Goal:
  
  A : Type
  cmp : A -> A -> comparison
  Hc : forall (c : comparison) (x y z : A),
       cmp x y = c -> cmp y z = c -> cmp x z = c
  He : forall x y : A, cmp x y = Eq -> x = y
  c : comparison
  x : A
  q' : comparison
  q'' : comparison
  Hqs : forall c0 : comparison, c = c0 -> q' = c0 -> q'' = c0
  ============================
   (c = c)


DEBUG:Going to execute:
let rec use_hyp H :=
            match type of H with
            | _ /\ _ => exact H || destruct_hyp H
            | _ => try (solve [ inversion H ])
            end
           with do_intro := let H := fresh in
                            intro H; use_hyp H
           with destruct_hyp H := case H; clear H; do_intro; do_intro
           in
           let rec use_hyps :=
            match goal with
            | H:_ /\ _ |- _ => exact H || (destruct_hyp H; use_hyps)
            | H:_ |- _ => solve [ inversion H ]
            | _ => idtac
            end
           in
           let do_atom := solve
           [ trivial
           with eq_true
           | Ltac.reflexivity
           | Ltac.symmetry; trivial
           | contradiction ]
           in
           let rec do_ccl :=
            try do_atom; repeat (do_intro; try do_atom); (solve
             [ Ltac.split; do_ccl ])
           in
           (solve [ do_atom | use_hyps; do_ccl ]) ||
             fail "Cannot solve this goal"