induction n in c, x, y |- *...
simpl.
intros.
rewrite IHn.
unfold eq_rec_r.
unfold eq_rec.
unfold eq_rect.
simpl plus.
case (sym_eq (plus_n_Sm c n))...
Qed.

(* Specifications: *)
Lemma cond_eq_neq (T: nat -> Set) n m c (x: T (c + n)) (y: T (c + m)): n <> m -> cond_eq T n m c x y = True.
Proof with auto.