Theorems · Theorem · convex and discrete geometry

PointedCone.mem_span_set

Deprecated since 2026-03-22Use PointedCone.mem_hull_set instead.

∀ {R : Type u_1} {E : Type u_2} [inst : Semiring R] [inst_1 : PartialOrder R] [inst_2 : IsOrderedRing R]
  [inst_3 : AddCommMonoid E] [inst_4 : Module R E] {x : E} {s : Set E},
  x ∈ PointedCone.hull R s ↔ ∃ c, ↑c.support ⊆ s ∧ (∀ (y : E), 0 ≤ c y) ∧ (c.sum fun m r => r • m) = x

Alias of PointedCone.mem_hull_set. Elements of the cone hull are expressible as conical combination of elements from s.

Defined in

Mathlib.Geometry.Convex.Cone.Pointed

Cited by

0 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderIsOrderedRingAddCommMonoidModule