Definition eqs (i j : int) : {i = j} + { i <> j } :=
  (if i =? j as b return ((b = true -> i = j) -> (b = false -> i <> j) -> {i=j} + {i <> j} )
    then fun (Heq : true = true -> i = j) _ => left _ (Heq (eq_refl true))
    else fun _ (Hdiff : false = false -> i <> j) => right _ (Hdiff (eq_refl false)))
  (eqb_correct i j)
  (eqb_false_correct i j).

Lemma eq_dec : forall i j:int, i = j \/ i <> j.