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_0 : forall(P Q:Prop), P -> P = Q -> Q.