lean2/tests/lean/run/new_obtain4.lean

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Text

import data.set
open set function eq.ops
variables {X Y Z : Type}
lemma image_compose (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 [compose] | rewrite Hz₂)))