Goal:
  
  hd : A.t
  tl'0 : t
  tl : t
  tl' : t
  H : lt_ tl tl'
  IHlt_ : forall z : t, lt tl' z -> lt tl z
  H' : lt_ tl' tl'0
  ============================
   (lt tl' tl'0)


DEBUG:Going to execute:
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"