

Defined in

Mathlib.Geometry.Convex.Cone.Dual

Cited by

2 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringPartialOrderIsOrderedRingAddCommMonoidModuleAddCommMonoidModule