Goal:
  
  A : Type
  P : A → A → Type
  Q : A → A → Type
  hd : A
  hd' : A
  tl : list A
  p : P hd hd'
  HPQ : ∀ x y : A, P x y → ∑ z : A, Q x z × Q y z
  x : A
  q : Q hd x
  q0 : Q hd' x
  ============================
   (Q hd' x)


DEBUG:Going to execute:
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"