Theorems · Theorem · convex and discrete geometry

wbtw_or_wbtw_smul_vadd_of_nonpos

∀ {R : Type u_1} {V : Type u_2} {P : Type u_4} [inst : Field R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R]
  [inst_3 : AddCommGroup V] [inst_4 : Module R V] [inst_5 : AddTorsor V P] (x : P) (v : V) {r₁ r₂ : R},
  r₁ ≤ 0 → r₂ ≤ 0 → Wbtw R x (r₁ • v +ᵥ x) (r₂ • v +ᵥ x) ∨ Wbtw R x (r₂ • v +ᵥ x) (r₁ • v +ᵥ x)

Defined in

Mathlib.Analysis.Convex.Between

Cited by

1 results in Mathlib

Foundations

Depth 49 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderIsStrictOrderedRingAddCommGroupModuleAddTorsor