Definition prod_eq_dec :
  forall A B
    (A_eq_dec : forall x y : A, {x = y} + {x <> y})
    (B_eq_dec : forall x y : B, {x = y} + {x <> y})
    (x y : A * B),
    {x = y} + {x <> y}.

Lemma equates_1 : forall(P:A0->Prop) x1 y1, P y1 -> x1 = y1 -> P x1.