Theorems · Theorem · convex and discrete geometry

Function.Injective.list_sbtw_map_iff

∀ {R : Type u_1} {V : Type u_2} {V' : Type u_3} {P : Type u_4} {P' : Type u_5} [inst : Ring R] [inst_1 : PartialOrder R]
  [inst_2 : AddCommGroup V] [inst_3 : Module R V] [inst_4 : AddTorsor V P] [inst_5 : AddCommGroup V']
  [inst_6 : Module R V'] [inst_7 : AddTorsor V' P'] {l : List P} {f : P →ᵃ[R] P'},
  Function.Injective ⇑f → (List.Sbtw R (List.map (⇑f) l) ↔ List.Sbtw R l)

Defined in

Mathlib.Analysis.Convex.BetweenList

Cited by

2 results in Mathlib

Foundations

Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingPartialOrderAddCommGroupModuleAddTorsorAddCommGroupModuleAddTorsor