Theorems · Theorem · convex and discrete geometry

affineSegment_image

∀ {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'] (f : P →ᵃ[R] P') (x y : P),
  ⇑f '' affineSegment R x y = affineSegment R (f x) (f y)

Defined in

Mathlib.Analysis.Convex.Between

Cited by

7 results in Mathlib

Foundations

Depth 47 from the axioms · uses propext, Quot.sound

Assumes

RingPartialOrderAddCommGroupModuleAddTorsorAddCommGroupModuleAddTorsor