Theorems · Theorem · geometry

Function.Injective.wSameSide_map_iff

∀ {R : Type u_1} {V : Type u_2} {V' : Type u_3} {P : Type u_4} {P' : Type u_5} [inst : CommRing R]
  [inst_1 : PartialOrder R] [inst_2 : IsStrictOrderedRing R] [inst_3 : AddCommGroup V] [inst_4 : Module R V]
  [inst_5 : AddTorsor V P] [inst_6 : AddCommGroup V'] [inst_7 : Module R V'] [inst_8 : AddTorsor V' P']
  {s : AffineSubspace R P} {x y : P} {f : P →ᵃ[R] P'},
  Function.Injective ⇑f → ((AffineSubspace.map f s).WSameSide (f x) (f y) ↔ s.WSameSide x y)

Defined in

Mathlib.Analysis.Convex.Side

Cited by

2 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Quot.sound

Assumes

CommRingPartialOrderIsStrictOrderedRingAddCommGroupModuleAddTorsorAddCommGroupModuleAddTorsor