14 lines
441 B
Text
14 lines
441 B
Text
import data.set
|
|
open set function eq.ops
|
|
|
|
variables {X Y Z : Type}
|
|
|
|
lemma image_comp (f : Y → X) (g : X → Y) (a : set X) : (f ∘ g) ' a = f ' (g ' a) :=
|
|
ext (take z,
|
|
iff.intro
|
|
(assume Hz,
|
|
obtain x Hx₁ Hx₂, from Hz,
|
|
by repeat (apply mem_image | assumption | reflexivity))
|
|
(assume Hz,
|
|
obtain y [x Hz₁ Hz₂] Hy₂, from Hz,
|
|
by repeat (apply mem_image | assumption | esimp [comp] | rewrite Hz₂)))
|