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(* Prelude *)
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(* export inj_pair without exporting the whole Eqdep library *)
Definition inj_pair2 := @inj_pair2.(* eta laws for pairs and units *)
Notation prod_eta := surjective_pairing.

Lemma prod_inj A B (x y : A * B) : x = y <-> (x.1, x.2) = (y.1, y.2).