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