Theorems · Theorem · convex and discrete geometry

List.exists_map_eq_of_sorted_nonempty_iff_wbtw

∀ {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] {l : List P} (hl : l ≠ []),
  (∃ l', l'.SortedLE ∧ List.map (⇑(AffineMap.lineMap (l.head hl) (l.getLast hl))) l' = l) ↔ List.Wbtw R l

Defined in

Mathlib.Analysis.Convex.BetweenList

Cited by

2 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderIsStrictOrderedRingAddCommGroupModuleAddTorsor