Theorems · Theorem · convex and discrete geometry

Convex.mem_of_wbtw

∀ {R : Type u_1} {V : Type u_2} [inst : Ring R] [inst_1 : PartialOrder R] [inst_2 : AddCommGroup V]
  [inst_3 : Module R V] [IsOrderedRing R] {p₀ p₁ p₂ : V} {s : Set V},
  Convex R s → Wbtw R p₀ p₁ p₂ → p₀ ∈ s → p₂ ∈ s → p₁ ∈ s

Defined in

Mathlib.Analysis.Convex.Between

Cited by

1 results in Mathlib

Foundations

Depth 50 from the axioms · uses propext, Quot.sound

Assumes

RingPartialOrderAddCommGroupModuleIsOrderedRing