Theorems · Theorem · convex and discrete geometry

mem_vadd_const_affineSegment

∀ {R : Type u_1} {V : Type u_2} {P : Type u_4} [inst : Ring R] [inst_1 : PartialOrder R] [inst_2 : AddCommGroup V]
  [inst_3 : Module R V] [inst_4 : AddTorsor V P] {x y z : V} (p : P),
  z +ᵥ p ∈ affineSegment R (x +ᵥ p) (y +ᵥ p) ↔ z ∈ affineSegment R x y

Defined in

Mathlib.Analysis.Convex.Between

Cited by

2 results in Mathlib

Foundations

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

Assumes

RingPartialOrderAddCommGroupModuleAddTorsor