Goal:
    P : Prop  Q : Prop  eq : P <-> Q  p : P
  ============================
   P


DEBUG:Going to execute:
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"