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[B] Remove Im_compose_inj_surj
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Is not used in coq-zorns-lemma and coq-topology. Also, now that more
lemmas are around (see previous commit which changed
`Im_compose_inj_surj`) the statement of `Im_compose_inj_surj` can be
deduced easily. This lemma is not seem useful enough to warrant its own
place in the library.
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Columbus240 committed Aug 12, 2024
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Showing 1 changed file with 0 additions and 12 deletions.
12 changes: 0 additions & 12 deletions theories/ZornsLemma/Image.v
Original file line number Diff line number Diff line change
Expand Up @@ -168,15 +168,3 @@ Proof.
apply Hf in H1; subst.
assumption.
Qed.

Corollary Im_compose_inj_surj {X Y Z : Type} (f : X -> Y) (g : Y -> Z) :
injective g -> Im Full_set (compose g f) = Im Full_set g ->
surjective f.
Proof.
intros Hg H0 y.
rewrite Im_compose in H0.
apply Im_injective in H0; auto.
clear g Hg.
apply Im_Full_set_surj.
congruence.
Qed.

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