Goal:
  
  G : t
  y_0 : V.t
  x_0 : V.t
  K : Z
  x : V.t
  y : V.t
  z : V.t
  e : EdgeOf G' x y
  q : PathOf G' y z
  IHq : PathOf G y z
  XX : (y_0, K, x_0) = (x, e.π1, y)
  ============================
   (PathOf G y z)


DEBUG:Going to execute:
let rec use_hyps :=
            match goal with
            | H:_ /\ _ |- _ => exact H || (destruct_hyp H; use_hyps)
            | H:(_ * _)%nat |- _ => exact H || (destruct_hyp H; use_hyps)
            | H:_ |- _ => solve [ inversion H ]
            | _ => idtac
            end
           in
           let do_atom := solve
           [ trivial
           with eq_true
           | reflexivity
           | symmetry; trivial
           | contradiction
           | congruence ]
           in
           let rec do_ccl :=
            try do_atom; repeat (do_intro; try do_atom); try arith_congr;
             (solve [ split; do_ccl ])
           in
           (solve [ do_atom | use_hyps; do_ccl ]) ||
             fail "Cannot solve this goal"