Definition eq_dec (E : Set) := forall a b : E, {a = b} + {a <> b}.

Lemma eq_couple_dec : forall (E F : Set) (eq_E_dec : eq_dec E) (eq_F_dec : eq_dec F) (x1 x2 : E) (y1 y2 : F), {x1 = x2 /\ y1 = y2} + {x1 <> x2 \/ y1 <> y2}.